arXiv subjects

Rajat K. Bhaduri

Publications and source records attributed to Rajat K. Bhaduri.

22 records · Page 2Linked to original sources

arXiv2002

Some exact results for a trapped quantum gas at finite temperature

We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3, exact expressions for the N-particle densities are used to calculate perturbatively the temperature dependence of the splittings of the energy levels in a given shell due to a very weak interparticle interaction in a dilute Fermi gas. In two dimensions, we obtain analytically the surprising result that the |l|-degeneracy in a harmonic oscillator shell is not lifted in the lowest order even when the exact, rather than the Thomas-Fermi expression for the particle density is used. We also demonstrate rigorously (in two dimensions) the reduction of the exact zero-temperature fermionic expressions to the Thomas-Fermi form in the large-N limit.

cond-mat.stat-mech↗

arXiv2002

General Logarithmic Corrections to Black Hole Entropy

We compute leading order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form $-k\ln(Area)$. For BTZ black holes, $k=3/2$, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner-Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black hole entropy and its corrections.

hep-th↗

arXiv1993

Some Exactly Solvable Three-Body Problems in One dimension

The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body potentials which can be solved algebraically. Analytic expressions for the eigenspectrum and the eigenfunctions are given with and without confinement.

hep-th↗

arXiv1993

Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential $$V(r,θ,ϕ)={ω^2\over 4}r^2 + {δ\over r^2}+{C\over r^2 sin^2θ}+{D\over r^2 cos^2θ} + {F\over r^2 sin^2θsin^2 αϕ} +{G\over r^2 sin^2θcos^2αϕ}$$ with 7 parameters.Other algebraically solvable examples are also given.

hep-th↗