Related papers: Quantum Ergodicity and Mixing
Various applications of quantum algebraic techniques in nuclear structure physics and molecular physics are briefly reviewed. Contains 81 references.
The development of classical ergodic theory has had a significant impact in the areas of mathematics, physics, and, in general, applied sciences. The quantum ergodic theory of Hamiltonian dynamics has its motivations to understand…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
Quantum electrodynamics near a boundary is investigated by considering the inertial mass shift of an electron near a dielectric or conducting surface. We show that in all tractable cases the shift can be written in terms of integrals over…
A brief exposition of the point of higher topos theory in (mathematical) physics, commissioned for the Encyclopedia of Mathematical Physics 2nd ed.
This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006).
A view on the physical meaning of the so called ergodic hypothesis: its role on the foundations of equilibrium statistical mechanics in mid '800, its interpretations and hints at its relevance for modern nonequilibrium statistical…
We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.
In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…
This paper briefly summarizes previous work on complex classical mechanics and its relation to quantum mechanics. It then introduces a previously unstudied area of research involving the complex particle trajectories associated with…
The physical reasons in favour of a two dimensional topological model of quantum electrodynamics are discussed. It is shown that in accord with this model there is a new uncertainty relation for photon which is compatible with QED.
In this note we review recent progress in the problem of mixing for a nonlinear PDE of parabolic type, perturbed by a bounded random force.
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…
An encyclopedia article on mathematical aspects of quantum field theory in curved spacetime. Section titles are: Introduction and preliminaries; Construction of *-algebra for a real linear scalar field on globally hyperbolic spacetimes and…
This is an expository article on the techniques of quantization as they are applied to Gromov-Witten theory and related areas.
This is a research announcement of the theory of orbifold quantum cohomology.
This is a reference volume on polyfold and Fredholm theory.
Sec I - Introduction Sec II - Equilibrium properties: generalities and methodology Sec III - Equilibrium properties: some important quantities Sec IV - Dynamical properties: heuristic approach Sec V - Dynamical properties: stochastic…
In this survey article for the Encyclopedia of Mathematical Physics, 2nd Edition, I give an introduction to quantum character varieties and quantum character stacks, with an emphasis on the unification between four different approaches to…