Finite quantum environments as thermostats: an analysis based on the Hilbert space average method

We consider discrete quantum systems coupled to finite environments which may possibly consist of only one particle in contrast to the standard baths which usually consist of continua of oscillators, spins, etc. We find that such finite environments may, nevertheless, act as thermostats, i.e., equilibrate the system though not necessarily in the way predicted by standard open system techniques. Thus, we apply a novel technique called the Hilbert space Average Method (HAM) and verify its results numerically.Comment: 12 pages, 10 figure

Scaling behavior of interactions in a modular quantum system and the existence of local temperature

We consider a quantum system of fixed size consisting of a regular chain of $n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems each, we show that the strength of interaction between the groups scales with $N^{- 1/2}$. As a consequence, if the total system is in a thermal state with inverse temperature $\beta$, a sufficient condition for subgroups of size $N$ to be approximately in a thermal state with the same temperature is $\sqrt{N} \gg \beta \bar{\delta E}$, where $\bar{\delta E}$ is the width of the occupied level spectrum of the total system. These scaling properties indicate on what scale local temperatures may be meaningfully defined as intensive variables. This question is particularly relevant for non-equilibrium scenarios such as heat conduction etc.Comment: 7 pages, accepted for publication in Europhysics Letter

Transient fluctuation theorem in closed quantum systems

Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schr\"odinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.Comment: 5 pages, 6 figure

Thermalization of quantum systems by finite baths

We consider a discrete quantum system coupled to a finite bath, which may consist of only one particle, in contrast to the standard baths which usually consist of continua of oscillators, spins, etc. We find that such finite baths may nevertheless equilibrate the system though not necessarily in the way predicted by standard open system techniques. This behavior results regardless of the initial state being correlated or not.Comment: 7 pages, 6 figures, accepted for publication in Eur. Phys. Let

Hilbert Space Average Method and adiabatic quantum search

We discuss some aspects related to the so-called Hilbert space Average Method, as an alternative to describe the dynamics of open quantum systems. First we present a derivation of the method which does not make use of the algebra satisfied by the operators involved in the dynamics, and extend the method to systems subject to a Hamiltonian that changes with time. Next we examine the performance of the adiabatic quantum search algorithm with a particular model for the environment. We relate our results to the criteria discussed in the literature for the validity of the above-mentioned method for similar environments.Comment: 6 pages, 1 figur

Eigenstate Thermalization Hypothesis and Quantum Jarzynski Relation for Pure Initial States

Since the first suggestion of the Jarzynski equality many derivations of this equality have been presented in both, the classical and the quantum context. While the approaches and settings greatly differ from one to another, they all appear to rely on the initial state being a thermal Gibbs state. Here, we present an investigation of work distributions in driven isolated quantum systems, starting off from pure states that are close to energy eigenstates of the initial Hamiltonian. We find that, for the nonintegrable system in quest, the Jarzynski equality is fulfilled to good accuracy.Comment: 9 pages, 7 figure

Equilibration of quantum systems and subsystems

We unify two recent results concerning equilibration in quantum theory. We first generalise a proof of Reimann [PRL 101,190403 (2008)], that the expectation value of 'realistic' quantum observables will equilibrate under very general conditions, and discuss its implications for the equilibration of quantum systems. We then use this to re-derive an independent result of Linden et. al. [PRE 79, 061103 (2009)], showing that small subsystems generically evolve to an approximately static equilibrium state. Finally, we consider subspaces in which all initial states effectively equilibrate to the same state.Comment: 5 page

Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics

We solve the Schroedinger equation for an interacting spin-chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin-chain as well as of single spins is analyzed. We show, that the total spin-chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but non-thermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of $0.1 \times \Delta E$, with $\Delta E$ denoting the Zeeman-splitting. We compare these results with a master equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.Comment: RevTeX, 8 pages, 14 figures, added DOI and forgotten reference

Quantum discord and local demons

Quantum discord was proposed as a measure of the "quantumness" of correlations. There are at least three different discord-like quantities, two of which determine the difference between the efficiencies of a Szilard's engine under different sets of restrictions. The three discord measures vanish simulataneosly. We introduce an easy way to test for zero discord, relate it to the Cerf-Adami conditional entropy and show that there is no relation between the discord and the local disitnguishability.Comment: 7 pages, RevTeX. Some minor changes after comments from colleagues, some references added. Similar to published versio