Related papers: Geometric phase and quantum potential
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
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 map the geometric quantum potential on the nonlinear sigma model and use homotopy to estimate the lower bound of the geometric quantum potential. We investigate a catenoid (wormhole section), a two dimensional bilayer geometry smoothly…
A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…
Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior…
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…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
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 geometric and open path phases of a four-state system subject to time varying cyclic potentials are computed from the Schr\"{o}dinger equation. Fast oscillations are found in the non-adiabatic case. For parameter values such that the…
We develop a new interpretation of the geometric phase in evolution with a non-Hermitian real value Hamiltonian by relating it to the angle developed during the parallel transport along a closed curve by a unit vector triad in the…
The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the…
Quaternion quantum mechanics is examined at the level of unbroken SU(2) gauge symmetry. A general quaternionic phase expression is derived from formal properties of the quaternion algebra.
Geometric phase is a promising element to induce high-fidelity and robust quantum operations due to its built-in noise-resilience feature. Unfortunately, its practical applications are usually circumscribed by requiring complex interactions…
Quantum geometry quantifies how the electron wavefunction evolves distinctly from conventional transport theory. In noncentrosymmetric materials, nonreciprocal transport with quantum geometric origin remains prominent with localized charge…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
The geometric phase requires the multivaluedness of solutions to Fuchsian second-order equations. The angle, or its complement, is given by half the area of a spherical triangle in the case of three singular points, or half the area of a…
Propagation of a localised wave function of a massive scalar field is investigated in its rest frame. The complete orthogonal Hermite-Gauss basis is presented, and the Gouy phase and Rayleigh scale notions are adapted. The leading and…
This is the second of the two related papers analysing origins and possible explanations of a paradoxical phenomenon of the quantum potential (QP). It arises in quantum mechanics'(QM) of a particle in the Riemannian $n$-dimensional…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
Three related topics on the quantum-vacuum geometric phases in a noncoplanarly curved optical fiber is presented: (i) a brief review: the investigation of vacuum effect and its experimental realization; (ii) the sequence of ideas of…