Related papers: Geometric Phase, Hannay's Angle, and an Exact Acti…
Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…
We provide geometric quantization of a completely integrable Hamiltonian system in the action-angle variables around an invariant torus with respect to polarization spanned by almost-Hamiltonian vector fields of angle variables. The…
It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
Conventionally while we talk about geometry associated with a simple harmonic oscillator, we draw a circle with a radius equal to the amplitude of Oscillator and imagine a particle moving along the perimeter with a frequency same as that of…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
The canonical tensor model, which is a tensor model in the Hamilton formalism, can be straightforwardly quantized and has an exactly solved physical state. The state is expressed by a wave function with a generalized form of the Airy…
We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the…
An exact invariant is derived for three-dimensional Hamiltonian systems of $N$ particles confined within a general velocity-independent potential. The invariant is found to contain a time-dependent function $f_{2}(t)$, embodying a solution…
We will present a consistent description of Hamiltonian dynamics on the ``symplectic extended phase space'' that is analogous to that of a time-\underline{in}dependent Hamiltonian system on the conventional symplectic phase space. The…
For one dimensional non-relativistic quantum mechanical problems, we investigate the conditions for all the position dependence of the propagator to be in its phase, that is, the semi-classical approximation to be exact. For velocity…
The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
The level crossing problem and associated geometric terms are neatly formulated by the second quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete…
In this paper, it is proposed a quantization procedure for the one-dimensional harmonic oscillator with time-dependent frequency, time-dependent driven force, and time-dependent dissipative term. The method is based on the construction of…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on…
In this work, we propose an experimentally feasible nonlinear optical realization of a type of non-integrable phase found in interacting quantum systems at quantum phase transitions. We show that an exotic term in the dynamical equation…