arXiv subjects

Swapan K. Ghosh

Publications and source records attributed to Swapan K. Ghosh.

3 recordsLinked to original sources

arXiv2021

Position-Dependent Diffusion induced Non-monotonic decay of Certain Non-Equilibrium Phenomena in Condensed Phase

The dynamics of various optically controlled non-equilibrium phenomena in the condensed phase are studied using the Liouville equation. We study a projection of the same in a slow moving coordinate, identified as the Reaction Coordinate approach, with a position dependent diffusion coefficient. Introduction of position dependence is shown to induce non-monotonicity in relaxations of certain Non-equilibrium correlation functions, previously unexplored in the theoretical as well as experimental studies. This is in contrast to the exponential relaxation of its position independent analogue, irrespective of initial conditions. We characterize the dependence of this non-monotonicity on the strength of spatial inhomogeneity of diffusion and on the strength of the restoring forces and also indicate ranges of combinations where this feature is exhibited to pave the way for its experimental detection.

quant-ph↗

arXiv2021

A Path Integral approach to Quantum Fluid Dynamics

In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs) simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential (QP), which, in turn, can generate the Quantum Trajectories. For cases, where closed form solution is not possible, the problem is formally boiled down to solving the classical path as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively, but the Quantum part is left exact. Using this we delve into seeking insight in one of the long standing debates with regard to Quantum Tunneling.

quant-ph↗

arXiv2013

Factorization method for nonlinear evolution equations Factorization method for nonlinear evolution equations

The traditional method of factorization can be used to obtain only the particular solutions of the Liénard type ordinary differential equations. We suggest a modification of the approach that can be used to construct general solutions . We first demonstrate the effectiveness of our method by dealing with a solvable form of the modified Emden-type equation and subsequently employ it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman (RH) and NLS equations. The solution of the mKdV equation, via the so-called Muira transform, leads to a singular solution of the KdV equation in addition to the well-known soliton solution supported by it. We obtain the solution of the non-integrable RH equation in terms of the Jacobi function and show that, although robust, it is structurally different from the KdV soliton. We also find the soliton solution of the NLS equation that accounts for the evolution of complex envelopes in an optical medium.

nlin.SI↗