2,214 research outputs found
Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions
Several authors have considered the possibility of a generalized
Bose-Einstein condensation (BEC) in which a band of low states is occupied so
that the total occupation number is macroscopic, even if the occupation number
of each state is not extensive. The Hohenberg theorem (HT) states that there is
no BEC into a single state in 2D; we consider its validity for the case of a
generalized condensation and find that, under certain conditions, the HT does
not forbid a BEC in 2D. We discuss whether this situation actually occurs in
any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys.,
Quantum Fluids and Solids Conference QFS200
Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles
The purpose of this article is to discuss cluster expansions in dense quantum
systems as well as their interconnection with exchange cycles. We show in
general how the Ursell operators of order 3 or more contribute to an
exponential which corresponds to a mean-field energy involving the second
operator U2, instead of the potential itself as usual. In a first part, we
consider classical statistical mechanics and recall the relation between the
reducible part of the classical cluster integrals and the mean-field; we
introduce an alternative method to obtain the linear density contribution to
the mean-field, which is based on the notion of tree-diagrams and provides a
preview of the subsequent quantum calculations. We then proceed to study
quantum particles with Boltzmann statistics (distinguishable particles) and
show that each Ursell operator Un with n greater or equal to 3 contains a
``tree-reducible part'', which groups naturally with U2 through a linear chain
of binary interactions; this part contributes to the associated mean-field
experienced by particles in the fluid. The irreducible part, on the other hand,
corresponds to the effects associated with three (or more) particles
interacting all together at the same time. We then show that the same algebra
holds in the case of Fermi or Bose particles, and discuss physically the role
of the exchange cycles, combined with interactions. Bose condensed systems are
not considered at this stage. The similarities and differences between
Boltzmann and quantum statistics are illustrated by this approach, in contrast
with field theoretical or Green's functions methods, which do not allow a
separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure
A multi-paradigm language for reactive synthesis
This paper proposes a language for describing reactive synthesis problems
that integrates imperative and declarative elements. The semantics is defined
in terms of two-player turn-based infinite games with full information.
Currently, synthesis tools accept linear temporal logic (LTL) as input, but
this description is less structured and does not facilitate the expression of
sequential constraints. This motivates the use of a structured programming
language to specify synthesis problems. Transition systems and guarded commands
serve as imperative constructs, expressed in a syntax based on that of the
modeling language Promela. The syntax allows defining which player controls
data and control flow, and separating a program into assumptions and
guarantees. These notions are necessary for input to game solvers. The
integration of imperative and declarative paradigms allows using the paradigm
that is most appropriate for expressing each requirement. The declarative part
is expressed in the LTL fragment of generalized reactivity(1), which admits
efficient synthesis algorithms, extended with past LTL. The implementation
translates Promela to input for the Slugs synthesizer and is written in Python.
The AMBA AHB bus case study is revisited and synthesized efficiently,
identifying the need to reorder binary decision diagrams during strategy
construction, in order to prevent the exponential blowup observed in previous
work.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
Shaping an ultracold atomic soliton in a travelling wave laser beam
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave
may form a many-atom soliton.This is disturbed by a homogeneous force field,
for example by the inevitable gravitation. The wave packet is accelerated and
therefore the laser frequency appears to be chirped in the rest frame of the
atoms. We derive the effective nonlinear Schr\"odinger equation. It shows a
time dependent nonlinearity coefficient which amounts to a damping or
antidamping, respectively. The accelerated packet solution remains a soliton
which changes its shape adiabatically. Similarly, an active shaping can be
obtained in the force-free case by chirping the laser frequency thus
representing a way of coherent control of the soliton form. The experimental
consequences are discussed.Comment: 5 pages, Latex, to published in Europhys. Let
Concept of Formation Length in Radiation Theory
The features of electromagnetic processes are considered which connected with
finite size of space region in which final particles (photon, electron-positron
pair) are formed. The longitudinal dimension of the region is known as the
formation length. If some external agent is acting on an electron while
traveling this distance the emission process can be disrupted. There are
different agents: multiple scattering of projectile, polarization of a medium,
action of external fields, etc. The theory of radiation under influence of the
multiple scattering, the Landau-Pomeranchuk-Migdal (LPM) effect, is presented.
The probability of radiation is calculated with an accuracy up to "next to
leading logarithm" and with the Coulomb corrections taken into account. The
integral characteristics of bremsstrahlung are given, it is shown that the
effective radiation length increases due to the LPM effect at high energy. The
LPM effect for pair creation is also presented. The multiple scattering
influences also on radiative corrections in a medium (and an external field
too) including the anomalous magnetic moment of an electron and the
polarization tensor as well as coherent scattering of a photon in a Coulomb
field. The polarization of a medium alters the radiation probability in soft
part of spectrum. Specific features of radiation from a target of finite
thickness include: the boundary photon emission, interference effects for thin
target, multi-photon radiation. The experimental study of LPM effect is
described. For electron-positron colliding beams following items are discussed:
the separation of coherent and incoherent mechanisms of radiation, the
beam-size effect in bremsstrahlung, coherent radiation and mechanisms of
electron-positron creation.Comment: Revised review paper, 96 pages, 28 figures. Description of SLAC E-146
experiment removed, discussion of CERN SPS experiment adde
Transition temperature of a dilute homogeneous imperfect Bose gas
The leading-order effect of interactions on a homogeneous Bose gas is
theoretically predicted to shift the critical temperature by an amount
\Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where
a_{scatt} is the scattering length and n is the density. There have been
several different theoretical estimates for the numerical coefficient #. We
claim to settle the issue by measuring the numerical coefficient in a lattice
simulation of O(2) phi^4 field theory in three dimensions---an effective theory
which, as observed previously in the literature, can be systematically matched
to the dilute Bose gas problem to reproduce non-universal quantities such as
the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to
improvement of analysis in the longer companion pape
Coupled Electron Ion Monte Carlo Calculations of Dense Metallic Hydrogen
We present a new Monte Carlo method which couples Path Integral for finite
temperature protons with Quantum Monte Carlo for ground state electrons, and we
apply it to metallic hydrogen for pressures beyond molecular dissociation. We
report data for the equation of state for temperatures across the melting of
the proton crystal. Our data exhibit more structure and higher melting
temperatures of the proton crystal than Car-Parrinello Molecular Dynamics
results. This method fills the gap between high temperature electron-proton
Path Integral and ground state Diffusion Monte Carlo methods
Instability in a Two-Dimensional Dilute Interacting Bose System
The formalism of Ursell operators provides a self-consistent integral equation for the one-particle reduced operator. In three dimensions this technique yields values of the shift in the Bose-Einstein condensation (BEC) transition temperature, as a function of the scattering length, that are in good agreement with those of Green’s function and quantum Monte Carlo methods. We have applied the same equations to a uniform two-dimensional system and find that, as we alter the chemical potential, an instability develops so that the self-consistent equations no longer have a solution. This instability, which seems to indicate that interactions restore a transition, occurs at a non-zero value of an effective chemical potential. The non-linear equations are limited to temperatures greater than or equal to Tc, so that they do not indicate the nature of the new stable state, but we speculate concerning whether it is a Kosterlitz-Thouless state or a “smeared” BEC, which might avoid any violation of the Hohenberg theorem, as described in an accompanying paper
The transition temperature of the dilute interacting Bose gas for internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and the scattering length. This
result is non-perturbative, and a direct perturbative calculation of the
amplitude is impossible due to infrared divergences familiar from the study of
the superfluid helium lambda transition. Therefore we introduce here another
standard expansion scheme, generalizing the initial model which depends on one
complex field to one depending on real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large result agrees remarkably well with
recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter
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