Related papers: Geometric phase and gauge theory structure in quan…
This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of…
We introduce the notion of the geometrically equivalent quantum systems (GEQS) as quantum systems that lead to the same geometric phases for a given complete set of initial state vectors. We give a characterization of the GEQS. These…
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…
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 propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
Geometric phase, associated with holonomy transformation in quantum state space, is an important quantum-mechanical effect. Besides fundamental interest, this effect has practical applications, among which geometric quantum computation is a…
The fundamental division of the total quantum evolution phase into geometric and dynamical components is a central problem in quantum physics. Here, we prove a remarkably simple and universal law demonstrating that this partitioning is…
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…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
We develop the widest possible generalisation of the well-known connection between quantum mechanical Bargmann invariants and geometric phases. The key notion is that of null phase curves in quantum mechanical ray and Hilbert spaces.…
A Hermitian quantum phase operator is formulated that mirrors the classical phase variable with proper time dependence and satisfies trigonometric identities. The eigenstates of the phase operator are solved in terms of Gegenbauer…
In the geometry of quantum-mechanical processes, the time-varying curvature coefficient of a quantum evolution is specified by the magnitude squared of the covariant derivative of the tangent vector to the state vector. In particular, the…
We investigate the evolution of a state which is dominated by a finite-dimensional non-Hermitian time-dependent Hamiltonian operator with a nondegenerate spectrum by using a biorthonormal approach. The geometric phase between any two…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases,…
We discuss the basic theoretical framework for non-Hermitian quantum systems with particular emphasis on the diagonalizability of non-Hermitian Hamiltonians and their $GL(1,\mathbb{C})$ gauge freedom, which are relevant to the adiabatic…
A precise definition of an adiabaticity parameter $\nu$ of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator…
We analyze the different ways to define the energy operator in geometric theories of quantum mechanics. In some formulations the operator contains the scalar curvature as a multiplicative term. We show that such term can be canceled or…