Related papers: Geometric phase distributions for open quantum sys…
The geometric phases for standard coherent states which are widely used in quantum optics have attracted a large amount of attention. Nevertheless, few physicists consider about the counterparts of non-linear coherent states, which are…
Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust…
In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
A generalised notion of geometric phase for pure states is proposed and its physical manifestations are shown. An appreciation of fact that the interference phenomenon also manifests in the average of an observable, allows us to define the…
In the first part of this review we introduce the basics theory behind geometric phases and emphasize their importance in quantum theory. The subject is presented in a general way so as to illustrate its wide applicability, but we also…
Geometric phases in particle diffusion systems, an intriguing aspect enlightened from thermal systems, offer a different understanding beyond traditional Brownian motion and Fick's laws. This concept introduces a phase factor with…
Through the quantum trajectory approach, we calculate the geometric phase acquired by a bipartite system subjected to decoherence. The subsystems that compose the bipartite system interact with each other, and then are entangled in the…
While most approaches to geometric quantum computation is based on geometric phase in cyclic evolution, noncyclic geometric gates have been proposed to increase further the flexibility. While these gates remove the dynamical phase of the…
A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may…
The geometric phases of cyclic evolutions for mixed states are discussed in the framework of unitary evolution. A canonical one-form is defined whose line integral gives the geometric phase which is gauge invariant. It reduces to the…
We describe in detail a general strategy for implementing a conditional geometric phase between two spins. Combined with single-spin operations, this simple operation is a universal gate for quantum computation, in that any unitary…
A sequence of completely positive maps can be decomposed into quantum trajectories. The geometric phase or holonomy of such a trajectory is delineated. For nonpure initial states, it is shown that well-defined holonomies can be assigned by…
We design several examples of constrained, symmetric quantum circuit dynamics that generate non-equilibrium steady states. The qubit networks maintain local memory of the initial conditions and display inhomogeneous subsystem dynamics over…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
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…
Time-dependent $\mathcal{PT}$-symmetric quantum mechanics is featured by a varying inner-product metric and has stimulated a number of interesting studies beyond conventional quantum mechanics. In this paper, we explore geometric aspects of…
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…