10 research outputs found
A Pair Hamiltonian Model of a Non-ideal Boson Gas
The pressure in the thermodynamic limit of a non-ideal Boson gas whose Hamiltonian includes only diagonal and pairing terms can be expressed as the infimum of a functional depending on two measures on momentum space: a positive measure describing the particle density and a complex measure describing the pair density. In this paper we examine this variational problem with the object of determining when the model exhibits Bose-Einstein condensation. In addition we show that if the pairing term in the Hamiltonian is positive then it has no effect
The Large Deviation Principle for the Kac Distribution
We prove that the Large Deviation Principle holds for the distribution of the particle number density (the Kac distribution) whenever the free energy density exists in the thermodynamic limit. We use this result to give a new proof of the Large Deviation Principle for the Kac distribution of the free Boson gas. In the case of mean-field models, non-convex rate functions can arise; this is illustrated in a model previously studied by E.B. Davies
A Dicke Type Model for Equilibrium BEC Superradiance
We study the effect of electromagnetic radiation on the condensate of a Bose
gas. In an earlier paper we considered the problem for two simple models
showing the cooperative effect between Bose-Einstein condensation and
superradiance. In this paper we formalise the model suggested by Ketterle et al
in which the Bose condensate particles have a two level structure. We present a
soluble microscopic Dicke type model describing a thermodynamically stable
system. We find the equilibrium states of the system and compute the
thermodynamic functions giving explicit formulae expressing the cooperative
effect between Bose-Einstein condensation and superradiance
The Canonical Perfect Bose Gas in Casimir Boxes
We study the problem of Bose-Einstein condensation in the perfect Bose gas in
the canonical ensemble, in anisotropically dilated rectangular parallelpipeds
(Casimir boxes). We prove that in the canonical ensemble for these anisotropic
boxes there is the same type of generalized Bose-Einstein condensation as in
the grand-canonical ensemble for the equivalent geometry. However the amount of
condensate in the individual states is different in some cases and so are the
fluctuations.Comment: 23 page
Correlation inequalities for noninteracting Bose gases
For a noninteracting Bose gas with a fixed one-body Hamiltonian H^0
independent of the number of particles we derive the inequalities _N <
_{N+1}, _N _N _N for i\neq j, \partial
_N/\partial \beta >0 and ^+_N _N. Here N_i is the occupation
number of the ith eigenstate of H^0, \beta is the inverse temperature and the
superscript + refers to adding an extra level to those of H^0. The results
follow from the convexity of the N-particle free energy as a function of N.Comment: a further inequality adde
On the nature of Bose-Einstein condensation in disordered systems
We study the perfect Bose gas in random external potentials and show that
there is generalized Bose-Einstein condensation in the random eigenstates if
and only if the same occurs in the one-particle kinetic-energy eigenstates,
which corresponds to the generalized condensation of the free Bose gas.
Moreover, we prove that the amounts of both condensate densities are equal. Our
method is based on the derivation of an explicit formula for the occupation
measure in the one-body kinetic-energy eigenstates which describes the
repartition of particles among these non-random states. This technique can be
adapted to re-examine the properties of the perfect Bose gas in the presence of
weak (scaled) non-random potentials, for which we establish similar results