R. K. Bhaduri

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.

Effects of three-body ΛNN forces in light hypernuclei

Abstract Effects of the two-pion-exchange ΛNN force on the binding energies of Λ 5 He and Λ 3 H are examined in detail. This ΛNN force W consists of two parts: W = W p + W s , where W p and W s are due to the p -wave and s -wave π-Λ interaction, respectively. For W p , the effect of Y 1 ∗ (1385) is also taken into account. For W s , a suppression factor of the s -wave π-Λ interaction is introduced in analogy to the π- N case. Since we do not know the short-range part of the ΛNN force, we introduce a cutoff radius d and W is set to be zero for ΛN distances less than d . The effect of W p in Λ 5 He is found to be repulsive and quite appreciable. For instance, for d = 1F, it reduces the binding energy of Λ 5 He by about 2 MeV. This results in a substantial reduction in the overbinding of Λ 5 He that was obtained when only a two-body ΛN force was used that fitted Alexander et al. s low-energy scattering parameters. Bulk of this contribution comes from the “tensor part” of W p which has been ignored in previous works. W s is unimportant provided the s -wave suppression factor is 10 or more. The ΛNN force plays only a minor role in Λ 3 H.

Semiclassical approximation in a realistic one-body potential

Abstract For a system of noninteracting fermions in a one-body potential including spin-orbit interaction, an explicit series in the expansion parameter h 2 is derived for the “smooth” part of the energy. The formalism is only valid for potentials with no discontinuous edges, and is based on the Wigner-Kirkwood semiclassical partition function. Some numerical calculations are done in realistic spherical and deformed potentials to demonstrate the practical utility of the method. Numerical comparisons with the corresponding Strutinsky calculations are also made.

Exactly solvable noncentral potentials in two and three dimensions

We show that the list of analytically solvable potentials in nonrelativistic quantum mechanics can be considerably enlarged. In particular, we show that those noncentral potentials for which the Schrodinger equation is separable are analytically solvable provided the separated problem for each of the coordinates belongs to the class of exactly solvable one dimensional problems. As an illustration, we discuss in detail two examples, one in two and the other in three dimensions. A list of analytically solvable noncentral potentials in spherical polar coordinates is also given. Extension of these ideas to other standard orthogonal coordinate systems as well as to higher dimensions is straightforward.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

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

V(r,\theta,\phi)={\omega^2\over 4}r^2 + {\delta\over r^2}+{C\over r^2 sin^2\theta}+{D\over r^2 cos^2\theta} + {F\over r^2 sin^2\theta sin^2 \alpha\phi} +{G\over r^2 sin^2\theta cos^2\alpha\phi}

Dark matter and dark energy from a Bose–Einstein condensate

with 7 parameters.Other algebraically solvable examples are also given.

On the quantum density of states and partitioning an integer

Abstract We consider, for doubly even nuclei, the excitation energy E 2 and the reduced electric quadrupole transition probability B (E2) between the ground state and first excited 2 + state. For a nucleus ( N , Z ), the quantity [E 2 B (E2)] −1 is denoted by F ( N , Z ), and it is shown, on the basis of a microscopic model, that F(N, Z) + F(N + 2, Z + 2) − F(N, Z + 2) − F(N + 2, Z) ≈ 0 , excepting in certain specified regions. The consistency of the above difference equation is tested with the available experimental data. A few predictions of unmeasured B (E2) values are also made to illustrate the possible use of this approach.

Novel correlations in two dimensions: Some exact solutions.

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a