Related papers: Geometric phases in the simple harmonic and pertur…
The gravitational field of a particle of small mass $\mu$ moving through curved spacetime, with metric $g_{ab}$, is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through $O(\mu)$.…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we…
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Paralleling the studies in continuous systems, we…
Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
Quantum mechanical methods for getting geometric phases for mixed states are analyzed. Parallel transport equations for pure states are generalized to mixed states by which dynamical phases are eliminated. The geometric phases of mixed…
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Floquet operators are found for nonperiodical systems…
The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…
We show that a large class of physical theories which has been under intensive investigation recently, share the same geometric features in their Hamiltonian formulation. These dynamical systems range from harmonic oscillations to WZW-like…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The canonical operator quantisation formulation corresponding to the Klauder-Daubechies construction of the phase space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator,…
We follow a generalized kinematic approach to compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models, which provide a fully quantum description for a two-level system interacting with a single mode of…
Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
We investigate the properties of motion in a map model derived from a galactic Hamiltonian made up of perturbed elliptic oscillators. The phase space portrait is obtained in all three different cases using the map and numerical integration…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…