Related papers: Geometric phases in the simple harmonic and pertur…
We study the geometric phase factors underlying the classical and the corresponding quantum dynamics of a driven nonlinear oscillator exhibiting chaotic dynamics. For the classical problem, we compute the geometric phase factors associated…
The geometrical phase of a time-dependent singular oscillator is obtained in the framework of Gaussian wave packet. It is shown by a simple geometrical approach that the geometrical phase is connected to the classical nonadiabatic Hannay…
A wave packet of a charged particle always make cyclic circular motion in a uniform magnetic field, just like a classical particle. The nonadiabatic geometric phase for an arbitrary wave packet can be expressed in terms of the mean value of…
We illustrate the geometric phase associated with the cyclic dynamics of a classical system of coupled oscillators. We use an analogy between a classical coupled oscillator and a two-state quantum mechanical system to represent the…
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the…
Geometric phases arise in a number of physical situations and often lead to systematic shifts in frequencies or phases measured in precision experiments. We describe, by working through some simple examples, a method to calculate geometric…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
Several definitions of phase have been proposed for stochastic oscillators, among which the mean-return-time phase and the stochastic asymptotic phase have drawn particular attention. Quantitative comparisons between these two definitions…
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting…
Geometric phase has historically been defined using closed cycles of polarization states, often derived using differential geometry on the Poincare sphere. Using the recently-developed wave model of geometric phase, we show that it is…
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…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
For a time-dependent $\tau$-periodic harmonic oscillator of two linearly independent homogeneous solutions of classical equation of motion which are bounded all over the time (stable), it is shown, there is a representation of states cyclic…
According to the pioneering work of Nielsen and collaborators, the length of the minimal geodesic in a geometric realization of a suitable operator space provides a measure of the quantum complexity of an operation. Compared with the…
The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of…
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
The wave description of geometric phase uses the superposition of light waves to explain the geometric phase's origin. While our previous work focused on a basis of linearly polarized waves, here we show that the same concepts can be…
The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is…