Shyamal Biswas

More accurate theory for Bose-Einstein condensation fraction

Abstract Bose–Einstein statistics is derived in the thermodynamic limit when the ratio of system size to thermal de Broglie wavelength goes to infinity. However, according to the experimental setup of Bose–Einstein condensation of harmonically trapped Bose gas of alkali atoms, the ratio near the condensation temperature ( T o ) is 30–50. And, at ultralow temperatures well below T o , this ratio becomes comparable to 1. We argue that finite size as well as the ultralow temperature induces corrections to Bose–Einstein statistics. From the corrected statistics we plot condensation fraction versus temperature graph. This theoretical plot satisfies well with the experimental plot [A. Griesmaier et al., Phys. Rev. Lett. 94 (2005) 160401].

Bose-Einstein condensation and the Casimir effect for an ideal bose gas confined between two slabs

We study the Casimir effect for a 3D system of ideal Bose gas in a slab geometry with a Dirichlet boundary condition. We calculate the temperature (T) dependence of the Casimir force below and above the Bose?Einstein condensation temperature (Tc). At T ? Tc the Casimir force vanishes as . For T Tc it weakly depends on temperature. For T Tc it vanishes exponentially. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of . At finite temperatures the Casimir force for our system depends on .

Truncated harmonic oscillator and parasupersymmetric quantum mechanics

We discuss in detail the parasupersymmetric quantum mechanics of arbitrary order where the parasupersymmetry is between the normal bosons and those corresponding to the truncated harmonic oscillator. We show that even though the parasusy algebra is different from that of the usual parasusy quantum mechanics, still the consequences of the two are identical. We further show that the parasupersymmetric quantum mechanics of arbitrary orderp can also be rewritten in terms ofp supercharges (i.e. all of which obeyQi2=0). However, the Hamiltonian cannot be expressed in a simple form in terms of thep supercharges except in a special case. A model of conformal parasupersymmetry is also discussed and it is shown that in this case, thep supercharges, thep conformal supercharges along with HamiltonianH, conformal generatorK and dilatation generatorD form a closed algebra.

Casimir force on an interacting Bose–Einstein condensate

We have presented an analytic theory for the Casimir force on a Bose–Einstein condensate which is confined between two parallel plates. We have considered Dirichlet boundary conditions for the condensate wavefunction as well as for the phonon field. We have shown that the condensate wavefunction (which obeys the Gross–Pitaevskii equation) is responsible for the mean field part of the Casimir force, which usually dominates over the quantum (fluctuations) part of the Casimir force.

Bose-Einstein condensation and Casimir effect of trapped ideal Bose gas in between two slabs

Abstract.We study the Bose-Einstein condensation for a 3-d system of ideal Bose gas which is harmonically trapped along two perpendicular directions and is confined in between two slabs along the other perpendicular direction. We calculate the Casimir force between the two slabs for this system of trapped Bose gas. At finite temperatures this force for thermalized photons in between two plates has a classical expression which is independent of ħ. At finite temperatures the Casimir force for our system depends on ħ. For the calculation of Casimir force we consider only the Dirichlet boundary condition. We show that below condensation temperature (Tc) the Casimir force for this non-interacting system decreases with temperature (T) and at

A complete theory for the magnetism of an ideal gas of electrons

T\gtrsim T_c

Thermodynamics of quantum gases for the entire range of temperature

, it is independent of temperature. We also discuss the Casimir effect on 3-d highly anisotropic harmonically trapped ideal Bose gas.

The critical Casimir force in the superfluid phase: effect of fluctuations

We have explored Pauli paramagnetism, Landau diamagnetism, and de Haas-van Alphen effect in a single framework, and unified these three effects for all temperatures as well as for all strengths of magnetic field. Our result goes beyond Pauli-Landau result on the magnetism of the 3-D ideal gas of electrons, and is able to describe crossover of the de Haas-van Alphen oscillation to the saturation of magnetization. We also have obtained a novel asymptotic series expansion for the low temperature properties of the system.

Energy fluctuation and discontinuity of specific heat

We have analytically explored the thermodynamics of free Bose and Fermi gases for the entire range of temperature, and have extended the same for harmonically trapped cases. We have obtained approximate chemical potentials for the quantum gases in closed forms of temperature so that the thermodynamic properties of the quantum gases become plausible, especially in the intermediate regime between the classical and quantum limits.

Finite temperature scaling theory for the collapse of Bose-Einstein condensate

We have considered the critical Casimir force on a 4 He film below and above the bulk point. We have explored the role of fluctuations around the mean field theory in a perturbative manner, and have substantially improved the mean field result of Zandi et al (2007 Phys. Rev. E 76 030601(R)). The Casimir scaling function obtained by us approaches a universal constant ( ( 3)/8 ) for T. 2.13K.