# LPTMS Publications

Archives :

• ## Correlation functions for some conformal theories on Riemann surfaces

### Michael Monastyrsky 1, Sergei K. Nechaev 2, 3

#### Modern Physics Letters A 12 (1997) 589-596

We discuss the geometrical connection between 2D conformal field theories, random walks on hyperbolic Riemann surfaces and knot theory. For the wide class of CFTs with monodromies being the discrete subgroups of SL(2,R), the determination of four-point correlation functions are related to construction of topological invariants for random walks on multipunctured Riemann surfaces

• 1. Institute of Theoretical and Experimental Physics, Institute of Theoretical and Experimental Physics
• 2. Landau Institute for Theoretical Physics, Landau Institute for Theoretical Physics
• 3. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Density Correlations of Magnetic Impurities and Disorder

### Jean Desbois 1, Cyril Furtlehner 1, Stéphane Ouvry 1

#### Journal of Physics A 30 (1997) 7291-7300

We consider an electron coupled to a random distribution of point vortices in the plane (magnetic impurities). We analyze the effect of the magnetic impurities on the density of states of the test particle, when the magnetic impurities have a spatial probability distribution governed by Bose or Fermi statistic at a given temperature. Comparison is made with the Poisson distribution, showing that the zero temperature Fermi distribution corresponds to less disorder. A phase diagram describing isolated impurities versus Landau level oscillations is proposed.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Hall Conductivity for Two Dimensional Magnetic Systems

### Jean Desbois 1, Stephane Ouvry 1, Christophe Texier 1

#### Nuclear Physics B 500 (1997) 486-510

A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic field, with the additional coupling of the spin degree of freedom of the electron to the local magnetic field (Pauli Hamiltonian). As an example, the homogeneous magnetic field Hall conductivity is rederived. The case of the vortex at the origin is worked out in detail. This system happens to display a transverse Hall conductivity ($P$ breaking effect) which is subleading in volume compared to the homogeneous field case, but diverging at small frequency like $1/\\omega^2$. A perturbative analysis is proposed for the conductivity in the random magnetic impurity problem (Poissonian vortices in the plane). At first order in perturbation theory, the Hall conductivity displays oscillations close to the classical straight line conductivity of the mean magnetic field.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

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• ## Mean field and corrections for the Euclidean Minimum Matching problem

### Jacques Boutet de Monvel 1, Olivier C. Martin 1

#### Physical Review Letters 79 (1997) 167-170

Consider the length $L_{MM}^E$ of the minimum matching of N points in d-dimensional Euclidean space. Using numerical simulations and the finite size scaling law $< L_{MM}^E > = \\beta_{MM}^E(d) N^{1-1/d}(1+A/N+... )$, we obtain precise estimates of $\\beta_{MM}^E(d)$ for $2 \\le d \\le 10$. We then consider the approximation where distance correlations are neglected. This model is solvable and gives at $d \\ge 2$ an excellent random link\'\' approximation to $\\beta_{MM}^E(d)$. Incorporation of three-link correlations further improves the accuracy, leading to a relative error of 0.4% at d=2 and 3. Finally, the large d behavior of this expansion in link correlations is discussed.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

Details Citations to the Article (5)
• ## On the distribution of the Wigner time delay in one-dimensional disordered systems

### Alain Comtet 1, 2, Christophe Texier 2

#### Journal of Physics A 30 (1997) 8017-8025

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.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. LPTPE, Université Paris VI - Pierre et Marie Curie

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• ## Percolation Transition in the random antiferromagnetic spin-1 chain

### C. Monthus 1, O. Golinelli 1, Th. Jolicoeur 1

#### Physical Review Letters 79 (1997) 3254-3257

We give a physical description in terms of percolation theory of the phase transition that occurs when the disorder increases in the random antiferromagnetic spin-1 chain between a gapless phase with topological order and a random singlet phase. We study the statistical properties of the percolation clusters by numerical simulations, and we compute exact exponents characterizing the transition by a real-space renormalization group calculation.

• 1. Service de Physique Théorique (SPhT), CNRS : URA2306 – CEA : DSM/SPHT

Details Citations to the Article (63)
• ## Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems

### D. Ullmo 1, 2, K. Richter 3, H. U. Baranger 1, F. Von Oppen 4, R. A. Jalabert 5

#### Physica E: Low-dimensional Systems and Nanostructures 1 (1997) 238-273

We study interaction effects on the orbital magnetism of diffusive mesoscopic quantum systems. By combining many-body perturbation theory with semiclassical techniques, we show that the interaction contribution to the ensemble averaged quantum thermodynamic potential can be reduced to an essentially classical operator. We compute the magnetic response of disordered rings and dots for diffusive classical dynamics. Our semiclassical approach reproduces the results of previous diagrammatic quantum calculations.

• 1. Bell Laboratories-Lucent Technologies, Bell Laboratories
• 2. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 3. Max-Planck-Institut für Physik komplexer Systeme, Max-Planck-Institut
• 4. Department of Condensed Matter Physics, Weizmann Institute of Science
• 5. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS), CNRS : UMR7504 – Université Louis Pasteur - Strasbourg I

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• ## The random link approximation for the Euclidean traveling salesman problem

### N. J. Cerf 1, J. Boutet de Monvel 1, O. Bohigas 1, O. C. Martin 1, A. G. Percus 1

#### Journal de Physique I 7 (1997) 117-136

The traveling salesman problem (TSP) consists of finding the length of the shortest closed tour visiting N cities\'\'. We consider the Euclidean TSP where the cities are distributed randomly and independently in a d-dimensional unit hypercube. Working with periodic boundary conditions and inspired by a remarkable universality in the kth nearest neighbor distribution, we find for the average optimum tour length = beta_E(d) N^{1-1/d} [1+O(1/N)] with beta_E(2) = 0.7120 +- 0.0002 and beta_E(3) = 0.6979 +- 0.0002. We then derive analytical predictions for these quantities using the random link approximation, where the lengths between cities are taken as independent random variables. From the cavity\'\' equations developed by Krauth, Mezard and Parisi, we calculate the associated random link values beta_RL(d). For d=1,2,3, numerical results show that the random link approximation is a good one, with a discrepancy of less than 2.1% between beta_E(d) and beta_RL(d). For large d, we argue that the approximation is exact up to O(1/d^2) and give a conjecture for beta_E(d), in terms of a power series in 1/d, specifying both leading and subleading coefficients.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud

Details Citations to the Article (9)
• ## Uniform approximation for diffractive contributions to the trace formula in billiard systems

### Martin Sieber 1, 2, Nicolas Pavloff 1, Charles Schmit 1

#### Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 55 (1997) 2279-2299

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller\'s trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.

• 1. Division de Physique Théorique, IPN, Université Paris XI - Paris Sud
• 2. Abteilung Theoretische Physik, Universität Ulm