684 research outputs found

### Equivalence of Bose-Einstein condensation and symmetry breaking

Based on a classic paper by Ginibre [Commun. Math. Phys. {\bf 8} 26 (1968)]
it is shown that whenever Bogoliubov's approximation, that is, the replacement
of a_0 and a_0^* by complex numbers in the Hamiltonian, asymptotically yields
the right pressure, it also implies the asymptotic equality of ||^2/V and
/V in symmetry breaking fields, irrespective of the existence or
absence of Bose-Einstein condensation. Because the former was proved by Ginibre
to hold for absolutely integrable superstable pair interactions, the latter is
equally valid in this case. Apart from Ginibre's work, our proof uses only a
simple convexity inequality due to Griffiths.Comment: An error in my summary of previous results (the definition of F') is
corrected. The correction is to be done also in the PR

### A rigorous approach to the magnetic response in disordered systems

This paper is a part of an ongoing study on the diamagnetic behavior of a
3-dimensional quantum gas of non-interacting charged particles subjected to an
external uniform magnetic field together with a random electric potential. We
prove the existence of an almost-sure non-random thermodynamic limit for the
grand-canonical pressure, magnetization and zero- field orbital magnetic
susceptibility. We also give an explicit formulation of these thermodynamic
limits. Our results cover a wide class of physically relevant random potentials
which model not only crystalline disordered solids, but also amorphous solids.Comment: 35 pages. Revised version. Accepted for publication in RM

### Dynamics of fast pattern formation in porous silicon by laser interference

Patterns are fabricated on 290 nm thick nanostructured porous silicon layers by phase-mask laser interference using single pulses of an excimer laser (193 nm, 20 ns pulse duration). The dynamics of pattern formation is studied by measuring in real time the intensity of the diffraction orders 0 and 1 at 633 nm. The results show that a transient pattern is formed upon melting at intensity maxima sites within a time 1-Âµs) upon melting induced by homogeneous beam exposure and related to the different scenario for releasing the heat from hot regions. The diffraction efficiency of the pattern is finally controlled by a combination of laser fluence and initial thickness of the nanostructured porous silicon layer and the present results open perspectives on heat release management upon laser exposure as well as have potential for alternative routes for switching applications.Postprint (published version

### On Long-Range Order in Low-Dimensional Lattice-Gas Models of Nematic Liquid Crystals

The problem of the orientational ordering transition for lattice-gas models
of liquid crystals is discussed in the low-dimensional case $d=1,2$. For
isotropic short-range interactions, orientational long-range order at finite
temperature is excluded for any packing of molecules on the lattice $Z^d$; on
the other hand, for reflection-positive long-range isotropic interactions, we
prove existence of an orientational ordering transition for high packing ($\mu
> \mu_0$) and low temperatures ($\beta > \beta_c(\mu)$).Comment: 11 page

### Absence of Embedded Mass Shells: Cerenkov Radiation and Quantum Friction

We show that, in a model where a non-relativistic particle is coupled to a
quantized relativistic scalar Bose field, the embedded mass shell of the
particle dissolves in the continuum when the interaction is turned on, provided
the coupling constant is sufficiently small. More precisely, under the
assumption that the fiber eigenvectors corresponding to the putative mass shell
are differentiable as functions of the total momentum of the system, we show
that a mass shell could exist only at a strictly positive distance from the
unperturbed embedded mass shell near the boundary of the energy-momentum
spectrum.Comment: Revised version: a remark added at the end of Section

### Large Deviations in the Superstable Weakly Imperfect Bose Gas

The superstable Weakly Imperfect Bose Gas {(WIBG)} was originally derived to
solve the inconsistency of the Bogoliubov theory of superfluidity. Its
grand-canonical thermodynamics was recently solved but not at {point of} the
{(first order)} phase transition. This paper proposes to close this gap by
using the large deviations formalism and in particular the analysis of the Kac
distribution function. It turns out that, as a function of the chemical
potential, the discontinuity of the Bose condensate density at the phase
transition {point} disappears as a function of the particle density. Indeed,
the Bose condensate continuously starts at the first critical particle density
and progressively grows but the free-energy per particle stays constant until
the second critical density is reached. At higher particle densities, the Bose
condensate density as well as the free-energy per particle both increase
{monotonously}

### A Droplet within the Spherical Model

Various substances in the liquid state tend to form droplets. In this paper
the shape of such droplets is investigated within the spherical model of a
lattice gas. We show that in this case the droplet boundary is always
diffusive, as opposed to sharp, and find the corresponding density profiles
(droplet shapes). Translation-invariant versions of the spherical model do not
fix the spatial location of the droplet, hence lead to mixed phases. To obtain
pure macroscopic states (which describe localized droplets) we use generalized
quasi-averaging. Conventional quasi-averaging deforms droplets and, hence, can
not be used for this purpose. On the contrary, application of the generalized
method of quasi-averages yields droplet shapes which do not depend on the
magnitude of the applied external field.Comment: 22 pages, 2 figure

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