Related papers: Bargmann Invariants and Geometric Phases - a Gener…
This paper focuses on the geometric phase of general mixed states under unitary evolution. Here we analyze both non-degenerate as well as degenerate states. Starting with the non-degenerate case, we show that the usual procedure of…
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…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
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…
Geometric phase has found a broad spectrum of applications in both classical and quantum physics, such as condensed matter and quantum computation. In this paper we introduce an operational geometric phase for mixed quantum states, based on…
Bohmian mechanics offers a deterministic alternative to conventional quantum theory through well-defined particle trajectories. While successful in nonrelativistic contexts, its extension to curved spacetime-and hence quantum…
It is a result of Gruson and Peskine that the invariants of a set points in $\ptwo$ in general position are connected. Associated to a space curve there are sequences of invariants which generalize the invariants of points in $\ptwo$. The…
We present and analyze a gauge-invariant quantum theory of the Friedmann-Robertson-Walker universe with dust. We construct the reduced phase space spanned by gauge-invariant quantities by using the so-called relational formalism at the…
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…
We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…
We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a…
A description of generalized coherent states and geometric phases in the light of the general theory of smooth loops is given.
The geometrical approximation of the extended Maxwell equation in curved spacetime incorporating interactions induced by the vacuum polarization effects is considered. Taking into account these QED interactions and employing the analogy…
Properties of the geometric phase for a nonstatic coherent light-wave arisen in a static environment are analyzed from various angles. The geometric phase varies in a regular nonlinear way, where the center of its variation increases…
The relation between quantum phase transitions, entanglement, and geometric phases is investigated with a system of two qubits with XY type interaction. A seam of level crossings of the system is a circle in parameter space of the…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of…