The Local Time Distribution of a Particle Diffusing on a Graph

We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show that the asymptotic behavior of this distribution has non-Gaussian tails characterized by a nontrivial large deviation function.Comment: 8 pages, two figures (included

Localization effects in a periodic quantum graph with magnetic field and spin-orbit interaction

A general technique for the study of embedded quantum graphs with magnetic fields and spin-orbit interaction is presented. The analysis is used to understand the contribution of Rashba constant to the extreme localization induced by magnetic field in the T3 shaped quantum graph. We show that this effect is destroyed at generic values of the Rashba constant. On the other hand, for certain combinations of the Rashba constant and the magnetic parameters another series of infinitely degenerate eigenvalues appears.Comment: 25 pages, typos corrected, references extende

Flow effects on multifragmentation in the canonical model

A prescription to incorporate the effects of nuclear flow on the process of multifragmentation of hot nuclei is proposed in an analytically solvable canonical model. Flow is simulated by the action of an effective negative external pressure. It favors sharpening the signatures of liquid-gas phase transition in finite nuclei with increased multiplicity and a lowered phase transition temperature.Comment: 13 pages, 5 Post Script figures (accepted for publication in PRC

Surgical treatment of large incisional hernias by intraperitoneal insertion of Parietex® composite mesh with an associated aponeurotic graft (280 cases)

AIMS OF THE STUDY: To evaluate post-operative complications and the recurrence rate after repair of large ventral incisional hernia with an open technique using intraperitoneal composite mesh and an associated aponeurotic overlay. PATIENTS AND METHODS: This prospective study included a total of 280 patients who underwent repair of large incisional hernia using Parietex(®) composite mesh. RESULTS: The post-operative mortality rate was 0.35%. Six patients (2%) developed subcutaneous surgical site infection without infection of the prosthesis. Six other patients (2%) developed a deep-seated infection; in three cases, the mesh had to be removed. Nine patients (3.2%) developed recurrent incisional hernia. CONCLUSION: Large ventral incisional hernias can be effectively treated by the intraperitoneal placement of Parietex(®) composite mesh overlaid by an aponeurotic graft; the incidence of complications in this prospective study was very low

Brownian Motion in wedges, last passage time and the second arc-sine law

We consider a planar Brownian motion starting from $O$ at time $t=0$ and stopped at $t=1$ and a set $F= \{OI_i ; i=1,2,..., n\}$ of $n$ semi-infinite straight lines emanating from $O$. Denoting by $g$ the last time when $F$ is reached by the Brownian motion, we compute the probability law of $g$. In particular, we show that, for a symmetric $F$ and even $n$ values, this law can be expressed as a sum of $\arcsin$ or $(\arcsin)^2$ functions. The original result of Levy is recovered as the special case $n=2$. A relation with the problem of reaction-diffusion of a set of three particles in one dimension is discussed

Statistical Interparticle Potential of an Ideal Gas of Non-Abelian Anyons

We determine and study the statistical interparticle potential of an ideal system of non-Abelian Chern-Simons (NACS) particles, comparing our results with the corresponding results of an ideal gas of Abelian anyons. In the Abelian case, the statistical potential depends on the statistical parameter and it has a "quasi-bosonic" behaviour for statistical parameter in the range (0,1/2) (non-monotonic with a minimum) and a "quasi-fermionic" behaviour for statistical parameter in the range (1/2,1) (monotonically decreasing without a minimum). In the non-Abelian case the behavior of the statistical potential depends on the Chern- Simons coupling and the isospin quantum number: as a function of these two parameters, a phase diagram with quasi-bosonic, quasi-fermionic and bosonic-like regions is obtained and investigated. Finally, using the obtained expression for the statistical potential, we compute the second virial coefficient of the NACS gas, which correctly reproduces the results available in literature.Comment: 21 pages, 4 color figure

Scattering theory on graphs

We consider the scattering theory for the Schr\"odinger operator -\Dc_x^2+V(x) on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves matrices that couple arcs (oriented bonds), the other involves matrices that couple vertices. We discuss a simple way to tune the coupling between the graph and the leads. The efficiency of the formalism is demonstrated on a few known examples.Comment: 21 pages, LaTeX, 10 eps figure

Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each link. We establish the boundary conditions to be used at the vertices and we derive general expressions for the average time spent on a part of the graph before absorption and, also, for the Laplace transform of the joint law of the occupation times. Exit times distributions and splitting probabilities are also studied and several examples are discussed.Comment: Accepted for publication in J. Phys.

Distribution of the area enclosed by a 2D random walk in a disordered medium

The asymptotic probability distribution for a Brownian particle wandering in a 2D plane with random traps to enclose the algebraic area A by time t is calculated using the instanton technique.Comment: 4 pages, ReVTeX. Phys. Rev. E (March 1999), to be publishe