3,930 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
Quantum trajectories of interacting pseudo-spin-networks
We consider quantum trajectories of composite systems as generated by the
stochastic unraveling of the respective Lindblad-master-equation. Their
classical limit is taken to correspond to local jumps between orthogonal
states. Based on statistical distributions of jump- and inter-jump-distances we
are able to quantify the non-classicality of quantum trajectories. To account
for the operational effect of entanglement we introduce the novel concept of
"co-jumps".Comment: 15 pages, 12 figure
Quantum network architecture of tight-binding models with substitution sequences
We study a two-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. Substitution sequences are known to underlie aperiodic
structures. We show that parameter inputs \alpha_m described by such sequences
can lead here to a quantum dynamics, intermediate between the regular and the
chaotic variant. Exponential parameter sensitivity characterizing chaotic
quantum Turing machines turns out to be an adequate criterion for induced
quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop
"Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure
Gaussian quantum fluctuations in interacting many particle systems
We consider a many particle quantum system, in which each particle interacts
only with its nearest neighbours. Provided that the energy per particle has an
upper bound, we show, that the energy distribution of almost every product
state becomes a Gaussian normal distribution in the limit of infinite number of
particles. We indicate some possible applications.Comment: 10 pages, formulation made mathematically more precise, two examples
added, accepted for publication in Letters in Mathematical Physic
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
Quantum-state tomography for spin-l systems
We show that the density matrix of a spin-l system can be described entirely
in terms of the measurement statistics of projective spin measurements along a
minimum of 4l+1 different spin directions. It is thus possible to represent the
complete quantum statistics of any N-level system within the spherically
symmetric three dimensional space defined by the spin vector. An explicit
method for reconstructing the density matrix of a spin-1 system from the
measurement statistics of five non-orthogonal spin directions is presented and
the generalization to spin-l systems is discussed.Comment: 10 pages, including 2 tables, minor modifications in section II,
final version for publication in Phys. Rev.
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