Related papers: Study of geometric phase using classical coupled o…
We consider arbitrary mixed state in unitary evolution and provide a comprehensive description of corresponding geometric phase in which two different points of view prevailing currently can be unified. Introducing an ancillary system and…
We characterize the geometrical and topological aspects of a dynamical system by associating a geometric phase with a phase space trajectory. Using the example of a nonlinear driven damped oscillator, we show that this phase is resilient to…
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…
Under certain conditions, the quantum delta-kicked harmonic oscillator displays quantum resonances. We consider an atom-optical realization of the delta-kicked harmonic oscillator, and present a theoretical discussion of the quantum…
Starting with the generally well accepted opinion that quantizing an arbitrary Hamiltonian system involves picking out some additional structure on the classical phase space (the {\sl shadow} of quantum mechanics in the classical theory),…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
We consider the quantum harmonic oscillator in contact with a finite temperature bath, modelled by the Caldeira-Leggett master equation. Applying periodic kicks to the oscillator, we study the system in different dynamical regimes between…
In a prevous paper (Phys. Rev. Lett. 96, 150403 (2006)) we have proposed a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon. The basic idea was to force the ground state of…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
We consider a harmonic oscillator under periodic driving and coupled to two harmonic-oscillator heat baths at different temperatures. We use the thermofield transformation with chain mapping for this setup, which allows us to study the…
Geometric phases, which accompany the evolution of a quantum system and depend only on its trajectory in state space, are commonly studied in two-level systems. Here, however, we study the adiabatic geometric phase in a weakly anharmonic…
We study a quantum oscillator interacting and back-reacting on a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system…
The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic…
The geometric phase, originating from the cyclic evolution of a state, such as polarization on the Poincar\'e sphere, is typically measured through interferometric approaches that often include unwanted contributions from the dynamic phase.…
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…
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…
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As…
The concept of off-diagonal geometric phases for mixed quantal states in unitary evolution is developed. We show that these phases arise from three basic ideas: (1) fulfillment of quantum parallel transport of a complete basis, (2) a…
The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the…