Related papers: Berry's Phase and Euclidean Path Integral
Introducing a perturbative definition, phase space path integrals can be calculated without slicing. This leads to a short-time expansion of the quantum-mechanical path amplitude, or a high-temperature expansion of the unnormalized density…
Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for…
We investigate the Berry phase arising from axion-photon and axion-fermion interactions. The effective Hamiltonians in both systems share the same form, enabling a unified description of the Berry phase and providing a novel perspective on…
The physical reality and observability of 2n\pi Berry phases, as opposed to the usually considered modulo 2\pi topological phases is demonstrated with the help of computer simulation of a model adiabatic evolution whose parameters are…
The effect of inter-subsystem couplings on the Berry phase of a composite system as well as that of its subsystem is investigated in this paper. We analyze two coupled spin-$\frac 1 2 $ particles with one driven by a quantized field as an…
We present a reformulation of quantum adiabatic theory in terms of an emergent electromagnetic framework, emphasizing the physical consequences of geometric structures in parameter space. Contrary to conventional approaches, we demonstrate…
We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of non-degenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical…
Efforts to give an improved mathematical meaning to Feynman's path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed…
Berry phase effect plays a central role in many mesoscale condensed matter and quantum chemical systems that are naturally under the environmental influence of dissipation. We propose and microscopically derive a prototypical quantum…
The quantum adiabatic theorem incorporating the Berry phase phenomenon can be characterized as a factorization of the time evolution operator into a path-dependent geometric factor, a usual dynamical factor and a non-adiabatic factor that…
We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons…
It is shown that even for large spins $J$ the fundamental difference between integer and half-integer spins persists. In a quasi-classical description this difference enters via Berry's connection. This general phenomenon is derived and…
Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes' Theorem, we relate the Optical Theorem to the Berry Phase, showing how the imaginary part of arbitrary one-loop…
A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin…
In the framework of the single-field slow-roll inflation, we derive the Hamiltonian of the linear primordial scalar and tensor perturbations in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of…
The manner in which probability amplitudes of paths sum up to form wave functions of a harmonic oscillator, as well as other, simple 1-dimensional problems, is described. Using known, closed-form, path-based propagators for each problem, an…
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase $\pi$ is accumulated and leads to interferences between different classical…
The Berry phase in a composite system with only one subsystem being driven has been studied in this Letter. We choose two spin-$\frac 1 2 $ systems with spin-spin couplings as the composite system, one of the subsystems is driven by a…