734 research outputs found

### Entanglement Entropy and Mutual Information in Bose-Einstein Condensates

In this paper we study the entanglement properties of free {\em
non-relativistic} Bose gases. At zero temperature, we calculate the bipartite
block entanglement entropy of the system, and find it diverges logarithmically
with the particle number in the subsystem. For finite temperatures, we study
the mutual information between the two blocks. We first analytically study an
infinite-range hopping model, then numerically study a set of long-range
hopping models in one-deimension that exhibit Bose-Einstein condensation. In
both cases we find that a Bose-Einstein condensate, if present, makes a
divergent contribution to the mutual information which is proportional to the
logarithm of the number of particles in the condensate in the subsystem. The
prefactor of the logarithmic divergent term is model dependent.Comment: 12 pages, 6 figure

### Description of thermal entanglement with the static path plus random-phase approximation

We discuss the application of the static path plus random phase approximation
(SPA+RPA) and the ensuing mean field+RPA treatment to the evaluation of
entanglement in composite quantum systems at finite temperature. These methods
involve just local diagonalizations and the determination of the generalized
collective vibrational frequencies. As illustration, we evaluate the pairwise
entanglement in a fully connected XXZ chain of $n$ spins at finite temperature
in a transverse magnetic field $b$. It is shown that already the mean field+RPA
provides an accurate analytic description of the concurrence below the mean
field critical region ($|b|<b_c$), exact for large $n$, whereas the full
SPA+RPA is able to improve results for finite systems in the critical region.
It is proved as well that for $T>0$ weak entanglement also arises when the
ground state is separable ($|b|>b_c$), with the limit temperature for pairwise
entanglement exhibiting quite distinct regimes for $|b|b_c$.Comment: 20 pages, 5 figure

### Thermal entanglement in fully connected spin systems and its RPA description

We examine the thermal pairwise entanglement in a symmetric system of $n$
spins fully connected through anisotropic $XYZ$-type couplings embedded in a
transverse magnetic field. We consider both the exact evaluation together with
that obtained with the static path + random phase approximation (RPA) and the
ensuing mean field + RPA. The latter is shown to provide an accurate analytic
description of both the parallel and antiparallel thermal concurrence in large
systems. We also analyze the limit temperature for pairwise entanglement, which
is shown to increase for large fields and to decrease logarithmically with
increasing $n$. Special finite size effects are as well discussed.Comment: 9 pages, 5 figure

### Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

The gauge invariant electromagnetic Wigner equation is taken as the basis for
a fluid-like system describing quantum plasmas, derived from the moments of the
gauge invariant Wigner function. The use of the standard, gauge dependent
Wigner function is shown to produce inconsistencies, if a direct correspondence
principle is applied. The propagation of linear transverse waves is considered
and shown to be in agreement with the kinetic theory in the long wavelength
approximation, provided an adequate closure is chosen for the macroscopic
equations. A general recipe to solve the closure problem is suggested.Comment: 12 pages, 1 figur

### Spatial Pattern Formation in External Noise: Theory and Simulation

Spatial pattern formation in excitable fluctuating media was researched
analytically from the point of view of the order parameters concept. The
reaction-diffusion system in external noise is considered as a model of such
medium. Stochastic equations for the unstable mode amplitudes (order
parameters), dispersion equations for the unstable mode averaged amplitudes,
and the Fokker-Planck equation for the order parameters have been obtained. The
developed theory makes it possible to analyze different noise-induced effects,
including the variation of boundaries of ordering and disordering phase
transitions depending on the parameters of external noiseComment: 22 pages, 10 figure

### Renormalized effective actions for the O(N) model at next-to-leading order of the 1/N expansion

A fully explicit renormalized quantum action functional is constructed for
the O(N)-model in the auxiliary field formulation at next-to-leading order
(NLO) of the 1/N expansion. Counterterms are consistently and explicitly
derived for arbitrary constant vacuum expectation value of the scalar and
auxiliary fields. The renormalized NLO pion propagator is exact at this order
and satisfies Goldstone's theorem. Elimination of the auxiliary field sector at
the level of the functional provides with order N^0 accuracy the renormalized
effective action of the model in terms of the original variables. Alternative
elimination of the pion and sigma propagators provides the renormalized NLO
effective potential for the expectation values of the N-vector and of the
auxiliary field with the same accuracy.Comment: RevTeX4, 19 pages, 3 figures. Version published Phys. Rev.

### Pressure inequalities for nuclear and neutron matter

We prove several inequalities using lowest-order effective field theory for
nucleons which give an upper bound on the pressure of asymmetric nuclear matter
and neutron matter. We prove two types of inequalities, one based on convexity
and another derived from shifting an auxiliary field.Comment: 16 pages, published journal version - includes inequalities for spin
polarized system

### Quantum canonical transformations in Weyl-Wigner-Groenewold-Moyal formalism

A conjecture in quantum mechanics states that any quantum canonical
transformation can decompose into a sequence of three basic canonical
transformations; gauge, point and interchange of coordinates and momenta. It is
shown that if one attempts to construct the three basic transformations in
star-product form, while gauge and point transformations are immediate in
star-exponential form, interchange has no correspondent, but it is possible in
an ordinary exponential form. As an alternative approach, it is shown that all
three basic transformations can be constructed in the ordinary exponential form
and that in some cases this approach provides more useful tools than the
star-exponential form in finding the generating function for given canonical
transformation or vice versa. It is also shown that transforms of c-number
phase space functions under linear-nonlinear canonical transformations and
intertwining method can be treated within this argument.Comment: 15 pages, no figures. Accepted for publication in Int. J. Mod. Phys.

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