Related papers: Geometric phases without geometry
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,…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
Geometric phases of simple harmonic oscillator system are studied. Complete sets of "eigenfunctions" are constructed, which depend on the way of choosing classical solutions. For an eigenfunction, two different motions of the probability…
Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory…
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and…
The differential geometric aspects of Geometric Phases are reviewed.
A general formalism of the relation between geometric phases produced by circularly evolving interacting spin systems and their criticality behavior is presented. This opens up the way for the use of geometric phases as a tool to study…
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…
Geometric phase (GP) independent of energy and time rely only on the geometry of state space. It has been argued to have potential fault tolerance and plays an important role in quantum information and quantum computation. We present the…
Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. The latter is a manifestation of a closed path in state space. Geometric phases underlie various…
We show that geometric phases may be generated in a quantum system subject to noise by adiabatic manipulations of the fluctuating fields, e.g., by variation of the system-environment coupling. For a two-state quantum system we express this…
The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…
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…
The state of a quantum system acquires a phase factor, called the geometric phase, when taken around a closed trajectory in the parameter space, which depends only on the geometry of the parameter space. Due to its sensitive nature, 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…
In this article, we provide theoretical support for the use of geometric measures of nonclassicality as a general tool to identify quantum phase transitions. We argue that divergences in the susceptibility of any geometric measure of…
Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
We analyze the geometric phase for an open quantum system when computed by resorting to a stochastic unravelling of the reduced density matrix (quantum jump approach or stochastic Schrodienger equations). We show that the resulting phase…