Related papers: Universal Constraints on Relaxation Times for d-le…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
The aims of this paper are two. The first is to give a brief review of the most relevant theoretical results concerning the uniqueness of the steady-state solution of the Lindblad-Gorini-Kossakowski-Sudarshan master equation and the…
Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…
We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are…
Master equations are commonly used to describe time evolution of open systems. We introduce a general method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time dependent transport…
Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov…
A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the…
We develop a Markovian master equation in the Lindblad form that enables the efficient study of a wide range of open quantum many-body systems that would be inaccessible with existing methods. The validity of the master equation is based…
Convolutionless and convolution master equations are the two mostly used physical descriptions of open quantum systems dynamics. We subject these equations to time deformations: local dilations and contractions of time scale. We prove that…
A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum…
Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…
Time-local quantum master equations that describe open quantum systems beyond the limit of ultraweak system-bath coupling are often not of Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. Prominent examples are the Redfield equation…
Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs" - explicit degrees of freedom associated with the…
We introduce a generalized classical model of Brownian motion for describing thermal relaxation processes which is thermodynamically consistent. Applying the canonical quantization to this model, a quantum equation for the density operator…
Recently, the concept of k-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of k-contraction properties has faced significant challenges due to the reliance on complex…
The Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher's…
A novel theoretical expression for the relaxation time of magnetic nanoparticles with dipolar interactions is derived from Kramers' theory, extending the Boltzmann-Gibbs framework to incorporate Tsallis statistics. The model provides a…
We consider the Markovian Master Equation over matrix algebra $\mathbb{M}_d$, governed by periodic Lindbladian $L_t$ in standard (Kossakowski-Lindblad-Gorini-Sudarshan) form. It is shown that under simplifying assumption of commutativity,…
Completely positive transformations play an important role in the description of state changes in quantum mechanics, including the time evolution of open quantum systems. One useful tool to describe them is the so-called Choi isomorphism,…
We study the scaling behavior of the relaxation dynamics to thermal equilibrium when a quantum system is near the quantum critical point. In particular, we investigate systems whose relaxation dynamics is described by a Lindblad master…