Related papers: Geometric Properties of Quantum Phases
We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport…
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…
In the previous parts of this work, we established the Prequantum Groupoid $\mathbf{T}_\omega$ as the universal geometric container for quantum mechanics. This approach, which we call the "Geometric Quantization by Paths" (GQbP) framework,…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Topological phases emerge as the parameters of a quantum system vary with time. Under the adiabatic approximation, the time dependence can be eliminated, allowing the Berry topological phase to be obtained from a closed trajectory in…
The regimes of growing phases (for electron numbers N~0-8) that pass into regions of self-returning phases (for N>8), found recently in quantum dot conductances by the Weizmann group are accounted for by an elementary Green function…
In this work, we present a geometrical formulation of quantum thermodynamics based on contact geometry and principal fiber bundles. The quantum thermodynamic state space is modeled as a contact manifold, with equilibrium Gibbs states…
The existence of several exotic phenomena, such as duality and spectral anholonomy is pointed out in one-dimensional quantum wire with a single defect. The topological structure in the spectral space which is behind these phenomena is…
Recently, dynamical anomalies more than critical slowing down are often observed near both the continuous and first-order phase transition points. We propose that the universal anomalies could originate from the geometric phase effects. A…
We examine a recent proposal to show the presence of nonlocal Pancharatnam type geometric phases in a quantum mechanical treatment of intensity interferometry measurements upon inclusion of polarizing elements in the setup. It is shown that…
The quantum nature of matter lies in the wave function phases that accumulate while particles move along their trajectories. A prominent example is the Aharonov-Bohm phase, which has been studied in connection with the conductance of…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
In the context of (2+1)--dimensional quantum gravity with negative cosmological constant and topology R x T^2, constant matrix--valued connections generate a q--deformed representation of the fundamental group, and signed area phases relate…
Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…
Quantum entanglement can manifest itself in the narrowing of wavepackets. We define the phenomenon of phase entanglement and describe its effect on the interpretation of spatial localization experiments.
The phase variation with angle of hadronic amplitudes is studied with a view to understanding the underlying physical quantities which control it and how well it can be determined in free space. We find that unitarity forces a moderately…
Geometric phases appear ubiquitously in many and diverse areas of physical sciences, ranging from classical and molecular dynamics to quantum mechanics and solid-state physics. In the realm of optics, similar phenomena are known to emerge…
Quantum Hall effects provide intuitive ways of revealing the topology in crystals, i.e., each quantized "step" represents a distinct topological state. Here, we seek a counterpart for "visualizing" quantum geometry, which is a broader…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
Geometric phases provide a unified framework for understanding diverse phenomena in quantum and classical physics. The Pancharatnam-Berry (PB) geometric phase, arising from variation of optical transverse polarization, has transformed light…