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Wang CZ, Kononchuk R, Kuhl U, Kottos T. Loss-Induced Violation of the Fundamental Transmittance-Asymmetry Bound in Nonlinear Complex Wave Systems. PHYSICAL REVIEW LETTERS 2023; 131:123801. [PMID: 37802952 DOI: 10.1103/physrevlett.131.123801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 08/28/2023] [Indexed: 10/08/2023]
Abstract
Nonlinearity-induced asymmetric transport (AT) can be utilized for on-chip implementation of nonreciprocal devices that do not require odd-vector biasing. This scheme, however, is subject to a fundamental bound dictating that the maximum transmittance asymmetry is inversely proportional to the asymmetry intensity range (AIR) over which AT occurs. Contrary to the conventional wisdom, we show that the implementation of losses can lead to an increase of the AIR without deteriorating the AT. We develop a general theory that provides a new upper bound for AT in nonlinear complex systems and highlights the importance of their structural complexity and of losses. Our predictions are confirmed numerically and experimentally using a microwave complex network of coaxial cables.
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Affiliation(s)
- Cheng-Zhen Wang
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Rodion Kononchuk
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
| | - Ulrich Kuhl
- Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06200, Nice, France
| | - Tsampikos Kottos
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA
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2
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Effective Field Theory of Random Quantum Circuits. ENTROPY 2022; 24:e24060823. [PMID: 35741543 PMCID: PMC9223178 DOI: 10.3390/e24060823] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Revised: 06/09/2022] [Accepted: 06/10/2022] [Indexed: 11/23/2022]
Abstract
Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.
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Chen L, Kottos T, Anlage SM. Perfect absorption in complex scattering systems with or without hidden symmetries. Nat Commun 2020; 11:5826. [PMID: 33203847 PMCID: PMC7673030 DOI: 10.1038/s41467-020-19645-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2019] [Accepted: 10/19/2020] [Indexed: 11/09/2022] Open
Abstract
Wavefront shaping (WFS) schemes for efficient energy deposition in weakly lossy targets is an ongoing challenge for many classical wave technologies relevant to next-generation telecommunications, long-range wireless power transfer, and electromagnetic warfare. In many circumstances these targets are embedded inside complicated enclosures which lack any type of (geometric or hidden) symmetry, such as complex networks, buildings, or vessels, where the hypersensitive nature of multiple interference paths challenges the viability of WFS protocols. We demonstrate the success of a general WFS scheme, based on coherent perfect absorption (CPA) electromagnetic protocols, by utilizing a network of coupled transmission lines with complex connectivity that enforces the absence of geometric symmetries. Our platform allows for control of the local losses inside the network and of the violation of time-reversal symmetry via a magnetic field; thus establishing CPA beyond its initial concept as the time-reversal of a laser cavity, while offering an opportunity for better insight into CPA formation via the implementation of semiclassical tools.
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Affiliation(s)
- Lei Chen
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA.
| | - Tsampikos Kottos
- Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University, Middletown, CT, 06459, USA
| | - Steven M Anlage
- Quantum Materials Center, Department of Physics, University of Maryland, College Park, MD, 20742, USA.
- Department of Electrical and Computer Engineering, University of Maryland, College Park, MD, 20742, USA.
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Altland A, Gnutzmann S, Haake F, Micklitz T. A review of sigma models for quantum chaotic dynamics. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:086001. [PMID: 26181515 DOI: 10.1088/0034-4885/78/8/086001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.
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Affiliation(s)
- Alexander Altland
- Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Deutschland
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Jalabert RA, Weick G, Weidenmüller HA, Weinmann D. Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052911. [PMID: 25353865 DOI: 10.1103/physreve.89.052911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2013] [Indexed: 06/04/2023]
Abstract
Experimentally, the phase of the amplitude for electron transmission through a quantum dot (transmission phase) shows the same pattern between consecutive resonances. Such universal behavior, found for long sequences of resonances, is caused by correlations of the signs of the partial-width amplitudes of the resonances. We investigate the stability of these correlations in terms of a statistical model. For a classically chaotic dot, the resonance eigenfunctions are assumed to be Gaussian distributed. Under this hypothesis, statistical fluctuations are found to reduce the tendency towards universal phase evolution. Long sequences of resonances with universal behavior only persist in the semiclassical limit of very large electron numbers in the dot and for specific energy intervals. Numerical calculations qualitatively agree with the statistical model but quantitatively are closer to universality.
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Affiliation(s)
- Rodolfo A Jalabert
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
| | - Guillaume Weick
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
| | | | - Dietmar Weinmann
- Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, F-67034 Strasbourg, France
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Pluhař Z, Weidenmüller HA. Universal quantum graphs. PHYSICAL REVIEW LETTERS 2014; 112:144102. [PMID: 24765968 DOI: 10.1103/physrevlett.112.144102] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Indexed: 06/03/2023]
Abstract
For time-reversal invariant graphs we prove the Bohigas-Giannoni-Schmit conjecture in its most general form: For graphs that are mixing in the classical limit, all spectral correlation functions coincide with those of the Gaussian orthogonal ensemble of random matrices. For open graphs, we derive the analogous identities for all S-matrix correlation functions.
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Affiliation(s)
- Z Pluhař
- Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8, Czech Republic
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Band R, Berkolaiko G. Universality of the momentum band density of periodic networks. PHYSICAL REVIEW LETTERS 2013; 111:130404. [PMID: 24116752 DOI: 10.1103/physrevlett.111.130404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2013] [Indexed: 06/02/2023]
Abstract
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic network. We show that this probability exhibits universal properties. More precisely, the probability to be in the spectrum does not depend on the edge lengths (as long as they are generic) and is also invariant within some classes of graph topologies.
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Affiliation(s)
- Ram Band
- Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel
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Pluhař Z, Weidenmüller HA. Chaotic scattering on individual quantum graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022902. [PMID: 24032896 DOI: 10.1103/physreve.88.022902] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2013] [Indexed: 06/02/2023]
Abstract
For chaotic scattering on quantum graphs, the semiclassical approximation is exact. We use this fact and employ supersymmetry, the color-flavor transformation, and the saddle-point approximation to calculate the exact expression for the lowest and asymptotic expressions in the Ericson regime for all higher correlation functions of the scattering matrix. Our results agree with those available from the random-matrix approach to chaotic scattering. We conjecture that our results hold universally for quantum-chaotic scattering.
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Affiliation(s)
- Z Pluhař
- Faculty of Mathematics and Physics, Charles University, 180 00 Praha 8, Czech Republic
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Waltner D, Gnutzmann S, Tanner G, Richter K. Subdeterminant approach for pseudo-orbit expansions of spectral determinants in quantum maps and quantum graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:052919. [PMID: 23767610 DOI: 10.1103/physreve.87.052919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2013] [Indexed: 06/02/2023]
Abstract
We study the implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into subdeterminants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo-orbits of different lengths than was known previously. We reformulate Newton identities and the spectral density in terms of subdeterminant expansions and point out the implications of the subdeterminant identity for these expressions. We analyze furthermore the effect of the identity on spectral correlation functions such as the autocorrelation and parametric cross-correlation functions of the spectral determinant and the spectral form factor.
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Affiliation(s)
- Daniel Waltner
- Weizmann Institute of Science, Physics Department, Rehovot, Israel
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Pluhař Z, Weidenmüller HA. Universal chaotic scattering on quantum graphs. PHYSICAL REVIEW LETTERS 2013; 110:034101. [PMID: 23373926 DOI: 10.1103/physrevlett.110.034101] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/03/2012] [Revised: 11/27/2012] [Indexed: 06/01/2023]
Abstract
We calculate the S-matrix correlation function for chaotic scattering on quantum graphs and show that it agrees with that of random-matrix theory. We also calculate all higher S-matrix correlation functions in the Ericson regime. These, too, agree with random-matrix theory results as far as the latter are known. We conjecture that our results give a universal description of chaotic scattering.
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Affiliation(s)
- Z Pluhař
- Faculty of Mathematics and Physics, Charles University, Praha 8, Czech Republic
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