5,780 research outputs found
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
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
Relaxation into equilibrium under pure Schr\"odinger dynamics
We consider bipartite quantum systems that are described completely by a
state vector and the fully deterministic Schr\"odinger equation.
Under weak constraints and without any artificially introduced decoherence or
irreversibility, the smaller of the two subsystems shows thermodynamic
behaviour like relaxation into an equilibrium, maximization of entropy and the
emergence of the Boltzmann energy distribution. This generic behaviour results
from entanglement.Comment: 5 pages, 9 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
-level subsystems, where is finite. Forming groups of subsystems
each, we show that the strength of interaction between the groups scales with
. As a consequence, if the total system is in a thermal state with
inverse temperature , a sufficient condition for subgroups of size
to be approximately in a thermal state with the same temperature is , where 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
Model Studies on the Quantum Jarzynski Relation
We study the quantum Jarzynski relation for driven quantum models embedded in
various environments. We do so by generalizing a proof presented by Mukamel
[Phys. Rev. Lett 90, 170604 (2003)] for closed quantum systems. In this way, we
are able to prove that the Jarzynski relation also holds for a bipartite system
with microcanonical coupling. Furthermore, we show that, under the assumption
that the interaction energy remains constant during the whole process, the
relation is valid even for canonical coupling. The same follows for open
quantum systems at high initial temperatures up to third order of the inverse
temperature. Our analytical study is complemented by a numerical investigation
of a special model system.Comment: 7 figure
Non Thermal Equilibrium States of Closed Bipartite Systems
We investigate a two-level system in resonant contact with a larger
environment. The environment typically is in a canonical state with a given
temperature initially. Depending on the precise spectral structure of the
environment and the type of coupling between both systems, the smaller part may
relax to a canonical state with the same temperature as the environment (i.e.
thermal relaxation) or to some other quasi equilibrium state (non thermal
relaxation). The type of the (quasi) equilibrium state can be related to the
distribution of certain properties of the energy eigenvectors of the total
system. We examine these distributions for several abstract and concrete (spin
environment) Hamiltonian systems, the significant aspect of these distributions
can be related to the relative strength of local and interaction parts of the
Hamiltonian.Comment: RevTeX, 8 pages, 13 figure
Local effective dynamics of quantum systems: A generalized approach to work and heat
By computing the local energy expectation values with respect to some local
measurement basis we show that for any quantum system there are two
fundamentally different contributions: changes in energy that do not alter the
local von Neumann entropy and changes that do. We identify the former as work
and the latter as heat. Since our derivation makes no assumptions on the system
Hamiltonian or its state, the result is valid even for states arbitrarily far
from equilibrium. Examples are discussed ranging from the classical limit to
purely quantum mechanical scenarios, i.e. where the Hamiltonian and the density
operator do not commute.Comment: 5 pages, 1 figure, published versio
On conjectures and problems of Ruzsa concerning difference graphs of S-units
Given a finite nonempty set of primes S, we build a graph with
vertex set by connecting x and y if the prime divisors of both the
numerator and denominator of x-y are from S. In this paper we resolve two
conjectures posed by Ruzsa concerning the possible sizes of induced
nondegenerate cycles of , and also a problem of Ruzsa concerning
the existence of subgraphs of which are not induced subgraphs.Comment: 15 page
Cavity-induced temperature control of a two-level system
We consider a two-level atom interacting with a single mode of the
electromagnetic field in a cavity within the Jaynes-Cummings model. Initially,
the atom is thermal while the cavity is in a coherent state. The atom interacts
with the cavity field for a fixed time. After removing the atom from the cavity
and applying a laser pulse the atom will be in a thermal state again. Depending
on the interaction time with the cavity field the final temperature can be
varied over a large range. We discuss how this method can be used to cool the
internal degrees of freedom of atoms and create heat baths suitable for
studying thermodynamics at the nanoscale
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