3,068 research outputs found
Modified semiclassical approximation for trapped Bose gases
A generalization of the semiclassical approximation is suggested allowing for
an essential extension of its region of applicability. In particular, it
becomes possible to describe Bose-Einstein condensation of a trapped gas in
low-dimensional traps and in traps of low confining dimensions, for which the
standard semiclassical approximation is not applicable. The results of the
modified approach are shown to coincide with purely quantum-mechanical
calculations for harmonic traps, including the one-dimensional harmonic trap.
The advantage of the semiclassical approximation is in its simplicity and
generality. Power-law potentials of arbitrary powers are considered. Effective
thermodynamic limit is defined for any confining dimension. The behaviour of
the specific heat, isothermal compressibility, and density fluctuations is
analyzed, with an emphasis on low confining dimensions, where the usual
semiclassical method fails. The peculiarities of the thermodynamic
characteristics in the effective thermodynamic limit are discussed.Comment: Revtex file, 13 page
Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros
We present a detailed description of a classification scheme for phase
transitions in finite systems based on the distribution of Fisher zeros of the
canonical partition function in the complex temperature plane. We apply this
scheme to finite Bose-systems in power law traps within a semi-analytic
approach with a continuous one-particle density of states for different values of and to a three dimensional harmonically
confined ideal Bose-gas with discrete energy levels. Our results indicate that
the order of the Bose-Einstein condensation phase transition sensitively
depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small
systems see "http://www.smallsystems.de
Convective intensification of magnetic fields in the quiet Sun
Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B_e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B_p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, “granular” motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B_e, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than B_p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of “convective collapse” within a thin flux tube that remains in overall pressure equilibrium with its surroundings
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