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Rassolov V, Garashchuk S. Local Measure of Quantum Effects in Quantum Dynamics. J Phys Chem A 2021; 125:4653-4667. [PMID: 34014096 DOI: 10.1021/acs.jpca.1c02533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The Madelung-de Broglie-Bohm formulation of the Schrödinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.
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Affiliation(s)
- Vitaly Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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LRTM effect and electronic crystal imaging on silicon surface. Sci Rep 2021; 11:8388. [PMID: 33863928 PMCID: PMC8052414 DOI: 10.1038/s41598-021-87629-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2020] [Accepted: 02/10/2021] [Indexed: 11/27/2022] Open
Abstract
Some interesting phenomena have been observed in the laser reflecting Talbot magnification (LRTM) effect discovered at first, in which the high-order nonlinear imaging and the plasmonic structures imaging occur. The LRTM effect images were obtained on the 1D and 2D photonic crystals fabricated by using nanosecond pulsed laser etching on silicon surface, where the high-order nonlinear imaging on the 1D and 2D photonic crystals was observed interestingly. The theory result is consistent with the experimental one, which exhibits that the suitable wave-front shape of injection beam selected in optical route can effectively enlarge the magnification rate and elevate the resolution of the Talbot image. Especially the periodic plasmonic structures on silicon surface have been observed in the LRTM effect images, which have a good application in the online detection of pulsed laser etching process. The temporary reflecting Talbot images exhibit that the electrons following with photonic frequency float on plasma surface to form electronic crystal observed on silicon at first, which is similar with the Wigner crystal structure.
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Albareda G, Riera A, González M, Bofill JM, Moreira IDPR, Valero R, Tavernelli I. Quantum equilibration of the double-proton transfer in a model system porphine. Phys Chem Chem Phys 2020; 22:22332-22341. [DOI: 10.1039/d0cp02991b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The equilibration of the double proton transfer in porphine is demonstrated using a model system Hamiltonian. This highly coherent process could be witnessed experimentally using state-of-the-art femtosecond spectroscopy.
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Affiliation(s)
- Guillermo Albareda
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science
- 22761 Hamburg
- Germany
- Institute of Theoretical and Computational Chemistry
- Universitat de Barcelona
| | - Arnau Riera
- ICFO-Institut de Ciències Fotòniques
- The Barcelona Institute of Science and Technology
- Castelldefels (Barcelona)
- Spain
| | - Miguel González
- Institute of Theoretical and Computational Chemistry
- Universitat de Barcelona
- 08028 Barcelona
- Spain
- Departament de Ciència de Materials i Química Física
| | - Josep Maria Bofill
- Institute of Theoretical and Computational Chemistry
- Universitat de Barcelona
- 08028 Barcelona
- Spain
- Departament de Química Inorgànica i Orgànica
| | - Iberio de P. R. Moreira
- Institute of Theoretical and Computational Chemistry
- Universitat de Barcelona
- 08028 Barcelona
- Spain
- Departament de Ciència de Materials i Química Física
| | - Rosendo Valero
- Institute of Theoretical and Computational Chemistry
- Universitat de Barcelona
- 08028 Barcelona
- Spain
- Departament de Ciència de Materials i Química Física
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Rudinsky S, Sanz AS, Gauvin R. A novel quantum dynamical approach in electron microscopy combining wave-packet propagation with Bohmian trajectories. J Chem Phys 2017; 146:104702. [PMID: 28298114 DOI: 10.1063/1.4978241] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
Abstract
The numerical analysis of the diffraction features rendered by transmission electron microscopy typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advantageous (relatively simple implementations and low computational costs), they involve important approximations and thus their range of applicability is limited. To overcome such limitations, an alternative, more general approach is proposed, based on an optimal combination of wave-packet propagation with the on-the-fly computation of associated Bohmian trajectories. For the sake of clarity, but without a loss of generality, the approach is used to analyze the diffraction of an electron beam by a thin aluminum slab as a function of three different incidence (working) conditions which are of interest in electron microscopy: the probe width, the tilting angle, and the beam energy. Specifically, it is shown that, because there is a dependence on particular thresholds of the beam energy, this approach provides a clear description of the diffraction process at any energy, revealing at the same time any diversion of the beam inside the material towards directions that cannot be accounted for by other conventional methods, which is of much interest when dealing with relatively low energies and/or relatively large tilting angles.
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Affiliation(s)
- S Rudinsky
- Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, Québec H3A 0C5, Canada
| | - A S Sanz
- Department of Optics, Faculty of Physical Science, Universidad Complutense de Madrid, Pza. Ciencias 1, 28040 Madrid, Spain
| | - R Gauvin
- Department of Mining and Materials Engineering, McGill University, 3610 University Street, Montreal, Québec H3A 0C5, Canada
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Walls JD, Hadad D. The Talbot Effect for two-dimensional massless Dirac fermions. Sci Rep 2016; 6:26698. [PMID: 27221604 PMCID: PMC4879638 DOI: 10.1038/srep26698] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Accepted: 05/04/2016] [Indexed: 12/02/2022] Open
Abstract
A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of zT. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array.
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Affiliation(s)
- Jamie D Walls
- Department of Chemistry, University of Miami, Coral Gables, Florida 33124, USA
| | - Daniel Hadad
- Department of Chemistry, University of Miami, Coral Gables, Florida 33124, USA
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Albareda G, Bofill JM, Tavernelli I, Huarte-Larrañaga F, Illas F, Rubio A. Conditional Born-Oppenheimer Dynamics: Quantum Dynamics Simulations for the Model Porphine. J Phys Chem Lett 2015; 6:1529-1535. [PMID: 26263307 DOI: 10.1021/acs.jpclett.5b00422] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We report a new theoretical approach to solve adiabatic quantum molecular dynamics halfway between wave function and trajectory-based methods. The evolution of a N-body nuclear wave function moving on a 3N-dimensional Born-Oppenheimer potential-energy hyper-surface is rewritten in terms of single-nuclei wave functions evolving nonunitarily on a 3-dimensional potential-energy surface that depends parametrically on the configuration of an ensemble of generally defined trajectories. The scheme is exact and, together with the use of trajectory-based statistical techniques, can be exploited to circumvent the calculation and storage of many-body quantities (e.g., wave function and potential-energy surface) whose size scales exponentially with the number of nuclear degrees of freedom. As a proof of concept, we present numerical simulations of a 2-dimensional model porphine where switching from concerted to sequential double proton transfer (and back) is induced quantum mechanically.
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Affiliation(s)
- Guillermo Albareda
- †Institut de Química Teòrica i Computacional, Universitat de Barcelona, Barcelona 08028, Spain
- ‡Departament de Química Física, Universitat de Barcelona, Barcelona 08028, Spain
| | - Josep Maria Bofill
- †Institut de Química Teòrica i Computacional, Universitat de Barcelona, Barcelona 08028, Spain
- §Departament de Química Orgànica, Universitat de Barcelona, Barcelona 08028, Spain
| | - Ivano Tavernelli
- ∥IBM Research Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
| | - Fermin Huarte-Larrañaga
- †Institut de Química Teòrica i Computacional, Universitat de Barcelona, Barcelona 08028, Spain
- ‡Departament de Química Física, Universitat de Barcelona, Barcelona 08028, Spain
| | - Francesc Illas
- †Institut de Química Teòrica i Computacional, Universitat de Barcelona, Barcelona 08028, Spain
- ‡Departament de Química Física, Universitat de Barcelona, Barcelona 08028, Spain
| | - Angel Rubio
- ⊥Max Planck Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761 Hamburg, Germany
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Chou CC. Complex quantum Hamilton-Jacobi equation with Bohmian trajectories: application to the photodissociation dynamics of NOCl. J Chem Phys 2014; 140:104307. [PMID: 24628169 DOI: 10.1063/1.4867636] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The complex quantum Hamilton-Jacobi equation-Bohmian trajectories (CQHJE-BT) method is introduced as a synthetic trajectory method for integrating the complex quantum Hamilton-Jacobi equation for the complex action function by propagating an ensemble of real-valued correlated Bohmian trajectories. Substituting the wave function expressed in exponential form in terms of the complex action into the time-dependent Schrödinger equation yields the complex quantum Hamilton-Jacobi equation. We transform this equation into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation describing the rate of change in the complex action transported along Bohmian trajectories is simultaneously integrated with the guidance equation for Bohmian trajectories, and the time-dependent wave function is readily synthesized. The spatial derivatives of the complex action required for the integration scheme are obtained by solving one moving least squares matrix equation. In addition, the method is applied to the photodissociation of NOCl. The photodissociation dynamics of NOCl can be accurately described by propagating a small ensemble of trajectories. This study demonstrates that the CQHJE-BT method combines the considerable advantages of both the real and the complex quantum trajectory methods previously developed for wave packet dynamics.
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Affiliation(s)
- Chia-Chun Chou
- Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan
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Investigating transition state resonances in the time domain by means of Bohmian mechanics: The F+HD reaction. Chem Phys 2012. [DOI: 10.1016/j.chemphys.2011.07.017] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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Garashchuk S, Rassolov V, Prezhdo O. Semiclassical Bohmian Dynamics. REVIEWS IN COMPUTATIONAL CHEMISTRY 2010. [DOI: 10.1002/9780470890905.ch6] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
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Chou CC, Wyatt RE. Quantum streamlines within the complex quantum Hamilton–Jacobi formalism. J Chem Phys 2008; 129:124113. [DOI: 10.1063/1.2977747] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chou CC, Wyatt RE. Quantum vortices within the complex quantum Hamilton–Jacobi formalism. J Chem Phys 2008; 128:234106. [DOI: 10.1063/1.2937905] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Sanz A, Miret-Artés S. Interplay of causticity and vorticality within the complex quantum Hamilton–Jacobi formalism. Chem Phys Lett 2008. [DOI: 10.1016/j.cplett.2008.04.103] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Chou CC, Wyatt RE. Quantum trajectories in complex space: One-dimensional stationary scattering problems. J Chem Phys 2008; 128:154106. [DOI: 10.1063/1.2850743] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
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Sanz AS, Miret-Artés S. Comment on “Bohmian mechanics with complex action: A new trajectory-based formulation of quantum mechanics” [J. Chem. Phys. 125, 231103 (2006)]. J Chem Phys 2007; 127:197101, author reply 197102. [DOI: 10.1063/1.2798761] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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Aspects of nonlocality from a quantum trajectory perspective: A WKB approach to Bohmian mechanics. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.08.002] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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