Related papers: Integration by parts formulae for degenerate diffu…
Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic functions extending earlier work in the elliptic case. Emphasis is placed on developing integration by parts formulas at the level of local martingales.…
Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
Modern geometric measure theory, developed largely to solve the Plateau problem, has generated a great deal of technical machinery which is unfortunately regarded as inaccessible by outsiders. Some of its tools (e.g., flat norm distance and…
We consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold that is the product of the total space of…
This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
Some new results on geometry of classical parabolic Monge-Amp\`ere equations (PMA) are presented. PMAs are either \emph{integrable}, or \emph{nonintegrable} according to integrability of its characteristic distribution. All integrable PMAs…
In this paper, we present a novel approach for analyzing the relationship between the supports of conditional measures and their geometric arrangement in Wasserstein space via the disintegration map. Our method establishes criteria to…
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction,…
We consider subdiffusion of a particle in a one-dimensional system with a thin partially permeable wall. Passing through the wall, the particle can be absorbed with a certain probability. We call such a wall partially permeable partially…
Coherent steering of a quantum state, induced by a sequence of weak measurements, has become an active area of theoretical and experimental study. For a closed steered trajectory, the underlying phase factors involve both geometrical and…
We propose a formulation of an absorbing boundary for a quantum particle. The formulation is based on a Feynman-type integral over trajectories that are confined to the non-absorbing region. Trajectories that reach the absorbing wall are…
We to define a Path Integral in Lorentzian time by restricting the relevant domain of integration on $C([0,1],M)$ over a Riemannian configuration manifold $(M,g)$ and considering the dynamics of a particle evolving between to fixed…
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
This note is devoted to representation of some evolution semigroups. The semigroups are generated by pseudo-differential operators, which are obtained by different (parametrized by a number $\tau$) procedures of quantization from a certain…
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…
Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…
The paper deals with the problem of integration of equations of motion in nonholonomic systems. By means of well-known theory of the differential equations with an invariant measure the new integrable systems are discovered. Among them…
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…