اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدFluctuations of the Lyapunov exponent in 2D disordered systems
108
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis.
قيم البحث
اقرأ أيضاً
We employ a functional renormalization group to study interfaces in the presence of a pinning potential in $d=4-epsilon$ dimensions. In contrast to a previous approach [D.S. Fisher, Phys. Rev. Lett. {bf 56}, 1964 (1986)] we use a soft-cutoff scheme.
With the method developed here we confirm the value of the roughness exponent $zeta approx 0.2083 epsilon$ in order $epsilon$. Going beyond previous work, we demonstrate that this exponent is universal. In addition, we analyze the generation of higher cumulants in the disorder distribution and the role of temperature as a dangerously irrelevant variable.
Products of random matrix products of $mathrm{SL}(2,mathbb{R})$, corresponding to transfer matrices for the one-dimensional Schrodinger equation with a random potential $V$, are studied. I consider both the case where the potential has a finite secon
d moment $langle V^2rangle<infty$ and the case where its distribution presents a power law tail $p(V)sim|V|^{-1-alpha}$ for $0<alpha<2$. I study the generalized Lyapunov exponent of the random matrix product (i.e. the cumulant generating function of the logarithm of the wave function). In the high energy/weak disorder limit, it is shown to be given by a universal formula controlled by a unique scale (single parameter scaling). For $langle V^2rangle<infty$, one recovers Gaussian fluctuations with the variance equal to the mean value: $gamma_2simeqgamma_1$. For $langle V^2rangle=infty$, one finds $gamma_2simeq(2/alpha),gamma_1$ and non Gaussian large deviations, related to the universal limiting behaviour of the conductance distribution $W(g)sim g^{-1+alpha/2}$ for $gto0$.
In a recent publication, J. Phys.: Condens. Matt. 14 13777 (2002), Kuzovkov et. al. announced an analytical solution of the two-dimensional Anderson localisation problem via the calculation of a generalised Lyapunov exponent using signal theory. Surp
risingly, for certain energies and small disorder strength they observed delocalised states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy to use a generalised Lyapunov exponent for studying Anderson localisation.
The nonlinear behavior of the Hall resistivity at low magnetic fields in single quantum well GaAs/In$_x$Ga$_{1-x}$As/GaAs heterostructures with degenerated electron gas is studied. It has been found that this anomaly is accompanied by the weaker temp
erature dependence of the conductivity as compared with that predicted by the first-order theory of the quantum corrections to the conductivity. We show that both effects in strongly disordered systems stem from the second order quantum correction caused by the effect of weak localization on the interaction correction and vice versa. This correction contributes mainly to the diagonal component of the conductivity tensor, it depends on the magnetic field like the weak localization correction and on the temperature like the interaction contribution.
Entanglement is a physical resource of a quantum system just like mass, charge or energy. Moreover it is an essential tool for many purposes of nowadays quantum information processing, e.g. quantum teleportation, quantum cryptography or quantum compu
tation. In this work we investigate an extended system of N qubits. In our system a qubit is the absence or presence of an electron at a site of a tight-binding system. Several measures of entanglement between a given qubit and the rest of the system and also the entanglement between two qubits and the rest of the system is calculated in a one-electron picture in the presence of disorder. We invoke the power law band random matrix model which even in one dimension is able to produce multifractal states that fluctuate at all length scales. The concurrence, the tangle and the entanglement entropy all show interesting scaling properties.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
