1
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Onizhuk M, Wang YX, Nagura J, Clerk AA, Galli G. Understanding Central Spin Decoherence Due to Interacting Dissipative Spin Baths. PHYSICAL REVIEW LETTERS 2024; 132:250401. [PMID: 38996232 DOI: 10.1103/physrevlett.132.250401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Revised: 04/30/2024] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
We propose a new approach to simulate the decoherence of a central spin coupled to an interacting dissipative spin bath with cluster-correlation expansion techniques. We benchmark the approach on generic 1D and 2D spin baths and find excellent agreement with numerically exact simulations. Our calculations show a complex interplay between dissipation and coherent spin exchange, leading to increased central spin coherence in the presence of fast dissipation. Finally, we model near-surface nitrogen-vacancy centers in diamond and show that accounting for bath dissipation is crucial to understanding their decoherence. Our method can be applied to a variety of systems and provides a powerful tool to investigate spin dynamics in dissipative environments.
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Affiliation(s)
| | | | | | | | - Giulia Galli
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
- Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA
- Materials Science Division and Center for Molecular Engineering, Argonne National Laboratory, Lemont, Illinois 60439, USA
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2
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Sinha S, Ray S, Sinha S. Classical route to ergodicity and scarring in collective quantum systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:163001. [PMID: 38190726 DOI: 10.1088/1361-648x/ad1bf5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2023] [Accepted: 01/08/2024] [Indexed: 01/10/2024]
Abstract
Ergodicity, a fundamental concept in statistical mechanics, is not yet a fully understood phenomena for closed quantum systems, particularly its connection with the underlying chaos. In this review, we consider a few examples of collective quantum systems to unveil the intricate relationship of ergodicity as well as its deviation due to quantum scarring phenomena with their classical counterpart. A comprehensive overview of classical and quantum chaos is provided, along with the tools essential for their detection. Furthermore, we survey recent theoretical and experimental advancements in the domain of ergodicity and its violations. This review aims to illuminate the classical perspective of quantum scarring phenomena in interacting quantum systems.
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Affiliation(s)
- Sudip Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
| | - Sayak Ray
- Physikalisches Institut, Universität Bonn, Nußallee 12, 53115 Bonn, Germany
| | - Subhasis Sinha
- Indian Institute of Science Education and Research Kolkata, Mohanpur, Nadia 741246, India
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3
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Villaseñor D, Barberis-Blostein P. Analysis of chaos and regularity in the open Dicke model. Phys Rev E 2024; 109:014206. [PMID: 38366466 DOI: 10.1103/physreve.109.014206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Accepted: 11/22/2023] [Indexed: 02/18/2024]
Abstract
We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which approximately represents the system spectrum. The isolated Dicke model has a well-defined classical limit with two degrees of freedom. We select two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open system as regular or chaotic, we study regions of the complex spectrum taking windows over the absolute value of its eigenvalues. Our results for this infinite-dimensional system agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative open quantum systems, finding the expected 2D Poisson distribution for regular regimes, and the distribution of the Ginibre unitary ensemble (GinUE) for the chaotic ones, respectively.
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Affiliation(s)
- David Villaseñor
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510 CDMX, Mexico
| | - Pablo Barberis-Blostein
- Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, C.P. 04510 CDMX, Mexico
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4
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Sarkar A, Sen S, Kumar S. Spectral crossovers in non-Hermitian spin chains: Comparison with random matrix theory. Phys Rev E 2023; 108:054210. [PMID: 38115444 DOI: 10.1103/physreve.108.054210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 10/10/2023] [Indexed: 12/21/2023]
Abstract
We present a systematic investigation of the short-range spectral fluctuation properties of three non-Hermitian spin-chain Hamiltonians using complex spacing ratios (CSRs). Specifically, we focus on the non-Hermitian variants of the standard one-dimensional anisotropic XY model having intrinsic rotation-time (RT) symmetry that has been explored analytically by Zhang and Song [Phys. Rev. A 87, 012114 (2013)1050-294710.1103/PhysRevA.87.012114]. The corresponding Hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the x direction together with the one along the z direction facilitates integrability and RT-symmetry breaking, leading to the emergence of quantum chaotic behavior. This is evidenced by a spectral crossover closely resembling the transition from Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two phenomenological random matrix models in this paper to examine 1D Poisson to GinUE and 2D Poisson to GinUE crossovers and the associated signatures in CSRs. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively. These crossovers reasonably capture spectral fluctuations observed in the spin-chain systems within a certain range of parameters.
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Affiliation(s)
- Ayana Sarkar
- Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh-201314, India
| | - Sunidhi Sen
- Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh-201314, India
| | - Santosh Kumar
- Department of Physics, Shiv Nadar Institution of Eminence, Gautam Buddha Nagar, Uttar Pradesh-201314, India
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5
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Cipolloni G, Kudler-Flam J. Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble. PHYSICAL REVIEW LETTERS 2023; 130:010401. [PMID: 36669222 DOI: 10.1103/physrevlett.130.010401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Revised: 10/22/2022] [Accepted: 12/13/2022] [Indexed: 06/17/2023]
Abstract
Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems, and the fluctuations are of equal order. We derive the novel entanglement spectrum that has infinite support in the complex plane and strong energy dependence. We provide evidence of universality, and similar behavior is found in the non-Hermitian Sachdev-Ye-Kitaev model, indicating the general applicability of the Ginibre ensemble to dissipative many-body quantum chaos.
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Affiliation(s)
- Giorgio Cipolloni
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - Jonah Kudler-Flam
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
- School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540 USA
- Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
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6
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Akemann G, Mielke A, Päßler P. Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at noninteger β. Phys Rev E 2022; 106:014146. [PMID: 35974587 DOI: 10.1103/physreve.106.014146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Accepted: 07/07/2022] [Indexed: 06/15/2023]
Abstract
A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2×2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β_{eff}(β) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β=0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β=1.4 and β=2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.
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Affiliation(s)
- Gernot Akemann
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
| | - Adam Mielke
- Technical University of Denmark, Asmussens Allé, Building 303B, 2800 Kgs. Lyngby, Denmark
| | - Patricia Päßler
- Faculty of Physics, Bielefeld University, Postfach 100131, 33501 Bielefeld, Germany
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7
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Cornelius J, Xu Z, Saxena A, Chenu A, Del Campo A. Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos. PHYSICAL REVIEW LETTERS 2022; 128:190402. [PMID: 35622025 DOI: 10.1103/physrevlett.128.190402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2021] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
The dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.
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Affiliation(s)
- Julien Cornelius
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Zhenyu Xu
- School of Physical Science and Technology, Soochow University, Suzhou 215006, China
| | - Avadh Saxena
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Aurélia Chenu
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Adolfo Del Campo
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg, Luxembourg
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8
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Dusa IG, Wettig T. Approximation formula for complex spacing ratios in the Ginibre ensemble. Phys Rev E 2022; 105:044144. [PMID: 35590658 DOI: 10.1103/physreve.105.044144] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 04/06/2022] [Indexed: 06/15/2023]
Abstract
Recently, Sá, Ribeiro, and Prosen [Phys. Rev. X 10, 021019 (2020)10.1103/PhysRevX.10.021019] introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.
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Affiliation(s)
- Ioachim G Dusa
- Department of Physics, University of Regensburg, 93040 Regensburg, Germany
| | - Tilo Wettig
- Department of Physics, University of Regensburg, 93040 Regensburg, Germany
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9
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Li J, Prosen T, Chan A. Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos. PHYSICAL REVIEW LETTERS 2021; 127:170602. [PMID: 34739275 DOI: 10.1103/physrevlett.127.170602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Accepted: 09/24/2021] [Indexed: 06/13/2023]
Abstract
We propose a measure, which we call the dissipative spectral form factor (DSFF), to characterize the spectral statistics of non-Hermitian (and nonunitary) matrices. We show that DSFF successfully diagnoses dissipative quantum chaos and reveals correlations between real and imaginary parts of the complex eigenvalues up to arbitrary energy scale (and timescale). Specifically, we provide the exact solution of DSFF for the complex Ginibre ensemble (GinUE) and for a Poissonian random spectrum (Poisson) as minimal models of dissipative quantum chaotic and integrable systems, respectively. For dissipative quantum chaotic systems, we show that the DSFF exhibits an exact rotational symmetry in its complex time argument τ. Analogous to the spectral form factor (SFF) behavior for Gaussian unitary ensemble, the DSFF for GinUE shows a "dip-ramp-plateau" behavior in |τ|: the DSFF initially decreases, increases at intermediate timescales, and saturates after a generalized Heisenberg time, which scales as the inverse mean level spacing. Remarkably, for large matrix size, the "ramp" of the DSFF for GinUE increases quadratically in |τ|, in contrast to the linear ramp in the SFF for Hermitian ensembles. For dissipative quantum integrable systems, we show that the DSFF takes a constant value, except for a region in complex time whose size and behavior depend on the eigenvalue density. Numerically, we verify the above claims and additionally show that the DSFF for real and quaternion real Ginibre ensembles coincides with the GinUE behavior, except for a region in the complex time plane of measure zero in the limit of large matrix size. As a physical example, we consider the quantum kicked top model with dissipation and show that it falls under the Ginibre universality class and Poisson as the "kick" is switched on or off. Lastly, we study spectral statistics of ensembles of random classical stochastic matrices or Markov chains and show that these models again fall under the Ginibre universality class.
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Affiliation(s)
- Jiachen Li
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Tomaž Prosen
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Amos Chan
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
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10
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Tarnowski W, Yusipov I, Laptyeva T, Denisov S, Chruściński D, Życzkowski K. Random generators of Markovian evolution: A quantum-classical transition by superdecoherence. Phys Rev E 2021; 104:034118. [PMID: 34654129 DOI: 10.1103/physreve.104.034118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2021] [Accepted: 08/27/2021] [Indexed: 11/07/2022]
Abstract
Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.
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Affiliation(s)
- W Tarnowski
- Institute of Theoretical Physics, Uniwersytet Jagielloński, 30-348 Kraków, Poland
| | - I Yusipov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia
| | - T Laptyeva
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia
| | - S Denisov
- Department of Computer Science, Oslo Metropolitan University, N-0130 Oslo, Norway
| | - D Chruściński
- Institute of Physics, Faculty of Physics, Astronomy and Informatics Nicolaus Copernicus University, 87-100 Toruń, Poland
| | - K Życzkowski
- Institute of Theoretical Physics, Uniwersytet Jagielloński, 30-348 Kraków, Poland.,Centrum Fizyki Teoretycznej PAN, 02-668 Warszawa, Poland
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11
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Chuang C, Brumer P. Extreme Parametric Sensitivity in the Steady-State Photoisomerization of Two-Dimensional Model Rhodopsin. J Phys Chem Lett 2021; 12:3618-3624. [PMID: 33825472 DOI: 10.1021/acs.jpclett.1c00577] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We computationally studied the photoisomerization reaction of the retinal chromophore in rhodopsin using a two-state two-mode model coupled to thermal baths. Reaction quantum yields at the steady state (10 ps and beyond) were found to be considerably different than their transient values, suggesting a weak correlation between transient and steady-state dynamics in these systems. Significantly, the steady-state quantum yield was highly sensitive to minute changes in system parameters, while transient dynamics was nearly unaffected. Correlation of such sensitivity with standard level spacing statistics of the nonadiabatic vibronic system suggests a possible origin in quantum chaos. The significance of this observation of quantum yield parametric sensitivity in biological models of vision has profound conceptual and fundamental implications.
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Affiliation(s)
- Chern Chuang
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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12
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Luo X, Ohtsuki T, Shindou R. Universality Classes of the Anderson Transitions Driven by Non-Hermitian Disorder. PHYSICAL REVIEW LETTERS 2021; 126:090402. [PMID: 33750149 DOI: 10.1103/physrevlett.126.090402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/15/2020] [Accepted: 02/03/2021] [Indexed: 06/12/2023]
Abstract
The interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of the Anderson transitions driven by non-Hermitian disorders for a three-dimensional (3D) Anderson model and 3D U(1) model, which belong to 3D class AI^{†} and 3D class A in the classification of non-Hermitian systems, respectively. Based on level statistics and finite-size scaling analysis, the critical exponent for the length scale is estimated as ν=0.99±0.05 for class AI^{†}, and ν=1.09±0.05 for class A, both of which are clearly distinct from the critical exponents for 3D orthogonal and 3D unitary classes, respectively. In addition, spectral rigidity, level spacing distribution, and level spacing ratio distribution are studied. These critical behaviors strongly support that the non-Hermiticity changes the universality classes of the Anderson transitions.
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Affiliation(s)
- Xunlong Luo
- Science and Technology on Surface Physics and Chemistry Laboratory, Mianyang 621907, China
| | - Tomi Ohtsuki
- Physics Division, Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan
| | - Ryuichi Shindou
- International Center for Quantum Materials, Peking University, Beijing 100871, China
- Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
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13
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Meyerov I, Kozinov E, Liniov A, Volokitin V, Yusipov I, Ivanchenko M, Denisov S. Transforming Lindblad Equations into Systems of Real-Valued Linear Equations: Performance Optimization and Parallelization of an Algorithm. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1133. [PMID: 33286901 PMCID: PMC7597275 DOI: 10.3390/e22101133] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/20/2020] [Revised: 09/26/2020] [Accepted: 09/30/2020] [Indexed: 11/30/2022]
Abstract
With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper, we address master equations of the Lindblad form, which are a popular theoretical tools in quantum optics, cavity quantum electrodynamics, and optomechanics. By using the generalized Gell-Mann matrices as a basis, any Lindblad equation can be transformed into a system of ordinary differential equations with real coefficients. Recently, we presented an implementation of the transformation with the computational complexity, scaling as O(N5logN) for dense Lindbaldians and O(N3logN) for sparse ones. However, infeasible memory costs remains a serious obstacle on the way to large models. Here, we present a parallel cluster-based implementation of the algorithm and demonstrate that it allows us to integrate a sparse Lindbladian model of the dimension N=2000 and a dense random Lindbladian model of the dimension N=200 by using 25 nodes with 64 GB RAM per node.
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Affiliation(s)
- Iosif Meyerov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
| | - Evgeny Kozinov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
| | - Alexey Liniov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
| | - Valentin Volokitin
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
| | - Igor Yusipov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
- Department of Applied Mathematics, Lobachevsky University, 603950 Nizhni Novgorod, Russia
| | - Mikhail Ivanchenko
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
- Department of Applied Mathematics, Lobachevsky University, 603950 Nizhni Novgorod, Russia
| | - Sergey Denisov
- Mathematical Center, Lobachevsky University, 603950 Nizhni Novgorod, Russia; (I.M.); (E.K.); (A.L.); (V.V.); (I.Y.)
- Department of Computer Science, Oslo Metropolitan University, N-0130 Oslo, Norway
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14
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Akemann G, Baake M, Chakarov N, Krüger O, Mielke A, Ottensmann M, Werdehausen R. Territorial behaviour of buzzards versus random matrix spacing distributions. J Theor Biol 2020; 509:110475. [PMID: 33017577 DOI: 10.1016/j.jtbi.2020.110475] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2020] [Revised: 08/06/2020] [Accepted: 09/01/2020] [Indexed: 10/23/2022]
Abstract
A deeper understanding of the processes underlying the distribution of animals in space is crucial for both basic and applied ecology. The Common buzzard (Buteo buteo) is a highly aggressive, territorial bird of prey that interacts strongly with its intra- and interspecific competitors. We propose and use random matrix theory to quantify the strength and range of repulsion as a function of the buzzard population density, thus providing a novel approach to model density dependence. As an indicator of territorial behaviour, we perform a large-scale analysis of the distribution of buzzard nests in an area of 300 square kilometres around the Teutoburger Wald, Germany, as gathered over a period of 20 years. The nearest and next-to-nearest neighbour spacing distribution between nests is compared to the two-dimensional Poisson distribution, originating from uncorrelated random variables, to the complex eigenvalues of random matrices, which are strongly correlated, and to a two-dimensional Coulomb gas interpolating between these two. A one-parameter fit to a time-moving average reveals a significant increase of repulsion between neighbouring nests, as a function of the observed increase in absolute population density over the monitored period of time, thereby proving an unexpected yet simple model for density-dependent spacing of predator territories. A similar effect is obtained for next-to-nearest neighbours, albeit with weaker repulsion, indicating a short-range interaction. Our results show that random matrix theory might be useful in the context of population ecology.
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Affiliation(s)
- Gernot Akemann
- Faculty of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany.
| | - Michael Baake
- Faculty of Mathematics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany.
| | - Nayden Chakarov
- Faculty of Biology, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany
| | - Oliver Krüger
- Faculty of Biology, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany.
| | - Adam Mielke
- Faculty of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany.
| | - Meinolf Ottensmann
- Faculty of Biology, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany
| | - Rebecca Werdehausen
- Faculty of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld, Germany
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