Within the framework of classical field theory, the connection between theDirac field as the field of matter and the spacetime metric is discussed.Polarization structure of the Dirac field is shown to be rich enough todetermine the spacetime metric locally and

We discuss the exact discretization of the classical harmonic oscillatorequation (including the inhomogeneous case and multidimensionalgeneralizations) with a special stress on the energy integral. We present andsuggest some numerical applications.

We present a generalization of the method of the local relaxation flow toestablish the universality of local spectral statistics of a broad class oflarge random matrices. We show that the local distribution of the eigenvaluescoincides with the local statistics of

We study geometric consistency relations between angles of 3-dimensional (3D)circular quadrilateral lattices -- lattices whose faces are planarquadrilaterals inscribable into a circle. We show that these relations generatecanonical transformations of a remarkable "ultra-local" Poisson bracket algebradefined on discrete 2D surfaces

The problem of skin effect with arbitrary specularity in maxwellian plasmawith specular--diffuse boundary conditions is solved. A new analytical methodis developed that makes it possible to to obtain a solution up to an arbitrarydegree of accuracy. The method is based

We study the divergence of the solution to a Schr\"odinger-type amplifierdriven by the square of a Gaussian noise in presence of a random potential. Wefollow the same approach as Mounaix, Collet, and Lebowitz (MCL) in terms of adistributional formulation of

Let \Lambda be a finite subset of Z^d. We study the following sandpile modelon \Lambda. The height at any given vertex x of \Lambda is a positive realnumber, and additions are uniformly distributed on some interval [a,b], whichis a subset

Discussed is relationship between nonlinearity and symmetry of dynamicalmodels. The special stress is laid on essential, non-perturbative nonlinearity,when none linear background does exist. This is nonlinearity essentiallydifferent from ones given by nonlinear corrections imposed onto some linearbackground. In a sense

Cette these est consacree a l' etude de differents modeles aleatoires depolymeres. On s'interesse en particulier a l'influence du desordre sur lalocalisation des trajectoires pour les modeles d'accrochage et pour lespolymeres diriges en milieu aleatoire. En plus des modeles classiques

In this paper we consider the model of $n$ non-intersecting squared Besselprocesses with parameter $\alpha$, in the confluent case where all particlesstart, at time $t=0$, at the same positive value $x=a$, remain positive, andend, at time $T=t$, at the position

The Cartan model of SO(3)/SO(2) matrices is applied to reduce of rotationaldegrees of freedom on coadjoint orbits of u^*(3) Poisson algebra. Theseven--dimensional Poisson algebra u_SO(3) obtained by SO(3) reduction ofu^*(3) algebra is found and canonical parametrization of u^*(3) orbits[p_1,p_2,p_3] is

We introduce new examples of mappings defining noncommutative root spacegeneralizations for the Witt, Ricci flow, and Poisson bracket continual Liealgebras.

The totally asymmetric simple exclusion process (TASEP) on Z with theBernoulli-rho measure as initial conditions, 0

A review of the stochastic stability property for the Gaussian spin glassmodels is presented and some perspectives discussed.

Instantonic theories are quantum field theories where all correlators aredetermined by integrals over the finite-dimensional space (space of generalizedinstantons). We consider novel geometrical observables in instantonictopological quantum mechanics that are strikingly different from standardevaluation observables. These observables allow jumps of

We discuss transport equations resulting from relativistic diffusions in theproper time. We show that a solution of the transport equation can be obtainedfrom the solution of the diffusion equation by means of an integration over theproper time. We study the

Canonical quantisation of constrained systems with first class constraintsvia Dirac's operator constraint method proceeds by the thory of Rigged Hilbertspaces, sometimes also called Refined Algebraic Quantisation (RAQ). This methodcan work when the constraints form a Lie algebra. When the constraints

In this work we study the Hilbert space space of N-valent SU(2) intertwinerswith fixed total spin, which can be identified, at the classical level, with aspace of convex polyhedra with N face and fixed total boundary area. We showthat this

We consider construction of Lagrangians which are candidates for p-adicsector of an adelic open scalar string. Such Lagrangians have their origin inLagrangian for a single p-adic string and contain the Riemann zeta functionwith the d'Alembertian in its argument. In particular,