arXiv subjects

T. Haugset

Publications and source records attributed to T. Haugset.

6 recordsLinked to original sources

arXiv1997

Exact Diagonalization of the Hamiltonian for Trapped Interacting Bosons

We consider systems of a small number of interacting bosons confined to harmonic potentials in one and two dimensions. By exact numerical diagonalization of the many-body Hamiltonian we determine the low lying excitation energies and the ground state energy and density profile. We discuss the dependence of these quantities on both interaction strength g and particle number N. The ground state properties are compared to the predictions of the Gross-Pitaevskii equation, which depends on these parameters only through the combination Ng. We also calculate the specific heat based on the obtained energy spectra.

cond-mat.stat-mech↗

arXiv1997

Thermodynamics of a weakly interacting Bose-Einstein gas

The one-loop effective potential for non-relativistic bosons with a delta function repulsive potential is calculated for a given chemical potential using functional methods. After renormalization and at zero temperature it reproduces the standard ground state energy and pressureas function of the particle density. At finite temperatures it is found necessary to include ring corrections to the one-loop result in order to satisfy the Goldstone theorem. It is natural to introduce an effective chemical potential directly related to the order parameter and which uniformly decreases with increasing temperatures. This is in contrast to the the ordinary chemical potential which peaks at the critical temperature. The resulting thermodynamics in the condensed phase at very low temperatures is found to be the same as in the Bogoliubov approximation where the degrees of freedom are given by the Goldstone bosons. At higher temperatures the ring corrections dominate and result in a critical temperature unaffected by the interaction.

cond-mat.stat-mech↗

arXiv1996

Bose-Einstein Condensation in Anisotropic Harmonic Traps

We study the thermodynamic behaviour of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and for one-dimensional systems we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.

cond-mat↗

arXiv1996

A more accurate analysis of Bose-Einstein condensation in harmonic traps

Using the Euler-Maclaurin summation we calculate analytically the internal energy for non-interacting bosons confined within a harmonic oscillator potential. The specific heat shows a sharp $λ$-like peak indicating a condensation into the ground state at a well-defined transition temperature. Full agreement is obtained with direct numerical calculation of the same quantities. When the number of trapped particles is very large and at temperatures near and above the transition temperature, the results also agree with previous approximate calculations. At extremely low temperatures both the specific heat and the number of particles excited from the condensate are exponentially suppressed.

cond-mat↗

arXiv1994

Ideal quantum gases in two dimensions

Thermodynamic properties of non-relativistic bosons and fermions in two spatial dimensions and without interactions are derived. All the virial coefficients are the same except for the second, for which the signs are opposite. This results in the same specific heat for the two gases. Existing equations of state for the free anyon gas are also discussed and shown to break down at low temperatures or high densities.

hep-th↗

arXiv1993

Scale anomalies in non-relativistic field theories in 2+1 dimensions

{}From the one-loop effective potential for a gas of non-relativistic bosons in two spatial dimensions interacting via a delta-function potential at zero-temperature and finite chemical potential, the anomaly of the energy-momentum tensor follows directly. It is also similarly derived when the bosons have an additional Chern-Simons interaction. In the special case of anyons, the scale anomaly vanishes to one-loop order in the effective potential and also to second order in the statistical angle.

hep-th↗