46 research outputs found
Upper limit on the transition temperature for non-ideal Bose gases
In this paper we show that for a non-ideal Bose gas there exists an upper
limit on the transition temperature above which Bose-Einstein condensation
cannot occur regardless of the pressure applied. Such upper limits for some
realistic Bose gases are estimated. This result implies that there may also
exist an upper limit on the transition temperature of superconductors.Comment: 7 pages, 1 figur
Momentum flux density, kinetic energy density and their fluctuations for one-dimensional confined gases of non-interacting fermions
We present a Green's function method for the evaluation of the particle
density profile and of the higher moments of the one-body density matrix in a
mesoscopic system of N Fermi particles moving independently in a linear
potential. The usefulness of the method is illustrated by applications to a
Fermi gas confined in a harmonic potential well, for which we evaluate the
momentum flux and kinetic energy densities as well as their quantal mean-square
fluctuations. We also study some properties of the kinetic energy functional
E_{kin}[n(x)] in the same system. Whereas a local approximation to the kinetic
energy density yields a multi-valued function, an exact single-valued
relationship between the density derivative of E_{kin}[n(x)] and the particle
density n(x) is demonstrated and evaluated for various values of the number of
particles in the system.Comment: 10 pages, 5 figure
Bose-Einstein condensation under external conditions
We discuss the phenomenon of Bose-Einstein condensation under general
external conditions using connections between partition sums and the
heat-equation. Thermodynamical quantities like the critical temperature are
given in terms of the heat-kernel coefficients of the associated Schr\"odinger
equation. The general approach is applied to situations where the gas is
confined by arbitrary potentials or by boxes of arbitrary shape.Comment: 11 pages, LaTeX, to appear in Phys. Lett.
Anomalous fluctuations of the condensate in interacting Bose gases
We find that the fluctuations of the condensate in a weakly interacting Bose
gas confined in a box of volume follow the law . This anomalous behaviour arises from the occurrence of infrared
divergencies due to phonon excitations and holds also for strongly correlated
Bose superfluids. The analysis is extended to an interacting Bose gas confined
in a harmonic trap where the fluctuations are found to exhibit a similar
anomaly.Comment: 4 pages, RevTe
Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap
We present a model which predicts the temperature of Bose-Einstein
condensation in atomic alkali gases and find excellent agreement with recent
experimental observations. A system of bosons confined by a harmonic oscillator
potential is not characterized by a critical temperature in the same way as an
identical system which is not confined. We discuss the problem of Bose-Einstein
condensation in an isotropic harmonic oscillator potential analytically and
numerically for a range of parameters of relevance to the study of low
temperature gases of alkali metals.Comment: 11 pages latex with two postscript figure
Dimensionality effects in restricted bosonic and fermionic systems
The phenomenon of Bose-like condensation, the continuous change of the
dimensionality of the particle distribution as a consequence of freezing out of
one or more degrees of freedom in the low particle density limit, is
investigated theoretically in the case of closed systems of massive bosons and
fermions, described by general single-particle hamiltonians. This phenomenon is
similar for both types of particles and, for some energy spectra, exhibits
features specific to multiple-step Bose-Einstein condensation, for instance the
appearance of maxima in the specific heat.
In the case of fermions, as the particle density increases, another
phenomenon is also observed. For certain types of single particle hamiltonians,
the specific heat is approaching asymptotically a divergent behavior at zero
temperature, as the Fermi energy is converging towards any
value from an infinite discrete set of energies: . If
, for any i, the specific heat is divergent at T=0
just in infinite systems, whereas for any finite system the specific heat
approaches zero at low enough temperatures. The results are particularized for
particles trapped inside parallelepipedic boxes and harmonic potentials.
PACS numbers: 05.30.Ch, 64.90.+b, 05.30.Fk, 05.30.JpComment: 7 pages, 3 figures (included
Bose-Einstein condensation in arbitrarily shaped cavities
We discuss the phenomenon of Bose-Einstein condensation of an ideal
non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the
finite extension of the cavity on all thermodynamical quantities, especially on
the critical temperature of the system, is considered. We use two main methods
which are shown to be equivalent. The first deals with the partition function
as a sum over energy levels and uses a Mellin-Barnes integral representation to
extract an asymptotic formula. The second method converts the sum over the
energy levels to an integral with a suitable density of states factor obtained
from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review
Theory of Bose-Einstein condensation in trapped gases
The phenomenon of Bose-Einstein condensation of dilute gases in traps is
reviewed from a theoretical perspective. Mean-field theory provides a framework
to understand the main features of the condensation and the role of
interactions between particles. Various properties of these systems are
discussed, including the density profiles and the energy of the ground state
configurations, the collective oscillations and the dynamics of the expansion,
the condensate fraction and the thermodynamic functions. The thermodynamic
limit exhibits a scaling behavior in the relevant length and energy scales.
Despite the dilute nature of the gases, interactions profoundly modify the
static as well as the dynamic properties of the system; the predictions of
mean-field theory are in excellent agreement with available experimental
results. Effects of superfluidity including the existence of quantized vortices
and the reduction of the moment of inertia are discussed, as well as the
consequences of coherence such as the Josephson effect and interference
phenomena. The review also assesses the accuracy and limitations of the
mean-field approach.Comment: revtex, 69 pages, 38 eps figures, new version with more references,
new figures, various changes and corrections, for publ. in Rev. Mod. Phys.,
available also at http://www-phys.science.unitn.it/bec/BEC.htm