819 research outputs found
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
Failure of Effective Potential Approach: Nucleus-Electron Entanglement in the He-Ion
Entanglement may be considered a resource for quantum-information processing,
as the origin of robust and universal equilibrium behaviour, but also as a
limit to the validity of an effective potential approach, in which the
influence of certain interacting subsystems is treated as a potential. Here we
show that a closed three particle (two protons, one electron) model of a He-ion
featuring realistic size, interactions and energy scales of electron and
nucleus, respectively, exhibits different types of dynamics depending on the
initial state: For some cases the traditional approach, in which the nucleus
only appears as the center of a Coulomb potential, is valid, in others this
approach fails due to entanglement arising on a short time-scale. Eventually
the system can even show signatures of thermodynamical behaviour, i.e. the
electron may relax to a maximum local entropy state which is, to some extent,
independent of the details of the initial state.Comment: Submitted to Europhysics Letter
Distribution of local entropy in the Hilbert space of bi-partite quantum systems: Origin of Jaynes' principle
For a closed bi-partite quantum system partitioned into system proper and
environment we interprete the microcanonical and the canonical condition as
constraints for the interaction between those two subsystems. In both cases the
possible pure-state trajectories are confined to certain regions in Hilbert
space. We show that in a properly defined thermodynamical limit almost all
states within those accessible regions represent states of some maximum local
entropy. For the microcanonical condition this dominant state still depends on
the initial state; for the canonical condition it coincides with that defined
by Jaynes' principle. It is these states which thermodynamical systems should
generically evolve into.Comment: Submitted to Physical Review
Necessity of eigenstate thermalization for equilibration towards unique expectation values when starting from generic initial states
We investigate dynamical equilibration of expectation values in closed
quantum systems for realistic non-equilibrium initial states. Thereby we find
that the corresponding long time expectation values depend on the initial
expectation values if eigenstate thermalization is violated. An analytical
expression for the deviation from the expected ensemble value is derived for
small displacements from equilibrium. Additional numerics for magnetization and
energy equilibration in an asymmetric anisotropic spin-1/2-ladder demonstrate
that the analytical predictions persist beyond the limits of the theory. The
results suggest eigenstate thermalization as physically necessary condition for
initial state independent equilibration.Comment: 5 pages, 4 figure
Boltzmann equation approach to transport in finite modular quantum systems
We investigate the transport behavior of finite modular quantum systems. Such
systems have recently been analyzed by different methods. These approaches
indicate diffusive behavior even and especially for finite systems. Inspired by
these results we analyze analytically and numerically if and in which sense the
dynamics of those systems are in agreement with an appropriate Boltzmann
equation. We find that the transport behavior of a certain type of finite
modular quantum systems may indeed be described in terms of a Boltzmann
equation. However, the applicability of the Boltzmann equation appears to be
rather limited to a very specific type of model
Entanglement and the factorization-approximation
For a bi-partite quantum system defined in a finite dimensional Hilbert space
we investigate in what sense entanglement change and interactions imply each
other. For this purpose we introduce an entanglement operator, which is then
shown to represent a non-conserved property for any bi-partite system and any
type of interaction. This general relation does not exclude the existence of
special initial product states, for which the entanglement remains small over
some period of time, despite interactions. For this case we derive an
approximation to the full Schroedinger equation, which allows the treatment of
the composite systems in terms of product states. The induced error is
estimated. In this factorization-approximation one subsystem appears as an
effective potential for the other. A pertinent example is the Jaynes-Cummings
model, which then reduces to the semi-classical rotating wave approximation.Comment: Accepted for publication in European Physical Journal
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