Related papers: Equilibration properties of small quantum systems:…
Investigation on foundational aspects of quantum statistical mechanics recently entered a renaissance period due to novel intuitions from quantum information theory and to increasing attention on the dynamical aspects of single quantum…
Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review…
Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic…
It has recently been shown that small quantum subsystems generically equilibrate, in the sense that they spend most of the time close to a fixed equilibrium state. This relies on just two assumptions: that the state is spread over many…
Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found…
The environment of an open quantum system is usually modelled as a large many-body quantum system. However, when an isolated quantum system itself is a many-body quantum system, the question of how large and complex it must be in order to…
Using the tools of random matrix theory we develop a statistical analysis of the transport properties of thermoelectric low-dimensional systems made of two electron reservoirs set at different temperatures and chemical potentials, and…
We study the equilibration dynamics of closed finite quantum systems and address the question of the time needed for the system to equilibrate. In particular we focus on the scaling of the equilibration time T_{\mathrm{eq}} with the system…
It has been recently shown that small subsystems of finite quantum systems generically equilibrate. We extend these results to infinite-dimensional Hilbert spaces of field theories and matrix models. We consider a quench setup, where…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
The effects of the measurement apparatus on quantum coherence are studied by considering a purely dephasing model of a qubit. The initial state is prepared from a thermal state of the whole system by performing a nonselective measurement on…
We consider quantum systems with a Hamiltonian containing a weak perturbation i.e. $\boldsymbol{H=H_0} + \boldsymbol{\lambda} \cdot \boldsymbol{\tilde{H}}$, $\boldsymbol{\lambda}= \{\lambda_1, \lambda_2,...\}$, $\boldsymbol{\tilde{H}}$ $=…
The evolution of a quasi-isolated finite quantum system from a nonequilibrium initial state is considered. The condition of quasi-isolation allows for the description of the system dynamics on the general basis, without specifying the…
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…
When a closed quantum system is driven periodically with period $T$, it approaches a periodic state synchronized with the drive in which any local observable measured stroboscopically approaches a steady value. For integrable systems, the…
In this work we investigate the equilibration dynamics after a sudden Hamiltonian quench of a quantum spin system initially prepared in a thermal state. To characterize the equilibration we evaluate the Loschmidt echo, a global measure for…
We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the…