arXiv subjects

Jean-Louis Pichard

Publications and source records attributed to Jean-Louis Pichard.

59 records · Page 4Linked to original sources

arXiv1995

Effective $σ$ Model Formulation for Two Interacting Electrons in a Disordered Metal

We derive an analytical theory for two interacting electrons in a $d$--dimensional random potential. Our treatment is based on an effective random matrix Hamiltonian. After mapping the problem on a nonlinear $σ$ model, we exploit similarities with the theory of disordered metals to identify a scaling parameter, investigate the level correlation function, and study the transport properties of the system. In agreement with recent numerical work we find that pair propagation is subdiffusive and that the pair size grows logarithmically with time.

cond-mat↗

arXiv1995

Brownian motion ensembles and parametric correlations of the transmission eigenvalues: Application to coupled quantum billiards and to disordered wires

The parametric correlations of the transmission eigenvalues $T_i$ of a $N$-channel quantum scatterer are calculated assuming two different Brownian motion ensembles. The first one is the original ensemble introduced by Dyson and assumes an isotropic diffusion for the $S$-matrix. The second Brownian motion ensemble assumes for the transfer matrix $M$ an isotropic diffusion yielded by a multiplicative combination law. We review the qualitative differences between transmission through two weakly coupled quantum dots and through a disordered line and we discuss the mathematical analogies between the Fokker-Planck equations of the two Brownian motion models.

cond-mat↗

arXiv1995

Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix

Using the Fokker-Planck equation describing the evolution of the transmission eigenvalues for Dyson's Brownian motion ensemble, we calculate the magnetoconductance of a ballistic chaotic dot in in the crossover regime from the orthogonal to the unitary symmetry. The correlation functions of the transmission eigenvalues are expressed in terms of quaternion determinants for arbitrary number $N$ of scattering channels. The corresponding average, variance and autocorrelation function of the magnetoconductance are given as a function of the Brownian motion time $t$. A microscopic derivation of this $S$-Brownian motion approach is discussed and $t$ is related to the applied flux. This exactly solvable random matrix model yields the right expression for the suppression of the weak localization corrections in the large $N$-limit and for small applied fluxes. An appropriate rescaling of $t$ could extend its validity to larger magnetic fluxes for the averages, but not for the correlation functions.

cond-mat↗

arXiv1994

Quantum Mesoscopic Scattering: Disordered Systems and Dyson Circular Ensembles

We consider elastic reflection and transmission of electrons by a disordered system characterized by a $2N\!\times\!2N$ scattering matrix $S$. Expressing $S$ in terms of the $N$ radial parameters and of the four $N\!\times\!N$ unitary matrices used for the standard transfer matrix parametrization, we calculate their probability distributions for the circular orthogonal (COE) and unitary (CUE) Dyson ensembles. In this parametrization, we explicitely compare the COE--CUE distributions with those suitable for quasi--$1d$ conductors and insulators. Then, returning to the usual eigenvalue--eigenvector parametrization of $S$, we study the distributions of the scattering phase shifts. For a quasi--$1d$ metallic system, microscopic simulations show that the phase sift density and correlation functions are close to those of the circular ensembles. When quasi--$1d$ longitudinal localization breaks $S$ into two uncorrelated reflection matrices, the phase shift form factor $b(k)$ exhibits a crossover from a behavior characteristic of two uncoupled COE--CUE (small $k$) to a single COE--CUE behavior (large $k$). Outside quasi--one dimension, we find that the phase shift density is no longer uniform and $S$ remains nonzero after disorder averaging. We use perturbation theory to calculate the deviations to the isotropic Dyson distributions. When the electron dynamics is no

cond-mat↗

arXiv1993

Quantum transmission in disordered insulators: random matrix theory and transverse localization

We consider quantum interferences of classically allowed or forbidden electronic trajectories in disordered dielectrics. Without assuming a directed path approximation, we represent a strongly disordered elastic scatterer by its transmission matrix ${\bf t}$. We recall how the eigenvalue distribution of ${\bf t.t}^{\dagger}$ can be obtained from a certain ansatz leading to a Coulomb gas analogy at a temperature $β^{-1}$ which depends on the system symmetries. We recall the consequences of this random matrix theory for quasi--$1d$ insulators and we extend our study to microscopic three dimensional models in the presence of transverse localization. For cubes of size $L$, we find two regimes for the spectra of ${\bf t.t}^{\dagger}$ as a function of the localization length $ξ$. For $L / ξ\approx 1 - 5$, the eigenvalue spacing distribution remains close to the Wigner surmise (eigenvalue repulsion). The usual orthogonal--unitary cross--over is observed for {\it large} magnetic field change $ΔB \approx Φ_0 /ξ^2$ where $Φ_0$ denotes the flux quantum. This field reduces the conductance fluctuations and the average log--conductance (increase of $ξ$) and induces on a given sample large magneto--conductance fluctuations of typical magnitude similar to the sample to sample fluctuations (ergodic behaviour). When $ξ$ is of the order of the

cond-mat↗