Related papers: Bloch Theory and Quantization of Magnetic Systems
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
A theoretical investigation of quantum-transport phenomena in mesoscopic systems is presented. In particular, a generalization to ``open systems'' of the well-known semiconductor Bloch equations is proposed. The presence of spatial boundary…
This paper investigates the relationship between algebraic quantum field theories and factorization algebras on globally hyperbolic Lorentzian manifolds. Functorial constructions that map between these two types of theories in both…
We consider a two-dimensional electron gas with Rashba's spin-orbit interaction and two in-plane potentials superimposed along directions perpendicular to each other. The first of these potentials is assumed to be a general periodic…
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows,…
Two field 2-forms on the space-time manifold, in a relationship of duality, are presented and included in the extended phase-space structure used to describe relativistic particles having both electric and magnetic charges. By exterior…
Two classes of observables defined on the configuration space of a particle are quantized, and the effects of the Yang-Mills field are discussed in the context of geometric quantization.
In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those…
Quantum theory of photons based on the first quantization technique, similar to that used by Schroedinger in the formulation of quantum mechanics, is considered. First, scalar quantum mechanics of photons operating with the photon wave…
We consider a system of non-interacting charged particles moving in two dimensions among fixed hard scatterers, and acted upon by a perpendicular magnetic field. Recollisions between charged particles and scatterers are unavoidable in this…
Magnetic singularities known as Bloch points (BPs) present a fundamental challenge for micromagnetic theory, which is based on the assumption of a fixed magnetization vector length. Due to the divergence of the effective field at a BP,…
The micromagnetic singularity, the so-called Bloch point, can form a metastable state in the nanosphere. We classify possible types of Bloch points and derive analytically the shape of magnetization distribution inside different Bloch…
The synthesis of molecular magnets has undergone rapid progress in recent years. Each of the identical molecular units can contain as few as two and up to several dozens of paramagnetic ions (spins). Although these materials appear as…
Bloch-type equations for description of coherent transport in mesoscopic systems are applied for a study of the continuous measurement process. Both the detector and the measured system are described quantum mechanically. It is shown that…
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to set the foundations for a study of weak solutions defined on…
We study the phase space structure and the quantization of a pointlike particle in 2+1 dimensional gravity. By adding boundary terms to the first order Einstein Hilbert action, and removing all redundant gauge degrees of freedom, we arrive…
We review known results on the relations between conformal field theory, the quantization of moduli spaces of flat PSL(2,R)-connections on Riemann surfaces, and the quantum Teichmueller theory.
Theory of pointlike magnetic monopole with an arbitrary magnetic charge is considered. It is shown that a proper description requires making use of nonunitary representations of the rotation group and the nonassociative generalization of…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pairing between quantitative operator $K$-theory and Lipschitz…