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Kumar M, Semperlotti F. On the role of geometric phase in the dynamics of elastic waveguides. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230357. [PMID: 39129407 DOI: 10.1098/rsta.2023.0357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 06/10/2024] [Accepted: 06/29/2024] [Indexed: 08/13/2024]
Abstract
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behaviour of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behaviour can emerge based on the geometric features of the waveguide. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.
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Affiliation(s)
- Mohit Kumar
- Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University , West Lafayette, IN 47907, USA
| | - Fabio Semperlotti
- Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University , West Lafayette, IN 47907, USA
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2
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Bengs C. Theory and calculation of abelian and non-abelian geometric phase factors with SpinDynamica. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2023; 357:107576. [PMID: 37956608 DOI: 10.1016/j.jmr.2023.107576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2023] [Revised: 10/14/2023] [Accepted: 10/22/2023] [Indexed: 11/15/2023]
Abstract
Cyclic quantum evolution is accompanied by a systematic change in the phase of the initial state vector. This change only depends upon the path traced out by the system itself. Such effects are collectively known as geometric phase factors. The geometric foundations of these phase factors are most elegantly formulated in terms of fibre bundle theory and differential forms, both of which can represent a significant hurdle to master. We present a derivation of the abelian and non-abelian Berry phase in terms of embedded manifolds of linear vector spaces. Embedded manifolds offer the advantage of being less abstract than fibre bundles, and are well-suited for explicit calculations. Essential features of the derivation reduce to matrix-vector manipulations. We further discuss a numerical strategy for the calculation of abelian and non-abelian phase factors. Our approach is based upon Hungarian method and the polar decomposition, and is made freely available as a SpinDynamica addon. Additionally, all derivations and analytic calculations are supported by Mathematica notebooks.
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Affiliation(s)
- Christian Bengs
- School of Chemistry, Southampton University, University, Road, SO17 1BJ, UK.
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3
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Fang W, Heller ER, Richardson JO. Competing quantum effects in heavy-atom tunnelling through conical intersections. Chem Sci 2023; 14:10777-10785. [PMID: 37829019 PMCID: PMC10566476 DOI: 10.1039/d3sc03706a] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 09/07/2023] [Indexed: 10/14/2023] Open
Abstract
Thermally activated chemical reactions are typically understood in terms of overcoming potential-energy barriers. However, standard rate theories break down in the presence of a conical intersection (CI) because these processes are inherently nonadiabatic, invalidating the Born-Oppenheimer approximation. Moreover, CIs give rise to intricate nuclear quantum effects such as tunnelling and the geometric phase, which are neglected by standard trajectory-based simulations and remain largely unexplored in complex molecular systems. We present new semiclassical transition-state theories based on an extension of golden-rule instanton theory to describe nonadiabatic tunnelling through CIs and thus provide an intuitive picture for the reaction mechanism. We apply the method in conjunction with first-principles electronic-structure calculations to the electron transfer in the bis(methylene)-adamantyl cation. Our study reveals a strong competition between heavy-atom tunnelling and geometric-phase effects.
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Affiliation(s)
- Wei Fang
- Department of Chemistry, Fudan University Shanghai 200438 P. R. China
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
| | - Eric R Heller
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich 8093 Zürich Switzerland
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4
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Sorce DJ, Michaeli S. On the geometric phases during radio frequency pulses with sine and cosine amplitude and frequency modulation. AIP ADVANCES 2023; 13:085210. [PMID: 37584043 PMCID: PMC10424156 DOI: 10.1063/5.0138779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 07/10/2023] [Indexed: 08/17/2023]
Abstract
In this work, we describe the formation of geometric phases during nonadiabatic frequency swept (FS) radio frequency (RF) pulses with sine amplitude modulation and cosine frequency modulation functions. The geometric phases during the FS pulse were analyzed using a Schrödinger equation formalism, and the unified analytical expression for the geometric phase was derived. We present the solutions for sub-geometric phase components incorporated in spinor wavefunctions for the RF Hamiltonian of spin ½ nuclei. We demonstrate that the geometric phases during sine/cosine RF pulses are opposite in signs for different initial conditions of the spinor and that geometric phases can accumulate in correspondence to different magnetization trajectories. The derived formalism could be extended for the evaluation of the geometric phases during a wide class of amplitude- and frequency-modulated pulses used in MRI and in high-resolution NMR.
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Affiliation(s)
- Dennis J. Sorce
- Independent Researcher, 6 Stonegate Court, Cockeysville, Maryland 21030, USA
| | - Shalom Michaeli
- Center for Magnetic Resonance Research, University of Minnesota, 2021 6th Street SE, Minneapolis, Minnesota 55455, USAs
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5
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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6
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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Analytic calculation of the Berry curvature and diagonal Born–Oppenheimer correction for molecular systems in uniform magnetic fields. J Chem Phys 2022; 156:044121. [DOI: 10.1063/5.0079304] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D. M. Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I. Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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7
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Farag MH, Mandal A, Huo P. Polariton induced conical intersection and berry phase. Phys Chem Chem Phys 2021; 23:16868-16879. [PMID: 34328152 DOI: 10.1039/d1cp00943e] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
We investigate the Polariton induced conical intersection (PICI) created from coupling a diatomic molecule with the quantized photon mode inside an optical cavity, and the corresponding Berry Phase effects. We use the rigorous Pauli-Fierz Hamiltonian to describe the quantum light-matter interactions between a LiF molecule and the cavity, and use the exact quantum propagation to investigate the polariton quantum dynamics. The molecular rotations relative to the cavity polarization direction play a role as the tuning mode of the PICI, resulting in an effective CI even within a diatomic molecule. To clearly demonstrate the dynamical effects of the Berry phase, we construct two additional models that have the same Born-Oppenheimer surface, but the effects of the geometric phase are removed. We find that when the initial wavefunction is placed in the lower polaritonic surface, the Berry phase causes a π phase-shift in the wavefunction after the encirclement around the CI, indicated from the nuclear probability distribution. On the other hand, when the initial wavefunction is placed in the upper polaritonic surface, the geometric phase significantly influences the couplings between polaritonic states and therefore, the population dynamics between them. These BP effects are further demonstrated through the photo-fragment angular distribution. PICI created from the quantized radiation field has the promise to open up new possibilities to modulate photochemical reactivities.
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Affiliation(s)
- Marwa H Farag
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA.
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8
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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Ab initio molecular dynamics with screened Lorentz forces. I. Calculation and atomic charge interpretation of Berry curvature. J Chem Phys 2021; 155:024104. [PMID: 34266267 DOI: 10.1063/5.0055388] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
The dynamics of a molecule in a magnetic field is significantly different from its zero-field counterpart. One important difference in the presence of a field is the Lorentz force acting on the nuclei, which can be decomposed as the sum of the bare nuclear Lorentz force and a screening force due to the electrons. This screening force is calculated from the Berry curvature and can change the dynamics qualitatively. It is therefore important to include the contributions from the Berry curvature in molecular dynamics simulations in a magnetic field. In this work, we present a scheme for calculating the Berry curvature numerically using a finite-difference technique, addressing challenges related to the arbitrary global phase of the wave function. The Berry curvature is calculated as a function of bond distance for H2 at the restricted and unrestricted Hartree-Fock levels of theory and for CH+ as a function of the magnetic field strength at the restricted Hartree-Fock level of theory. The calculations are carried out using basis sets of contracted Gaussian functions equipped with London phase factors (London orbitals) to ensure gauge-origin invariance. In this paper, we also interpret the Berry curvature in terms of atomic charges and discuss its convergence in basis sets with and without London phase factors. The calculation of the Berry curvature allows for its inclusion in ab initio molecular dynamics simulations in a magnetic field.
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Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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9
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Rodin B, Ivanov K. Representation of population exchange at level anti-crossings. MAGNETIC RESONANCE (GOTTINGEN, GERMANY) 2020; 1:347-365. [PMID: 38111911 PMCID: PMC10726024 DOI: 10.5194/mr-1-347-2020] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 11/18/2020] [Indexed: 12/20/2023]
Abstract
A theoretical framework is proposed to describe the spin dynamics driven by coherent spin mixing at level anti-crossings (LACs). We briefly introduce the LAC concept and propose to describe the spin dynamics using a vector of populations of the diabatic eigenstates. In this description, each LAC gives rise to a pairwise redistribution of eigenstate populations, allowing one to construct the total evolution operator of the spin system. Additionally, we take into account that in the course of spin evolution a "rotation" of the eigenstate basis case take place. The approach is illustrated by a number of examples, dealing with magnetic field inversion, cross-polarization, singlet-state nuclear magnetic resonance and parahydrogen-induced polarization.
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Affiliation(s)
- Bogdan A. Rodin
- International Tomography Center, Siberian Branch of the Russian Academy of Science, Novosibirsk, 630090, Russia
- Physics Department, Novosibirsk State University, Novosibirsk, 630090, Russia
| | - Konstantin L. Ivanov
- International Tomography Center, Siberian Branch of the Russian Academy of Science, Novosibirsk, 630090, Russia
- Physics Department, Novosibirsk State University, Novosibirsk, 630090, Russia
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10
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Miao G, Bian X, Zhou Z, Subotnik J. A "backtracking" correction for the fewest switches surface hopping algorithm. J Chem Phys 2020; 153:111101. [PMID: 32962370 DOI: 10.1063/5.0022436] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).
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Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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11
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Yuan D, Huang Y, Chen W, Zhao H, Yu S, Luo C, Tan Y, Wang S, Wang X, Sun Z, Yang X. Observation of the geometric phase effect in the H+HD→H 2+D reaction below the conical intersection. Nat Commun 2020; 11:3640. [PMID: 32686682 PMCID: PMC7371868 DOI: 10.1038/s41467-020-17381-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 06/26/2020] [Indexed: 11/24/2022] Open
Abstract
It has long been known that there is a conical intersection (CI) between the ground and first excited electronic state in the H3 system. Its associated geometric phase (GP) effect has been theoretically predicted to exist below the CI since a long time. However, the experimental evidence has not been established yet and its dynamical origin is waiting to be elucidated. Here we report a combined crossed molecular beam and quantum reactive scattering dynamics study of the H+HD → H2+D reaction at 2.28 eV, which is well below the CI. The GP effect is clearly identified by the observation of distinct oscillations in the differential cross section around the forward direction. Quantum dynamics theory reveals that the GP effect arises from the phase alteration of a small part of the wave function, which corresponds to an unusual roaming-like abstraction pathway, as revealed by quasi-classical trajectory calculations. The geometric phase effect associated with a conical intersection between the ground and first excited electronic state has been predicted in the H3 system below the conical intersection energy. The authors, by a crossed molecular beam technique and quantum dynamic calculations, provide experimental evidence and insight into its origin.
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Affiliation(s)
- Daofu Yuan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Yin Huang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China
| | - Wentao Chen
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Hailin Zhao
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China
| | - Shengrui Yu
- Hangzhou Institute of Advanced Studies, Zhejiang Normal University, Hangzhou, 311231, China
| | - Chang Luo
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Yuxin Tan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Siwen Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China
| | - Xingan Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Zhigang Sun
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China.
| | - Xueming Yang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023, China.,Department of Chemistry, College of Science, Southern University of Science and Technology, Shenzhen, 518055, China
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12
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Weike T, Williams DMG, Viel A, Eisfeld W. Quantum dynamics and geometric phase in E ⊗ e Jahn-Teller systems with general Cnv symmetry. J Chem Phys 2019; 151:074302. [DOI: 10.1063/1.5115396] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Thomas Weike
- Theoretische Chemie, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
| | - David M. G. Williams
- Theoretische Chemie, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
| | - Alexandra Viel
- Univ Rennes, CNRS, IPR (Institut de Physique de Rennes) - UMR 6251, F-35000 Rennes, France
| | - Wolfgang Eisfeld
- Theoretische Chemie, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
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13
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Subotnik J, Miao G, Bellonzi N, Teh HH, Dou W. A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians. J Chem Phys 2019; 151:074113. [DOI: 10.1063/1.5116210] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323, USA
| | - Wenjie Dou
- Department of Chemistry, University of California, Berkeley, California 94720, USA
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14
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Ghahari F, Walkup D, Gutiérrez C, Rodriguez-Nieva JF, Zhao Y, Wyrick J, Natterer FD, Cullen WG, Watanabe K, Taniguchi T, Levitov LS, Zhitenev NB, Stroscio JA. An on/off Berry phase switch in circular graphene resonators. Science 2018; 356:845-849. [PMID: 28546211 DOI: 10.1126/science.aal0212] [Citation(s) in RCA: 85] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2016] [Accepted: 04/27/2017] [Indexed: 11/02/2022]
Abstract
The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached. This behavior results from turning on a π Berry phase associated with the topological properties of Dirac fermions in graphene. The Berry phase can be switched on and off with small magnetic field changes on the order of 10 millitesla, potentially enabling a variety of optoelectronic graphene device applications.
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Affiliation(s)
- Fereshte Ghahari
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.,Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA
| | - Daniel Walkup
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.,Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA
| | - Christopher Gutiérrez
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.,Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA
| | - Joaquin F Rodriguez-Nieva
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Yue Zhao
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.,Maryland NanoCenter, University of Maryland, College Park, MD 20742, USA.,Department of Physics, South University of Science and Technology of China, Shenzhen, China
| | - Jonathan Wyrick
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Fabian D Natterer
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.,Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - William G Cullen
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Kenji Watanabe
- National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - Takashi Taniguchi
- National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan
| | - Leonid S Levitov
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Nikolai B Zhitenev
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Joseph A Stroscio
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
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15
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Wu Y, Zhang C, Ma H. Ab initio conical intersections for the Si( 1D) + H 2 reaction system: a lowest five singlet states study. RSC Adv 2017. [DOI: 10.1039/c7ra01021d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Conical intersections and geometric phase effects of the Si(1D) + H2 system were clarified intuitively, and important features of them are revealed.
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Affiliation(s)
- Yanan Wu
- Beijing National Laboratory for Molecular Sciences
- Institute of Chemistry
- Chinese Academy of Sciences
- Beijing 100190
- China
| | - Chunfang Zhang
- Beijing National Laboratory for Molecular Sciences
- Institute of Chemistry
- Chinese Academy of Sciences
- Beijing 100190
- China
| | - Haitao Ma
- Beijing National Laboratory for Molecular Sciences
- Institute of Chemistry
- Chinese Academy of Sciences
- Beijing 100190
- China
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16
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Li T, Duca L, Reitter M, Grusdt F, Demler E, Endres M, Schleier-Smith M, Bloch I, Schneider U. Bloch state tomography using Wilson lines. Science 2016; 352:1094-7. [DOI: 10.1126/science.aad5812] [Citation(s) in RCA: 117] [Impact Index Per Article: 14.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2015] [Accepted: 04/15/2016] [Indexed: 11/02/2022]
Affiliation(s)
- Tracy Li
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Lucia Duca
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Martin Reitter
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Fabian Grusdt
- Department of Physics and Research Center OPTIMAS, University of Kaiserslautern, Germany
- Graduate School Materials Science in Mainz, Gottlieb-Daimler-Strasse 47, 67663 Kaiserslautern, Germany
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Eugene Demler
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Manuel Endres
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
- Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, CA 91125, USA
| | | | - Immanuel Bloch
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
| | - Ulrich Schneider
- Fakultät für Physik, Ludwig-Maximilians-Universität München, Schellingstrasse 4, 80799 Munich, Germany
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching, Germany
- Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK
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17
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Felderhof BU. Self-propulsion of a spherical electric or magnetic microbot in a polar viscous fluid. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023014. [PMID: 25768604 DOI: 10.1103/physreve.91.023014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2014] [Indexed: 06/04/2023]
Abstract
The self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field that polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid, causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.
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Affiliation(s)
- B U Felderhof
- Institut für Theorie der Statistischen Physik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
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18
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Jones JA. Quantum computing with NMR. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2011; 59:91-120. [PMID: 21742157 DOI: 10.1016/j.pnmrs.2010.11.001] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2010] [Accepted: 11/02/2010] [Indexed: 05/31/2023]
Affiliation(s)
- Jonathan A Jones
- Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
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20
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Cina JA, Smith TJ, Romero-Rochín V. Time-Resolved Optical Tests for Electronic Geometric Phase Development. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141410.ch1] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/14/2023]
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21
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Pacher T, Cederbaum LS, Köppel H. Adiabatic and Quasidiabatic States in a Gauge Theoretical Framework. ADVANCES IN CHEMICAL PHYSICS 2007. [DOI: 10.1002/9780470141427.ch4] [Citation(s) in RCA: 180] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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22
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Abstract
To predict the branching between energetically allowed product channels, chemists often rely on statistical transition state theories or exact quantum scattering calculations on a single adiabatic potential energy surface. The potential energy surface gives the energetic barriers to each chemical reaction and allows prediction of the reaction rates. Yet, chemical reactions evolve on a single potential energy surface only if, in simple terms, the electronic wavefunction can evolve from the reactant electronic configuration to the product electronic configuration on a time scale that is fast compared to the nuclear dynamics through the transition state. The experiments reviewed here investigate how the breakdown of the Born-Oppenheimer approximation at a barrier along an adiabatic reaction coordinate can alter the dynamics of and the expected branching between molecular dissociation pathways. The work reviewed focuses on three questions that have come to the forefront with recent theory and experiments: Which classes of chemical reactions evidence dramatic nonadiabatic behavior that influences the branching between energetically allowed reaction pathways? How do the intramolecular distance and orientation between the electronic orbitals involved influence the nonadiabaticity in the reaction? How can the detailed nuclear dynamics mediate the effective nonadiabatic coupling encountered in a chemical reaction?
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Affiliation(s)
- L J Butler
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
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23
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Venkatramani R, Mukamel S. Correlated line broadening in multidimensional vibrational spectroscopy. J Chem Phys 2002. [DOI: 10.1063/1.1518001] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
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24
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Brill TM, Ryu S, Gaylor R, Jundt J, Griffin DD, Song YQ, Sen PN, Hürlimann MD. Nonresonant multiple spin echoes. Science 2002; 297:369-72. [PMID: 12130777 DOI: 10.1126/science.1072245] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
Nonresonant manipulation of nuclear spins can probe large volumes of sample situated in inhomogeneous fields outside a magnet, a geometry suitable for mobile sensors for the inspection of roads, buildings, and geological formations. However, the interference by Earth's magnetic field causes rapid decay of the signal within a few milliseconds for protons and is detrimental to this method. Here we describe a technique to suppress the effects of Earth's field by using adiabatic rotations and sudden switching of the applied fields. We observed hundreds of spin echo signals lasting for more than 600 milliseconds and accurately measured the relaxation times of a liquid sample.
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Affiliation(s)
- Thilo M Brill
- Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877, USA.
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26
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Kendrick BK, Alden Mead C, Truhlar DG. Properties of nonadiabatic couplings and the generalized Born–Oppenheimer approximation. Chem Phys 2002. [DOI: 10.1016/s0301-0104(02)00281-1] [Citation(s) in RCA: 76] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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27
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Liu K. Crossed-beam studies of neutral reactions: state-specific differential cross sections. Annu Rev Phys Chem 2001; 52:139-64. [PMID: 11326062 DOI: 10.1146/annurev.physchem.52.1.139] [Citation(s) in RCA: 201] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Crossed-molecular-beam and laser techniques have enabled experimentalists to measure the state-resolved differential cross sections of elementary chemical reactions. This article reviews recent progress in this area. Particular emphasis is placed on some intriguing physical phenomena associated with a few benchmark reactions and how these measurements help in answering fundamental questions about reaction dynamics. We examine specifically the geometric phase effects in the reaction H + D2, the dynamical resonance phenomenon in F + HD, the unusually large spin-orbit reactivity in Cl((2)P) + H2, the insertion reaction O((1)D) + H2, and the mode-specific reactivity in Cl + CH4(nu). The give-and-take between experiment and theory in unraveling the physical picture of the dynamics is illustrated throughout this review.
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Affiliation(s)
- K Liu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan 10764, Republic of China.
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28
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Bersuker IB. Modern aspects of the Jahn-Teller effect theory and applications to molecular problems. Chem Rev 2001; 101:1067-114. [PMID: 11709858 DOI: 10.1021/cr0004411] [Citation(s) in RCA: 426] [Impact Index Per Article: 18.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- I B Bersuker
- Institute for Theoretical Chemistry, Department of Chemistry & Biochemistry, University of Texas at Austin, Austin, Texas 78712, USA.
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29
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Wesendrup R, Hunt T, Schwerdtfeger P. Relativistic coupled cluster calculations for neutral and singly charged Au3 clusters. J Chem Phys 2000. [DOI: 10.1063/1.481556] [Citation(s) in RCA: 113] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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30
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Krishna MMG, Das R, Periasamy N, Nityananda R. Translational diffusion of fluorescent probes on a sphere: Monte Carlo simulations, theory, and fluorescence anisotropy experiment. J Chem Phys 2000. [DOI: 10.1063/1.481453] [Citation(s) in RCA: 47] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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WATSON JAMESKG. Multiple groups in the symmetry classification of adiabatic electronic wavefunctions. Mol Phys 1999. [DOI: 10.1080/00268979909483115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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32
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Marinelli L, Wi S, Frydman L. A density matrix description of 14N overtone nuclear magnetic resonance in static and spinning solids. J Chem Phys 1999. [DOI: 10.1063/1.477906] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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33
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Schön J, Köppel H. Geometric phases and quantum dynamics in spin–orbit coupled systems. J Chem Phys 1998. [DOI: 10.1063/1.475522] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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34
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Kendrick B, Pack RT. Geometric phase effects in the resonance spectrum, state-to-state transition probabilities and bound state spectrum of HO2. J Chem Phys 1997. [DOI: 10.1063/1.473449] [Citation(s) in RCA: 73] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Affiliation(s)
- David R. Yarkony
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218
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37
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Kendrick B, Pack RT. Geometric phase effects in H+O2 scattering. I. Surface function solutions in the presence of a conical intersection. J Chem Phys 1996. [DOI: 10.1063/1.471460] [Citation(s) in RCA: 92] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Schön J, Köppel H. Geometric phase effects and wave packet dynamics on intersecting potential energy surfaces. J Chem Phys 1995. [DOI: 10.1063/1.469988] [Citation(s) in RCA: 82] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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39
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A magnetic resonance study of non-adiabatic evolution of spin quantum states. ACTA ACUST UNITED AC 1995. [DOI: 10.1007/bf01439380] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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40
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41
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Kendrick B, Mead CA. The geometric vector potential in molecular systems with arbitrarily many identical nuclei. J Chem Phys 1995. [DOI: 10.1063/1.468544] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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42
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Schnurr C, Savard T, Wang LJ, Thomas JE. Detection of atomic interference through collective radiation. OPTICS LETTERS 1995; 20:413. [PMID: 19859205 DOI: 10.1364/ol.20.000413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
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43
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Tachibana A. Reaction holonomy and the geometric phase of quantum evolution in chemical reaction systems. ACTA ACUST UNITED AC 1994. [DOI: 10.1016/s0166-1280(09)80077-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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44
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Tachibana A. Reaction holonomy and the geometric phase of quantum evolution in chemical reaction systems. J Mol Struct 1994. [DOI: 10.1016/s0022-2860(10)80049-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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45
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Appelt S, Wäckerle G, Mehring M. Deviation from Berry's adiabatic geometric phase in a 131Xe nuclear gyroscope. PHYSICAL REVIEW LETTERS 1994; 72:3921-3924. [PMID: 10056334 DOI: 10.1103/physrevlett.72.3921] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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46
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Yin L, Alden Mead C. Magnetic screening of nuclei by electrons as an effect of geometric vector potential. J Chem Phys 1994. [DOI: 10.1063/1.466806] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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47
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Kawai R, Tombrello JF, Weare JH. Li5 as a pseudorotating planar cluster. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 49:4236-4239. [PMID: 9910727 DOI: 10.1103/physreva.49.4236] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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48
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50
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Woywod C, Domcke W, Sobolewski AL, Werner H. Characterization of theS1–S2conical intersection in pyrazine usingabinitiomulticonfiguration self‐consistent‐field and multireference configuration‐interaction methods. J Chem Phys 1994. [DOI: 10.1063/1.466618] [Citation(s) in RCA: 178] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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