16 research outputs found
Proof of the Variational Principle for a Pair Hamiltonian Boson Model
We give a two parameter variational formula for the grand-canonical pressure
of the Pair Boson Hamiltonian model. By using the Approximating Hamiltonian
Method we provide a rigorous proof of this variational principle
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
On the nature of Bose-Einstein condensation enhanced by localization
In a previous paper we established that for the perfect Bose gas and the
mean-field Bose gas with an external random or weak potential, whenever there
is generalized Bose-Einstein condensation in the eigenstates of the single
particle Hamiltonian, there is also generalized condensation in the kinetic
energy states. In these cases Bose-Einstein condensation is produced or
enhanced by the external potential. In the present paper we establish a
criterion for the absence of condensation in single kinetic energy states and
prove that this criterion is satisfied for a class of random potentials and
weak potentials. This means that the condensate is spread over an infinite
number of states with low kinetic energy without any of them being
macroscopically occupied
The Approximating Hamiltonian Method for the Imperfect Boson Gas
The pressure for the Imperfect (Mean Field) Boson gas can be derived in
several ways. The aim of the present note is to provide a new method based on
the Approximating Hamiltonian argument which is extremely simple and very
general.Comment: 7 page
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
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