Non-equilibrium steady states of a Markov generator of weak coupling limit type modeling absorption-emission of m and n photons

2016 ◽  
Vol 19 (04) ◽  
pp. 1650023 ◽  
Author(s):  
Marco A. Cruz-de la Rosa ◽  
Roberto Quezada
Keyword(s):  
Linear Combination ◽  
Weak Coupling ◽  
Detailed Balance ◽  
Weak Coupling Limit ◽  
Steady States ◽  
Emission Rates ◽  
Simultaneous Emission ◽  
Markov Generator ◽  
Convex Linear Combination ◽  
Non Equilibrium

We study detailed balance and non-equilibrium steady states of a Markov generator of weak coupling limit type, modeling absorption and simultaneous emission of [Formula: see text]- and [Formula: see text]-photons, with [Formula: see text]. In the case [Formula: see text], under natural constraints on the absorption and emission rates, there exist infinitely many non-equilibrium steady states which are convex linear combination of even and odd states.

scholarly journals Stationary states of weak coupling limit-type Markov generators and quantum transport models

2020 ◽  
Vol 23 (01) ◽  
pp. 2050003
Author(s):  
A. Hernández-Cervantes ◽  
R. Quezada
Keyword(s):  
Quantum Transport ◽  
Weak Coupling ◽  
Energy Transport ◽  
Transport Model ◽  
Weak Coupling Limit ◽  
Stationary States ◽  
Transport Models ◽  
Markov Generator ◽  
Kraus Operators ◽  
Creation Operators

We prove that every stationary state in the annihilator of all Kraus operators of a weak coupling limit-type Markov generator consists of two pieces, one of them supported on the interaction-free subspace and the second one on its orthogonal complement. In particular, we apply the previous result to describe in detail the structure of a slightly modified quantum transport model due to Arefeva et al. (modified AKV’s model) studied first in [J. C. García et al., Entangled and dark stationary states of excitation energy transport models in many-particles systems and photosynthesis, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 21(3) (2018), Article ID: 1850018, p. 21, doi:10.1142/S0219025718500182], in terms of generalized annihilation and creation operators.

scholarly journals Entropy Production and Detailed Balance for a Class of Quantum Markov Semigroups

2015 ◽  
Vol 22 (03) ◽  
pp. 1550013 ◽  
Author(s):  
F. Fagnola ◽  
R. Rebolledo
Keyword(s):  
Entropy Production ◽  
Weak Coupling ◽  
Detailed Balance ◽  
Weak Coupling Limit ◽  
Invariant State ◽  
Markov Semigroups ◽  
Detailed Balance Condition ◽  
Balance Condition ◽  
Do So

We give an explicit entropy production formula for a class of quantum Markov semigroups, arising in the weak coupling limit of a system coupled with reservoirs, whose generators [Formula: see text] are sums of other generators [Formula: see text] associated with positive Bohr frequencies [Formula: see text] of the system. As a consequence, we show that any such semigroup satisfies the quantum detailed balance condition with respect to an invariant state if and only if all semigroups generated by each [Formula: see text] do so with respect to the same invariant state.

scholarly journals On three new principles in non-equilibrium statistical mechanics and Markov semigroups of weak coupling limit type

2016 ◽  
Vol 19 (02) ◽  
pp. 1650009 ◽  
Author(s):  
Luigi Accardi ◽  
Franco Fagnola ◽  
Roberto Quezada
Keyword(s):  
Statistical Mechanics ◽  
Master Equation ◽  
Weak Coupling ◽  
Detailed Balance ◽  
Weak Coupling Limit ◽  
Markov Semigroups ◽  
Equilibrium Statistical Mechanics ◽  
Equation Formulation ◽  
The Third ◽  
Kms Condition

We introduce three new principles: the nonlinear Boltzmann–Gibbs prescription, the local KMS condition and the generalized detailed balance (GDB) condition. We prove the equivalence of the first two under general conditions and we discuss a master equation formulation of the third one.

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.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment

2018 ◽  
Vol 54 (5) ◽  
pp. 427-444 ◽  
Author(s):  
R. D. Astumian
Keyword(s):  
Steady States ◽  
Absolute Amount ◽  
Fluctuating Environment ◽  
The Absolute ◽  
Non Equilibrium

Fluctuations favour state B = (B,B′) based on kinetic asymmetry combined with moderate dissipation rather than state A = (A,A′) in which the absolute amount of dissipation is greater but where there is no kinetic asymmetry.

scholarly journals An obstacle to sub-AdS holography for SYK-like models

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang ◽  
Yingfei Gu ◽  
Alexei Kitaev
Keyword(s):  
Lyapunov Exponent ◽  
Weak Coupling ◽  
Kinetic Coefficient ◽  
Weak Coupling Limit ◽  
Branching Time ◽  
Quasiparticle Lifetime

Abstract We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

ENERGY BAND OVERLAPPING IN HIGH-Tc SUPERCONDUCTORS

1996 ◽  
Vol 10 (30) ◽  
pp. 1483-1490 ◽  
Author(s):  
M. MORENO ◽  
R. M. MÉNDEZ-MORENO ◽  
M. A. ORTIZ ◽  
S. OROZCO
Keyword(s):  
Weak Coupling ◽  
Cuprate Superconductors ◽  
Weak Coupling Limit ◽  
Band Model ◽  
Coupling Constant ◽  
High Tc Superconductors ◽  
Energy Bands ◽  
Effective Coupling ◽  
High Tc ◽  
Two Band Model

Multi-band superconductors are analyzed and the relevance of overlapping energy bands to the high-T c of these materials is studied. Within the BCS framework, a two band model with generalized Fermi surface topologies is developed. Values of the overlapped occupancy parameters for typical cuprate superconductors are obtained as a function of the ratio R and the effective coupling constant, λ, in the weak-coupling limit. The overlap scale is of the order or lower than the cutoff (Debye) energy. The typical behavior of the isotope effect is obtained. As these superconductors have transition temperatures above the phonon barrier, the results of this approach are important to the generic understanding of the high-T c superconducting mechanism.

Sign in / Sign up

Export Citation Format

Share Document