Related papers: Some Aspects of Classical and Quantum Phases
We introduce a classical analog of quantum matter in ultracold molecule -- or Rydberg atom -- synthetic dimensions, extending the Potts model to include interactions J1 between atoms adjacent in both real and synthetic space and studying…
The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum…
We investigate the geometric phase or Berry phase of adiabatic quantum evolution in an atom-molecule conversion system, and find that the Berry phase in such system consists of two parts: the usual Berry connection term and a novel term…
We present an approach for carrying out non-adiabatic molecular dynamics simulations of systems in which non-adiabatic transitions arise from the coupling between the classical atomic motions and a quasi-continuum of electronic quantum…
We analyze the quantum phase transition for a set of $N$-two level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical…
In these notes, we review the role of Berry phases and topology in noninteracting electron systems. Topics including the adiabatic theorem, parallel transport, and Wannier functions are reviewed, with a focus on the connection to…
We introduce a pedagogical discussion on Bohmian mechanics and its physical implications in connection with the important role played by the quantum phase in the dynamics of quantum processes. In particular, we focus on phenomena such as…
The basic materials of Berry's phase and chiral anomalies are presented to appreciate the phenomena related to those notions. As for Berry's phase, a general survey of the subject is presented using both Lagrangian and Hamiltonian…
The second quantized approach to geometric phases is reviewed. The second quantization generally induces a hidden local (time-dependent) gauge symmetry. This gauge symmetry defines the parallel transport and holonomy, and thus it controls…
Symmetry protected quantization of the Berry phase is discussed in relation to edge states. Assuming an existence of some adiabatic process which protects quantization of the Berry phase, non trivial Berry phase $\gamma=\pm 2\pi\rho$…
Smooth composite bundles provide the adequate geometric description of classical mechanics with time-dependent parameters. We show that the Berry's phase phenomenon is described in terms of connections on composite Hilbert space bundles.
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
It is shown that Berry's phase associated with the adiabatic change of local variables in the Hamiltonian can be used to characterize the multimode Peierls state, which has been proposed as a new type of the ground state of the…
This work is the second part of an investigation aiming at the study of optical wave equations from a field-theoretic point of view. Here, we study classical and quantum aspects of scalar fields satisfying the paraxial wave equation. First,…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
Coherent states, and the Hilbert space representations they generate, provide ideal tools to discuss classical/quantum relationships. In this paper we analyze three separate classical/quantum problems using coherent states, and show that…
An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum…
Unitary evolution in PT-symmetric quantum mechanics with a time-dependent metric is found to yield a new class of adiabatic processes. As an explicit example, a Berry-like phase associated with a PT-symmetric two-level system is derived and…
We investigate quantum phase transitions, quantum criticality, and Berry phase for the ground state of an ensemble of non-interacting two-level atoms embedded in a non-linear optical medium, coupled to a single-mode quantized…