Gautam Ghosh

Coherent states for quons

Coherent states for quons are constructed as eigenstates of the annihilation operator and their properties are studied. In particular, it is shown that these states form a complete set with respect to a measure.

Entropy production due to coupling to a heat bath in the kicked rotor problem

Considering a kicked rotor coupled to a model heat bath both the classical and quantum entropy productions are calculated exactly. Starting with an initial wave packet, the von Neumann entropy as a function of time is determined from the reduced density matrix while the Liouville evolution of the corresponding Husimi distribution provides us with the classical entropy. It is found that both these entropies agree reasonably satisfying the same asymptotic growth law and more importantly both are proportional to the classical Lyapunov exponent.

Effects of the Nature of Index Profile on the Validity of the Eikonal Approximation

Abstract We investigate the effects of the nature of the index profile of the scatterer on the validity of the eikonal approximation. For simplicity we concentrate on one-dimensional models where exact solutions can be obtained. Three kinds of scatterer are studied: (i) homogeneous with sharp boundaries (ii) inhomogeneous (continuously varying refractive index) and (iii) a model for rough surfaces. The relevance of such studies to the realistic case in three dimensions is pointed out.

Quantum chaos: Reduced density matrix fluctuations in coupled systems

Following a recent work (briefly reviewed below), we consider temporal fluctuations in the reduced density matrix elements for a coupled system involving a pair of kicked rotors as also one made up of a pair of Harper Hamiltonians. These dynamical fluctuations are found to constitute a reliable indicator of the degree of chaos in the quantum dynamics, and are related to stationary features like the eigenvalue and eigenvector distributions of the system under consideration. A brief comparison is made with the evolution of the reduced distribution function in the classical phase space.

Action-angle variables in quantum mechanics

Abstract Guided by the classical action-angle transformation and the correspondence principle, a formalism is developed whereby an exact diagonalization of the Hamiltonian for separable systems can be effected through a transformation to quantum action-angle operators. The usual problems involving the use of the angle operator, e.g., the non-unitarity of exp(±iφ), are circumvented by using only those operators that leave the Hilbert space invariant.

Generalized annihilation operator coherent states

A set of generalized coherent states as eigenstates of the annihilation operator is proposed. These states are analytic functions of a complex variable and admit a resolution of identity with positive measure. Guided by the classical action angle transformation and the correspondence principle a formalism is developed for the construction of the annihilation operator for a given Hamiltonian.

An adiabatic phase in scattering

Abstract The scattering phase shift is defined in a way analogous to the adiabatic phase for bound states. An iterative procedure results in an expansion whose leading term resembles the geometric phase of Berry. The method works when reflection is negligible. Examples are worked out for illustration.

The Saha ionization equation

A single hydrogen atom in the universe kept at temperature T cannot exist in a bound state. This constitutes a surprise according to Peierls because the ionization in an assembly of hydrogen atoms is finite. The behaviour of a single hydrogen atom is first considered on its own and then as a limiting case of an assembly of atoms. Since the partition sum for the bound part diverges, care is needed in the derivation of the ionization formula proposed by Saha.

Geometric phase for charged bosons

Abstract We study the effect of charge conservation on the geometric phase acquired by bosons under continuation in a closed cycle in the state space. We show explicitly that the intrinsic geometric properties of a fixed charged submanifold depends, in general, on the charge.

Geometric phase in q-deformed quantum mechanics'

Abstract The geometric structure of Hilbert space corresponding to several q -deformed algebras is studied. It is shown that deformations can change the curvature of Hilbert space and as a consequence lead to q -dependent alterations in the geometric phase.