arXiv subjects

E. Hofstetter

Publications and source records attributed to E. Hofstetter.

6 recordsLinked to original sources

arXiv1998

Disordered systems and the metal-insulator Transition: A super universality class

The critical behaviour of three-dimensional disordered systems is investigated by analysing the spectral fluctuations of the energy spectrum. Our results suggest that the initial symmetries (orthogonal, unitary and symplectic) are broken by the disorder at the critical point. The critical behaviour, determinedby the symmetry at the critical point, should therefore be independent of the previous invariances and be described by a ``super'' universality class. This result is strongly supported by the fact that we obtain the same critical exponent $ν\simeq 1.35$ in the three cases: orthogonal, unitary and symplectic.

cond-mat.dis-nn↗

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

Critical behaviour at the metal-insulator transition in 3-dimensional disordered systems in a strong magnetic field

The critical behaviour of 3-dimensional disordered systems in a strong magnetic field is investigated by analysing the spectral fluctuations of the energy spectrum. The level spacing distribution $P(s)$ as well the Dyson-Mehta statistics $Δ_{3}(L)$ are considered. Except for the small $s$ behaviour of $P(s)$, which depends on the presence or absence of a magnetic field but not on its strength, the other quantities, large $s$ behaviour of $P(s)$ and $Δ_{3}(L)$, turn out to be independent of its presence or absence and therefore of the time reversal symmetry. This suggests that the metal-insulator transition, which is defined by the symmetry of the system {\it at} the critical point, is independent of the presence or absence of the time reversal symmetry.

cond-mat↗

arXiv1995

2-Dimensional Electron Gas in a Linearly Varying Magnetic Field. ``Quantisation'' of the Electron and Current Density

We have developed new methods to calculate dispersion curves (analytically in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field varies linearly with position and the results provide useful insights into the properties of this and other field distributions. We consider spin as well as a confining electrostatic potential. We show that the electron and the current density exhibit a very rich structure related to the quantisation of the energy. Moreover there is a direct contribution to the current density due to the spin which could be of interest in relation to spin polarised current.

cond-mat↗

arXiv1994

Does a magnetic field modify the critical behaviour at the metal-insulator transition in 3-dimensional disordered systems?

The critical behaviour of 3-dimensional disordered systems with magnetic field is investigated by analyzing the spectral fluctuations of the energy spectrum. We show that in the thermodynamic limit we have two different regimes, one for the metallic side and one for the insulating side with different level statistics. The third statistics which occurs only exactly at the critical point is {\it independent} of the magnetic field. The critical behaviour which is determined by the symmetry of the system {\it at} the critical point should therefore be independent of the magnetic field.

cond-mat↗

arXiv1994

Relation between Energy Level Statistics and Phase Transition and its Application to the Anderson Model

A general method to describe a second-order phase transition is discussed. It starts from the energy level statistics and uses of finite-size scaling. It is applied to the metal-insulator transition (MIT) in the Anderson model of localization, evaluating the cumulative level-spacing distribution as well as the Dyson-Metha statistics. The critical disorder $W_{c}=16.5$ and the critical exponent $ν=1.34$ are computed.

cond-mat↗