Quantum master equation for a system influencing its environment

Abstract

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 system and the environment and the conservation of energy in the finite total system. This master equation describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system.

Dissipation in a superconducting artificial atom due to a single nonequilibrium quasiparticle

“…Indeed, when the quasiparticle performs a transition from a level with the energy on one island into a bunch of levels with energies spread over an interval of width ∼h TL around ±hω p on the other island, the off-diagonal terms beating at relative frequencies ∼ TL have already dephased on the quasiparticle tunneling time scale. Thus, the quasiparticle is treated as a "minibath," in the sense that the coherence is neglected, but change of the quasiparticle state by exciting or deexciting the JJ is accounted for [20].…”

“…[17,18], but the quasiparticle degrees of freedom are included in the reduced density matrix following the approach of Refs. [19,20] and its application to a Cooper-pair box in Ref. [21].…”

Lattice mapping for many-body open quantum systems and its application to atoms in photonic crystals

“…However, in most cases, quantum systems shall be considered as open (OQS) [1,2], i.e., interacting with environments such as the radiation field or phonons within a lattice. In addition, to describe such an interaction, it is often not accurate to assume a large separation of scales between the quantum system and its environment, like in the weak coupling or Markov approximations, or to assume that the relevant part of the system can be described in a reduced subspace of the total Hilbert space, like in the so-called projection operator techniques [1,[3][4][5][6][7][8]. Hence, an alternative approach that allows to go beyond these assumptions is highly desirable.…”

Describing many-body localized systems in thermal environments

“…Under the dynamics of equation (4), the coherences, k q r á ñ |ˆ| with k q ¹ , decay such that the steady state reached asymptotically in the long-time limit is diagonal in the energy basis, p k k k k r r  = å ñá ¥ˆ| | [59][60][61]. This can be seen most easily by noting that in the limit γ → 0, the first term in equation (2) has to vanish for the steady state with 0 t r ¶ = ¥ .…”