3,172 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
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
Elliptical orbits in the Bloch sphere
As is well known, when an SU(2) operation acts on a two-level system, its
Bloch vector rotates without change of magnitude. Considering a system composed
of two two-level systems, it is proven that for a class of nonlocal
interactions of the two subsystems including \sigma_i\otimes\sigma_j (with i,j
\in {x,y,z}) and the Heisenberg interaction, the geometric description of the
motion is particularly simple: each of the two Bloch vectors follows an
elliptical orbit within the Bloch sphere. The utility of this result is
demonstrated in two applications, the first of which bears on quantum control
via quantum interfaces. By employing nonunitary control operations, we extend
the idea of controllability to a set of points which are not necessarily
connected by unitary transformations. The second application shows how the
orbit of the coherence vector can be used to assess the entangling power of
Heisenberg exchange interaction.Comment: 9 pages, 4 figures, few corrections, J. Opt. B: Quantum Semiclass.
Opt. 7 (2005) S1-S
Effective environments: Preparation of stationary states with inverse temperature ranging from positive to negative values
In this paper, we discuss how effective environments incorporating periodic
measurements can be used to prepare a two-level system (TLS) in almost
arbitrary thermal states: Concretely, we study a TLS coupled to a spin
environment, the magnetization of which is measured periodically. In ensemble
average these measurements cause a relaxation of the TLS into a thermal
(diagonal) state. By adjusting the time between the measurements and the
detuning of the environmental spins, the creation of very low temperatures as
well as inversion becomes possible. Our analytical results derived for large
environments are numerically shown to be valid even for quite small
environments, down to only a few spins.Comment: 20 pages, 3 figures, accepted for publication in Phys. Rev.
On the concept of pressure in quantum mechanics
Heat and work are fundamental concepts for thermodynamical systems. When
these are scaled down to the quantum level they require appropriate embeddings.
Here we show that the dependence of the particle spectrum on system size giving
rise to a formal definition of pressure can, indeed, be correlated with an
external mechanical degree of freedom, modelled as a spatial coordinate of a
quantum oscillator. Under specific conditions this correlation is reminiscent
of that occurring in the classical manometer.Comment: 7 pages, 3 figure
Abrupt and gradual changes of information through the Kane solid state computer
The susceptibility of the transformed information to the filed and system
parameters is investigated for the Kane solid state computer. It has been
shown, that the field polarization and the initial state of the system play the
central roles on the abrupt and gradual quench of the purity and the fidelity.
If the field and the initial state are in different polarizations, then the
purity and the fidelity decrease abruptly, while for the common polarization
the decay is gradual and smooth. For some class of initial states one can send
the information without any loss. Therefore, by controlling on the devices one
can increase the time of safe communication, reduce the amount of exchange
information between the state and its environment and minimize the purity
decrease rate
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