Related papers: Restriction on relaxation times derived from the L…
In 1976, Gorini, Kossakowski, Sudarshan and Lindblad independently discovered a general form of master equations for an open quantum Markovian dynamics. In honor of all the authors, the equation is nowadays called the GKLS master equation.…
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…
We study relaxation times, also called mixing times, of quantum many-body systems described by a Lindblad master equation. We in particular study the scaling of the spectral gap with the system length, the so-called dynamical exponent,…
We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its…
The perturbative master equation (Bloch-Redfield) is extensively used to study dissipative quantum mechanics - particularly for qubits - despite the 25 year old criticism that it violates positivity (generating negative probabilities). We…
Relaxation rates are key characteristics of quantum processes, as they determine how quickly a quantum system thermalizes, equilibrates, decoheres, and dissipates. While they play a crucial role in theoretical analyses, relaxation rates are…
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations…
The objective of this article is to complete preliminary results concerning the time-minimal control of dissipative two-level quantum systems whose dynamics is governed by Lindblad equations. The extremal system is described by a…
The relaxation time of a classical spin interacting with a large conduction-electron system is computed for a weak magnetic field, which initially drives the spin out of equilibrium. We trace the spin and the conduction-electron dynamics on…
We consider an open quantum system described by a Lindblad-type master equation with two times-scales. The fast time-scale is strongly dissipative and drives the system towards a low-dimensional decoherence-free space. To perform the…
This paper proposes a bilevel hierarchy of strengthened complex moment relaxations for complex polynomial optimization. The key trick entails considering a class of positive semidefinite conditions that arise naturally in characterizing the…
The time evolution of Markovian open quantum systems is governed by Lindblad master equations, whose solution can be formally written as the Lindbladian exponential acting on the initial density matrix. By expanding this Lindbladian…
The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus…
Given a linear open quantum system which is described by a Lindblad master equation, we detail the calculation of the moment evolution equations from this master equation. We stress that the moment evolution equations are well-known, but…
The relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model is studied numerically by solving the full set of equations of motion. A Lindblad…
We consider the problem of computing the maximal invariant set of discrete-time linear systems subject to a class of non-convex constraints that admit quadratic relaxations. These non-convex constraints include semialgebraic sets and other…
We define a perturbative approximation for the solution of Lindblad master equations with time-dependent generators that satisfies the fundamental property of complete positivity, as essential for quantum simulations and optimal control.…
The Lindblad equation for a two-level system under an electric field is analyzed by mapping to a linear equation with a non-Hermitian matrix. Exceptional points of the matrix are found to be extensive; the second-order ones are located on…
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…
We study the concepts of complete positivity, positivity and non-Markovianity in a two-level open quantum system whose dynamics are governed by a time-local quantum master equation. We establish necessary and sufficient conditions on the…