scholarly journals Analysis Technique for Exceptional Points in Open Quantum Systems and QPT Analogy for the Appearance of Irreversibility

2012 ◽  
Vol 51 (11) ◽  
pp. 3536-3550 ◽  
Author(s):  
Savannah Garmon ◽  
Ingrid Rotter ◽  
Naomichi Hatano ◽  
Dvira Segal
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Exceptional Points ◽  
Analysis Technique

scholarly journals Loss, Gain, and Singular Points in Open Quantum Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Hichem Eleuch ◽  
Ingrid Rotter
Keyword(s):  
Parameter Space ◽  
Critical Points ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Experimental Results ◽  
Open Quantum ◽  
Exceptional Points ◽  
Complex Eigenvalues ◽  
Dynamical Properties

Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues Ei≡Ei+iΓi/2 of the non-Hermitian Hamiltonian H coalesce (where Ei is the energy and Γi is the inverse lifetime of the state i). We show that also the eigenfunctions Φi of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points a=acr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

scholarly journals EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS

2014 ◽  
Vol 54 (2) ◽  
pp. 106-112 ◽  
Author(s):  
Hichem Eleuch ◽  
Ingrid Rotter
Keyword(s):  
Open Quantum Systems ◽  
Level Density ◽  
Quantum Systems ◽  
Point Of View ◽  
Eigenvalues And Eigenfunctions ◽  
Open Quantum ◽  
Exceptional Points ◽  
Characteristic Features ◽  
High Level ◽  
Symmetric Systems

Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian) relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Hamiltonian assignment for open quantum systems

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Eugene F. Dumitrescu ◽  
Pavel Lougovski
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

scholarly journals Matrix Product State Simulations of Non-Equilibrium Steady States and Transient Heat Flows in the Two-Bath Spin-Boson Model at Finite Temperatures

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 77
Author(s):  
Angus J. Dunnett ◽  
Alex W. Chin
Keyword(s):  
Finite Temperature ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Steady States ◽  
Matrix Product ◽  
Open Quantum ◽  
Matrix Product State ◽  
Wide Range ◽  
Boson Model ◽  
Non Equilibrium

Simulating the non-perturbative and non-Markovian dynamics of open quantum systems is a very challenging many body problem, due to the need to evolve both the system and its environments on an equal footing. Tensor network and matrix product states (MPS) have emerged as powerful tools for open system models, but the numerical resources required to treat finite-temperature environments grow extremely rapidly and limit their applications. In this study we use time-dependent variational evolution of MPS to explore the striking theory of Tamascelli et al. (Phys. Rev. Lett. 2019, 123, 090402.) that shows how finite-temperature open dynamics can be obtained from zero temperature, i.e., pure wave function, simulations. Using this approach, we produce a benchmark dataset for the dynamics of the Ohmic spin-boson model across a wide range of coupling strengths and temperatures, and also present a detailed analysis of the numerical costs of simulating non-equilibrium steady states, such as those emerging from the non-perturbative coupling of a qubit to baths at different temperatures. Despite ever-growing resource requirements, we find that converged non-perturbative results can be obtained, and we discuss a number of recent ideas and numerical techniques that should allow wide application of MPS to complex open quantum systems.

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