Related papers: Topological properties of geometric phases
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
Within the Hamiltonian framework, the propositions about a classical physical system are described in the Borel {\sigma}-algebra of a symplectic manifold (the phase space) where logical connectives are the standard set operations.…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
Quantum eigenstates undergoing cyclic changes acquire a phase factor of geometric origin. This phase, known as the Berry phase, or the geometric phase, has found applications in a wide range of disciplines throughout physics, including…
We develop a framework that systematically casts the solvability and uniqueness conditions of linearized geometric boundary-value problems into cohomological terms. The theory is designed to be applicable without assumptions on the…
It is demonstrated in the context of the simple one-dimensional example of a barrier in an infinite well, that highly complex behavior of the time evolution of a wave function is associated with the almost degeneracy of levels in the…
We perform a microcanonical study of classical lattice phi^4 field models in 3 dimensions with O(n) symmetries. The Hamiltonian flows associated to these systems that undergo a second order phase transition in the thermodynamic limit are…
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
The geometric phase effect arises from the dependence on the nuclear coordinates in the electronic Hamiltonian, leading to sign changes of the electronic wave functions upon traversal of certain paths in nuclear configuration space. The…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
In this note we show the existence of the hyperbolical geometric quantum phase that is different from the ordinary trigonometric geometric quantum phase. Gravitomagnetic charge (dual mass) is the gravitational analogue of magnetic monopole…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
The study of phase transitions using data-driven approaches is challenging, especially when little prior knowledge of the system is available. Topological data analysis is an emerging framework for characterizing the shape of data and has…
In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…
A theory of transformation is presented for the diagonalization of a Hamiltonian that is quadratic in creation and annihilation operators or in coordinates and momenta. It is the systemization and theorization of Dirac and…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…