Related papers: Generalized Geometrical Phase in the Case of Conti…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
The gauge invariance of geometric phases for mixed states is analyzed by using the hidden local gauge symmetry which arises from the arbitrariness of the choice of the basis set defining the coordinates in the functional space. This…
An effect of geometrical phase shift is predicted for a light beam propagating in the field of a gravitational wave. Gravitational radiation detection experiments are proposed using this new effect, the corresponding estimates being given.
We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous…
We describe the geometric (Berry) phases arising when some quantum systems are driven by control classical parameters but also by outer classical stochastic processes (as for example classical noises). The total geometric phase is then…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
In this paper, we investigate the geometric phase (GP) acquired by two-mode mixed squeezed-coherent states (SCSs) during unitary cyclic evolution, focusing on the influence of squeezing parameters and classical weight. We analyze the GP for…
We construct a generalized dynamics for particles moving in a symmetric space-time, i.e. a space-time admitting one or more Killing vectors. The generalization implies that the effective mass of particles becomes dynamical. We apply this…
In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…
Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…
We consider a periodically driven quantum system described by a Hamiltonian which is the product of a slowly varying Hermitian operator $V\left(\boldsymbol{\lambda}\left(t\right)\right)$ and a dimensionless periodic function with zero…
In a scenario where the constituent quarks are composite systems, Generalized Parton Distributions (GPDs) are built from wave functions to be evaluated in a Constituent Quark Model (CQM), convoluted with the GPDs of the constituent quarks…
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different order, in analogy…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous…
Nodal free geometric phases are the eigenvalues of the final member of a parallel transporting family of unitary operators. These phases are gauge invariant, always well-defined, and can be measured interferometrically. Nodal free geometric…
On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
We consider a quantum limit-cycle oscillator implemented in a spin system whose quantization axis is slowly rotated. Using a kinematic approach to define geometric phases in nonunitary evolution, we show that the quantum limit-cycle…
The generalized invariant and its eigenstates of a general quadratic oscillator are found. The Schr\"odinger wave functions for the eigenstates are also found in analytically closed forms. The conditions for the existence of the cyclic…