Relaxation, thermalization, and Markovian dynamics of two spins coupled to a spin bath

Abstract

It is shown that by fitting a Markovian quantum master equation to the numerical solution of the time-dependent Schrödinger equation of a system of two spin-1/2 particles interacting with a bath of up to 34 spin-1/2 particles, the former can describe the dynamics of the two-spin system rather well. The fitting procedure that yields this Markovian quantum master equation accounts for all non-Markovian effects in as much the general structure of this equation allows and yields a description that is incompatible with the Lindblad equation.

Introduction to Quantum Thermodynamics: History and Prospects

“…A Hilbert size of ∼ 10 11 employed for the study is on the limit of simulation by currently available classical computers. The ETH proved to be correct with respect to the asymptotic system expectation values [190,191]. In addition, for the one qubit case a Bloch-type equation with time-dependent coefficients provides a simple and accurate description of the dynamics of a spin particle in contact with a thermal bath.…”

Testing quantum fault tolerance on small systems

“…(1) with the piecewise time-independent Hamiltonian given in Eqs. (4)- (7) to machine precision by means of the Chebyshev polynomial representation of exp(−itH) [42][43][44]. The environment is prepared at an inverse temperature β using the randomstate technology [44,45].…”

Markovian heat sources with the smallest heat capacity

“…z ∞ is the polarization of the system after it fully equilibrates with the microbath to a state where all the N+1 spins have the same polarization. The dependence of z ∞ on the system initial state is a direct consequence of having a heat source with initial energy that is not overwhelmingly larger than that of the system (i.e., small heat capacity, see also [31]).…”