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A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz…
A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behaviour through a change of stability…
We consider the effects of certain forms of decoherence applied to both adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit we illustrate path-dependent sensitivity to anisotropic noise and for two qubits we…
The concept of geometric phase was applied to initiate the geometric-phase portrayal of electromagnetic scattering by a three-dimensional object in free space. Whereas the incident electromagnetic field is that of an arbitrarily polarized…
The behavior of the geometric phase gained by a single spin-1/2 nucleus immersed into a thermal or a squeezed environment is investigated. Both the time dependence of the phase and its value at infinity are examined against several physical…
Coupled cluster theory in the standard formulation is unable to correctly describe conical intersections among states of the same symmetry. This limitation has restricted the practical application of an otherwise highly accurate electronic…
We study the geometric phase (GP) of a two-level atom coupled to an environment composed of free space and a dielectric nanosphere in thermal and out of thermal equilibrium. We analytically and numerically analyze the optical properties and…
$\Lambda$-doubling of diatomic molecules is a subtle microscopic phenomenon that has long attracted the attention of experimental groups, insofar as rotation of molecular $\textit{nuclei}$ induces small energetic changes in the (degenerate)…
Geometric phases, arising from cyclic evolutions in a curved parameter space, appear in a wealth of physical settings. Recently, and largely motivated by the need of an experimentally realistic definition for quantum computing applications,…
We first explore the liquid-gas mixed phase in a bulk calculation, where two phases coexist without the geometrical structures. In the case of symmetric nuclear matter, the system behaves congruently, and the Maxwell construction becomes…
We investigate the qubit geometric phase and its properties in dependence on the mechanism for decoherence of a qubit weakly coupled to its environment. We consider two sources of decoherence: dephasing coupling (without exchange of energy…
The existence of macroscopic shell structure of submicron metal clusters is known for several decades. Since the most studies provide theoretical analysis for clusters of spherical shape, the electron density inhomogeneities caused by shell…
We calculate the geometric phase associated to the evolution of a system subjected to decoherence through a quantum-jump approach. The method is general and can be applied to many different physical systems. As examples, two main source of…
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 presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum…
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…
We study the effect of a hidden gauge symmetry on complex holomorphic systems. For this purpose, we show that intrinsically any holomorphic system has this gauge symmetry. We establish that this symmetry is related to the Cauchy-Riemann…
The effect of small forced symmetry breaking on the dynamics near a structurally stable heteroclinic cycle connecting two equilibria and a periodic orbit is investigated. This type of system is known to exhibit complicated, possibly chaotic…
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.