scholarly journals Simulating time-dependent thermoelectric transport in quantum systems

2020 ◽  
Vol 101 (23) ◽  
Author(s):  
Adel Kara Slimane ◽  
Phillipp Reck ◽  
Geneviève Fleury
Keyword(s):  
Quantum Systems ◽  
Time Dependent ◽  
Thermoelectric Transport

scholarly journals Time-Dependent Pseudo-Hermitian Hamiltonians and a Hidden Geometric Aspect of Quantum Mechanics

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 471 ◽  
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Hermitian Operator ◽  
Quantum Systems ◽  
Time Dependent ◽  
Inner Product ◽  
Geometric Framework ◽  
Heisenberg Picture ◽  
Metric Operator ◽  
Recent Developments

A non-Hermitian operator H defined in a Hilbert space with inner product ⟨ · | · ⟩ may serve as the Hamiltonian for a unitary quantum system if it is η -pseudo-Hermitian for a metric operator (positive-definite automorphism) η . The latter defines the inner product ⟨ · | η · ⟩ of the physical Hilbert space H η of the system. For situations where some of the eigenstates of H depend on time, η becomes time-dependent. Therefore, the system has a non-stationary Hilbert space. Such quantum systems, which are also encountered in the study of quantum mechanics in cosmological backgrounds, suffer from a conflict between the unitarity of time evolution and the unobservability of the Hamiltonian. Their proper treatment requires a geometric framework which clarifies the notion of the energy observable and leads to a geometric extension of quantum mechanics (GEQM). We provide a general introduction to the subject, review some of the recent developments, offer a straightforward description of the Heisenberg-picture formulation of the dynamics for quantum systems having a time-dependent Hilbert space, and outline the Heisenberg-picture formulation of dynamics in GEQM.

Optical potentials in time dependent quantum systems: evaluation ofQ space probabilities

1990 ◽  
Vol 15 (2) ◽  
pp. 141-144 ◽  
Author(s):  
H. J. L�dde ◽  
A. Henne ◽  
R. M. Dreizler
Keyword(s):  
Quantum Systems ◽  
Time Dependent ◽  
Optical Potentials

scholarly journals Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

2020 ◽  
Vol 2 (1) ◽  
pp. 166-188 ◽  
Author(s):  
Carlo Cafaro ◽  
Steven Gassner ◽  
Paul M. Alsing
Keyword(s):  
Resonance Condition ◽  
Transition Probability ◽  
Geometric Analysis ◽  
Quantum Systems ◽  
Time Dependent ◽  
Population Transfer ◽  
Resonance Effects ◽  
Hamiltonian Models ◽  
Exactly Solvable ◽  
Geodesic Paths

We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su 2 ; ℂ time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios.

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