Related papers: A Supplement: on the Quantum-vacuum Geometric Phas…
The presence of noncyclic geometric invariant is revealed in all the phenomena where particle generation from vacuum or vacuum condensates appear. Aharonov--Anandan invariants then can help to study such systems and can represent a new tool…
In this article we provide a review of geometrical methods employed in the analysis of quantum phase transitions and non-equilibrium dissipative phase transitions. After a pedagogical introduction to geometric phases and geometric…
Non-Hermitian systems have attracted considerable interest in recent years owing to their unique topological properties that are absent in Hermitian systems. While such properties have been thoroughly characterized in free fermion models,…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
The features of vacuum particle creation in an external classical field are studied for simplest external field models in $3 + 1$ dimensional QED. The investigation is based on a kinetic equation that is a nonperturbative consequence of the…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
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),…
Geometric phase plays a fundamental role in quantum theory and accounts for wide phenomena ranging from the Aharanov-Bohm effect, the integer and fractional quantum hall effects, and topological phases of matter, including topological…
In this brief review we describe the idea of holonomic quantum computation. The idea of geometric phase and holonomy is introduced in a general way and we provide few examples that should help the reader understand the issues involved.
We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the…
We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In…
We show that the optical Kerr effect can be used to construct a quantum phase gate. It is well known from quantum nondemolition techniques that, as two photon field modes pass through a Kerr medium, the phase of each mode will be shifted,…
In this work we address quantum vacuum amplification effects in time-varying media with an arbitrary time-modulation profile. To this end, we propose a theoretical formalism based on the concept of conjugated harmonic oscillators,…
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer…
We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer…
It is shown that three-dimensional systems of coupled quantum wires support fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems. These phases have topologically…
We propose a scheme to realize cubic quantum nondemolition (QND) Hamiltonian with optical parametric interactions. We show that strongly squeezed fundamental and second harmonic fields propagating in a $\chi^{(2)}$ nonlinear medium…
Recent theoretical work has concentrated on calculating the Casimir effect in curved spacetime. In this paper we outline the forward problem of metrical variation due to the Casimir effect for spherical geometries. We consider a scalar…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties…