相关论文: Berry's Phase and Euclidean Path Integral

It is known that in the WKB approximation of multicomponent systems like Dirac equation or Born-Oppenheimer approximation, an additional phase appears apart from the Berry phase. So far, this phase was only examined in special cases, or…

Resorting to Berry's phase, a new idea to detect, at quantum level, the gravitomagnetic field of any metric theory of gravity, is put forward. It is found in this proposal that the magnitude of the gravitomagnetic field appears only in the…

A simple technique is used to obtain a general formula for the Berry phase (and the corresponding Hannay angle) for an arbitrary Hamiltonian with an equally-spaced spectrum and appropriate ladder operators connecting the eigenstates. The…

We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed…

We calculate the open path phase in a two state model with a slowly (nearly adiabatically) varying time-periodic Hamiltonian and trace its continuous development during a period. We show that the topological (Berry) phase attains $\pi$ or…

We study classical and quantum phases in the adiabatic Born-Oppenheimer context. These include a classical astronomical case, the general dual description of the phases, a new "Paradox" connected to scattering Berry phase and its resolution…

We present quadratic dynamical invariant and evaluate Berry's phase for the time-dependent Schroedinger equation with the most general variable quadratic Hamiltonian.

In 1984 Michael Berry discovered that an isolated eigenstate of an adiabatically changing periodic Hamiltonian $H(t)$ acquires a phase, called the Berry phase. We show that under very general assumptions the adiabatic approximation of the…

We study the adiabatic evolution of a two-level model in the presence of an external classical electric field. The coupling between the quantum model and the classical field is taken in the electric dipole approximation. In this regime, we…

This paper proposes a numerical method using neural networks to solve the path integral problem in quantum mechanics for arbitrary potentials. The method is based on a radial basis function expansion of the interaction term that appears in…

Studying phase transitions in interacting quantum field theories generally requires the numerical study of the dynamical system on an N-dimensional lattice, which is, in most cases, computationally quite the challenging task even with…

We consider in sufficient detail how the Berry phase arises in a rotating electric field in a model system with spin one. The goal is to help the student who first encountered this interesting problem, which is fraught with some subtleties…

We outline a path integral derivation of both the transverse force, the Berry phase, and friction for a vortex from the microscopic fermionic superfluid theory. The derivation manifests transparently the mutual independence of the Berry…

Path integrals represent a powerful route to quantization: they calculate probabilities by summing over classical configurations of variables such as fields, assigning each configuration a phase equal to the action of that configuration.…

The Berry phase is analyzed for Weyl and Dirac fermions in a phase space representation of the worldline formalism. Kinetic theories are constructed for both at a classical level. Whereas the Weyl fermion case reduces in dimension,…

We design an adiabatic quantum algorithm for the counting problem, i.e., approximating the proportion, $\alpha$, of the marked items in a given database. As the quantum system undergoes a designed cyclic adiabatic evolution, it acquires a…

The effect of fluctuations in the classical control parameters on the Berry phase of a spin 1/2 interacting with a adiabatically cyclically varying magnetic field is analyzed. It is explicitly shown that in the adiabatic limit dephasing is…

Despite their apparent simplicity, coupled oscillators exhibit surprisingly complex phenomena. Two notable examples are Berry phase (a geometric or topological aspect of the oscillators' memory) and non-Hermiticity (the often…

We present a new perspective on bulk reconstruction using Berry phases in the boundary CFT. Our parallel transport of modular Hamiltonians is associated to a trajectory in the space of states, which we obtain from the insertion of a source…

A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The…