Related papers: Geometric phases in the simple harmonic and pertur…
We introduce an exactly solvable example of timelike geodesic motion and geodesic deviation in the background geometry of a well-known two-dimensional black hole spacetime. The effective potential for geodesic motion turns out to be either…
We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We construct a class of generalized phase coherent states indexed by points of the unit circle and depending on three positive parameters "gamma","alpha" and "epsilon" by replacing the labelling coefficients of the canonical coherent states…
We present an algorithm for constructing analytically approximate integrals of motion in simple time periodic Hamiltonians of the form $H=H_0+ \varepsilon H_i$, where $\varepsilon$ is a perturbation parameter. We apply our algorithm in a…
Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase-space, a credible possibility of their detection lies in the present day gravitational wave…
A trajectory of a harmonic oscillator obeying the Schreodinger wave equation is exactly derived and illustrated. The trajectory resembles well the classical orbit between the turning points, and also runs through the tunneling region. The…
The optical geometric phase encoded by the in-plane spatial orientation of microstructures has promoted the rapid development of numerous new-type optical meta-devices. However, pushing the concept of the geometric phase toward the acoustic…
A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a…
We investigate geometric phase of fermion states under relative vibrations of two sublattices in graphene by solving time-dependent Sch\"{o}dinger equation using Floquet scheme. In a period of vibration the fermions acquire different…
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…
We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase…
We report on recent results showing that the geometric phase can be used as a tool in the analysis of many different physical systems, as mixed boson systems, CPT and CP violations, Unruh effects and thermal states. We show that the…
We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
The geometric phase effect arises from the dependence on the nuclear coordinates in the electronic Hamiltonian, leading to sign changes of the electronic wave functions upon traversal of certain paths in nuclear configuration space. The…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
The geometric phase of a bi-particle model is discussed. For different initial states, especially when the initial state is pure or mixed, the geometric phase will show different properties. The relationship between the geometric phase and…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…