arXiv subjects

G. Montambaux

Publications and source records attributed to G. Montambaux.

45 records · Page 3Linked to original sources

arXiv1998

Many-body spectral statistics of interacting Fermions

We have studied the appearance of chaos in the many-body spectrum of interacting Fermions. The coupling of a single state to the Fermi sea is considered. This state is coupled to a hierarchy of states corresponding to one or several particle-hole excitations. We have considered various couplings between two successive generations of this hierarchy and determined under which conditions this coupling can lead to Wigner-Dyson correlations. We have found that the cross-over from a Poisson to a Wigner distribution is characterized not only by the ratio $V/Δ_c$, but also by the ratio $Δ_c/δ$. $V$ is the typical interaction matrix element, $δ$ is the energy distance between {\it many-body} states and $Δ_c$ is the distance between many-body states coupled by the interaction.

cond-mat.mes-hall↗

arXiv1998

Boundary conditions at the mobility edge

It is shown that the universal behavior of the spacing distribution of nearest energy levels at the metal--insulator Anderson transition is indeed dependent on the boundary conditions. The spectral rigidity $Σ^2(E)$ also depends on the boundary conditions but this dependence vanishes at high energy $E$. This implies that the multifractal exponent $D_2$ of the participation ratio of wave functions in the bulk is not affected by the boundary conditions.

cond-mat.mes-hall↗

arXiv1998

Comment on "Peierls Gap in Mesoscopic Ring Threated by a Magnetic Flux"

In a recent letter, Yi et al. PRL 78, 3523 (1997), have considered the stability of a Charge Density Wave in a one-dimensional ring, in the presence of an Aharonov-Bohm flux. This comment shows that, in one dimension, the stability of the Charge Density Wave depends on the parity of the number of electrons in the ring. This effect is similar to the parity effect known for the persistent current in one-dimensional rings.

cond-mat.mes-hall↗

arXiv1998

The Quantum Hall Effect in Quasi-1D Conductors

The theory and experiments showing Quantum Hall effect in the quasi-one-dimensional conductors of the Bechgaard salts family are briefly reviewed. The sign reversals observed under some experimental conditions are explained within the framework of the Quantized Nesting Model. The sequence of reversals is driven by slight modifications of the geometry of the Fermi surface. It is explained why only even phases can have sign reversals and why negative phases are less stable than positive ones.

cond-mat↗

arXiv1996

Level Curvatures and Conductances: A Numerical Study of the Thouless Relation

The Thouless conjecture states that the average conductance of a disordered metallic sample in the diffusive regime can be related to the sensitivity of the sample's spectrum to a change in the boundary conditions. Here we present results of a direct numerical study of the conjecture for the Anderson model. They were obtained by calculating the Landauer-Büttiker conductance $g_L$ for a sample connected to perfect leads and the distribution of level curvatures for the same sample in an isolated ring geometry, when the ring is pierced by an Aharonov-Bohm flux. In the diffusive regime ($L\gg l_e$) the average conductance $g_L$ is proportional to the mean absolute curvature $< |c| >$: $ g_L = π<| c | > / Δ$, provided the system size $L$ is large enough, so that the contact resistance can be neglected. $l_e$ is the elastic mean free path, $Δ$ is the mean level spacing. When approaching the ballistic regime, the limitation of the conductance due to the contact resistance becomes essential and expresses itself in a deviation from the above proportionality. However, in both regimes and for all system sizes the same proportionality is recovered when the contact resistance is subtracted from the inverse conductance, showing that the ``curvatures measure the conductance in the bulk''. In the localized regime, the mean logarithm of the absolute curvature and the mean logarithm of the Landauer-Büttiker conductance are proportional.

cond-mat.mes-hall↗

arXiv1996

Sign reversals of the Quantum Hall Effect in quasi-1D conductors

The sign reversals of the Quantum Hall Effect observed in quasi-one-dimensional conductors of the Bechgaard salts family are explained within the framework of the quantized nesting model. The sequence of reversals is driven by slight modifications of the geometry of the Fermi surface. It is explained why only even phases can have signign reversals and why negative phases are less stable than positive ones.

cond-mat↗

arXiv1995

Phase Diagram for Charge Density Waves in a Magnetic Field

The influence of an external magnetic field on a quasi one-dimensional system with a charge density wave (CDW) instability is treated within the random phase approximation which includes both CDW and spin density wave correlations. We show that the CDW is sensitive to both orbital and Pauli effects of the field. In the case of perfect nesting, the critical temperature decreases monotonously with the field, and the wave vector of the instability starts to shift above some critical value of magnetic field. Depending on the ratio between the spin and charge coupling constants and on the direction of the applied magnetic field, the wave vector shift is either parallel ($CDW_x$ order) or perpendicular ($CDW_y$ order) to the most conducting direction. The $CDW_x$ order is a field dependent linear combination of the charge and spin density waves and is sensible only to the Pauli effect. The wave vector shift in $CDW_y$ depends on the interchain coupling, but the critical temperature does not. This order is affected by the confinement of the electronic orbits. By increasing the relative strength of the orbital effect with respect to the Pauli effect, one can destroy the $CDW_y$, establishing either a $CDW_x$, or a $CDW_0$ (corresponding to perfect nesting wave vector). We also show that by increasing the imperfect nesting parameter, one passes from the regime where the critical temperature decreases with the field to the regime where it is initially enhanced by the orbital effect and eventually suppressed by the Pauli effect. For a bad nesting, the quantized phases of the field-induced CDW appear.

cond-mat↗

arXiv1995

Spectral Correlations from the Metal to the Mobility Edge

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R(s,s')$. In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $<δn^2(s)>$ predicted by Al'tshuler and Shklovski\uı. At the transition, at small energy scales, $R(s-s')$ starts linearly, with a slope larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-γ}$ with $c \sim 0.041$ and $γ\sim 0.83$, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $\tilde K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance contains two terms $<δn^2(s) >= B < n >^γ+ 2 π\tilde K(0)< n > where $\tilde{K}(0)$ is the limit of the form factor for $t \to 0$.

cond-mat↗

arXiv1993

Persistent Currents in 1D Disordered Rings of Interacting Electrons

We calculate the persistent current of 1D rings of spinless fermions with short-range interactions on a lattice with up to 20 sites, and in the presence of disorder, for various band fillings. We find that {\it both} disorder and interactions always decrease the persistent current by localizing the electrons. Away from half-filling, the interaction has a much stronger influence in the presence of disorder than in the pure case.

cond-mat↗