arXiv subjects

Alain Comtet

Publications and source records attributed to Alain Comtet.

43 records · Page 3Linked to original sources

arXiv1998

Exact Results on Sinai's Diffusion

We study the continuum version of Sinai's problem of a random walker in a random force field in one dimension. A method of stochastic representations is used to represent various probability distributions in this problem (mean probability density function and first passage time distributions). This method reproduces already known rigorous results and also confirms directly some recent results derived using approximation schemes. We demonstrate clearly, in the Sinai scaling regime, that the disorder dominates the problem and that the thermal distributions tend to zero-one laws.

cond-mat↗

arXiv1997

On the distribution of the Wigner time delay in one-dimensional disordered systems

We consider the scattering by a one-dimensional random potential and derive the probability distribution of the corresponding Wigner time delay. It is shown that the limiting distribution is the same for two different models and coincides with the one predicted by random matrix theory. It is also shown that the corresponding stochastic process is given by an exponential functional of the potential.

cond-mat.dis-nn↗

arXiv1997

Random Operator Approach for Word Enumeration in Braid Groups

We investigate analytically the problem of enumeration of nonequivalent primitive words in the braid group B_n for n >> 1 by analysing the random word statistics and the target space on the basis of the locally free group approximation. We develop a "symbolic dynamics" method for exact word enumeration in locally free groups and bring arguments in support of the conjecture that the number of very long primitive words in the braid group is not sensitive to the precise local commutation relations. We consider the connection of these problems with the conventional random operator theory, localization phenomena and statistics of systems with quenched disorder. Also we discuss the relation of the particular problems of random operator theory to the theory of modular functions

cond-mat.stat-mech↗

arXiv1996

Exponential functionals of Brownian motion and disordered systems

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential functionals in relation with the problem of a particle coupled to a heat bath in a Wiener potential. Explicit expressions for the distribution of the free energy are presented.

cond-mat↗

arXiv1995

ON A DYNAMICAL MODEL OF GLASSES

We analyze a simple dynamical model of glasses, based on the idea that each particle is trapped in a local potential well, which itself evolves due to hopping of neighbouring particles. The glass transition is signalled by the fact that the equilibrium distribution ceases to be normalisable, and dynamics becomes non-stationary. We generically find stretching of the correlation function at low temperatures and a Vogel-Fulcher like behaviour of the terminal time.

cond-mat↗

arXiv1994

Magnetic Moment and Perturbation Theory with Singular Magnetic Fields

The spectrum of a charged particle coupled to Aharonov-Bohm/anyon gauge fields displays a nonanalytic behavior in the coupling constant. Within perturbation theory, this gives rise to certain singularities which can be handled by adding a repulsive contact term to the Hamiltonian. We discuss the case of smeared flux tubes with an arbitrary profile and show that the contact term can be interpreted as the coupling of a magnetic moment spinlike degree of freedom to the magnetic field inside the flux tube. We also clarify the ansatz for the redefinition of the wave function.

cond-mat↗

arXiv1994

Persistent Current of Free Electrons in the Plane

Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $α$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.

cond-mat↗