Barnali Chakrabarti

Application of supersymmetry to a coupled system of equations: the concept of a superpotential matrix

We apply supersymmetric quantum mechanics (SUSY QM) to multidimensional Schrodinger equations involving nonseparable potentials, which result in a system of coupled differential equations, where instead of the conventional definition of a scalar superpotential we introduce a superpotential matrix and succeed in applying SUSY QM to the coupled system. Finally, we discuss the shape-invariance condition for the potential matrix of such a system.

An approximate many-body calculation for trapped bosons with attractive interaction

The stability of trapped interacting bosons with attractive interactions is studied using an approximate many-body calculation. Instead of using the traditional hyperspherical harmonics expansion method we prescribe a potential harmonics expansion method (PHEM). The justification of the use of PHEM in connection with dilute condensates is presented. The choice of a correlation function is justified as it correctly reproduces the short-range two-body correlation in the wavefunction as also the correct value of the s-wave scattering length (as). Applications to 7Li and 85Rb condensates with the realistic van der Waals interaction give good agreement with the Rice and JILA experiments, respectively. The JILA experiment used controlled collapse of the 85Rb condensate for different values of as. Our calculations agree with the experimental results within the experimental error bars.

Analytic superpotential for Yukawa potential by perturbation of the Riccati equation

Abstract The basic ingredient of supersymmetry is the analytic superpotential, which demands analytic ground state wave function, which does not exist for an arbitrary potential. We present a nice perturbative solution of the Riccati equation leading to an analytic superpotential for any arbitrary potential. Application to Yukawa potential gives excellent results.

Many-body entropies, correlations, and emergence of statistical relaxation in interaction quench dynamics of ultracold bosons

We study the quantum many-body dynamics and the entropy production triggered by an interaction quench in a system of N = 10 interacting identical bosons in an external one-dimensional harmonic trap. The multiconfigurational time-dependent Hartree method for bosons (MCTDHB) is used for solving the time-dependent Schrodinger equation at a high level of accuracy. We consider many-body entropy measures such as the Shannon information entropy, number of principal components, and occupation entropy that are computed from the time-dependent many-body basis set used in MCTDHB. These measures quantify relevant physical features such as irregular or chaotic dynamics, statistical relaxation, and thermalization. We monitor the entropy measures as a function of time and assess how they depend on the interaction strength. For larger interaction strength, the many-body information and occupation entropies approach the value predicted for the Gaussian orthogonal ensemble of random matrices. This implies statistical relaxation. The basis states of MCTDHB are explicitly time-dependent and optimized by the variational principle in away that minimizes the number of significantly contributing ones. It is therefore a non-trivial fact that statistical relaxation prevails in MCTDHB computations. Moreover, we demonstrate a fundamental connection between the production of entropy, the buildup of correlations and loss of coherence in the system. Our findings imply that mean-field approaches such as the time-dependent Gross-Pitaevskii equation cannot capture statistical relaxation and thermalization because they neglect correlations. Since the coherence and correlations are experimentally accessible, their present connection to many-body entropies can be scrutinized to detect statistical relaxation. In this work we use the recent recursive software implementation of the MCTDHB (R-MCTDHB).

Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

We present a statistical analysis of eigenenergies and discuss several measures of spectral fluctuations and spectral correlations for the van der Waals clusters of different sizes. We show that the clusters become more and more complex with increase in cluster size. We study nearest-neighbour level spacing distribution

Correlated many-body calculation to study characteristics of Shannon information entropy for ultracold trapped interacting bosons

P(s)

Energy eigenvalues of a quantum anharmonic oscillator from supersymmetry : the concept of conditional shape-invariance symmetry

, the level number variance

Level correlation in coupled harmonic oscillator systems

\Sigma^2(L)

Calculation of resonances using isospectral potentials

, and the Dyson-Mehta

STUDY OF THE EXCITED STATE OF DOUBLE-Λ HYPERNUCLEI BY HYPERSPHERICAL SUPERSYMMETRIC APPROACH

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