اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNonmonotonic confining potential and eigenvalue density transition for generalized random matrix model
150
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent $gamma$ (called the $gamma$-ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with $gamma=1$ (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the $gamma$-ensembles. It enables us to numerically compute the eigenvalue density of $gamma$-ensembles for all $gamma > 0$. We show that one important effect of the two-particle interaction parameter $gamma$ is to generate or enhance the non-monotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing $gamma$ can lead to a large non-monotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of $gamma$-ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.
قيم البحث
اقرأ أيضاً
We introduce a log-gas model that is a generalization of a random matrix ensemble with an additional interaction, whose strength depends on a parameter $gamma$. The equilibrium density is computed by numerically solving the Riemann-Hilbert problem as
sociated with the ensemble. The effect of the additional parameter $gamma$ associated with the two-body interaction can be understood in terms of an effective $gamma$-dependent single-particle confining potential.
Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known as highly relevant, in topics rang
ing from ferroelectrics to quotation networks. Combining these two points leads to examine finite size random matrices. To obtain basic materials properties, the Green function associated to the matrix has to be calculated. In order to obtain the first finite size correction a perturbative scheme is hereby developed within the framework of the replica method. The averaged eigenvalue spectrum and the corresponding Green function of Wigner random sign real symmetric N x N matrices to order 1/N are in fine obtained analytically. Related simulation results are also presented. The comparison between the analytical formulae and finite size matrices numerical diagonalization results exhibits an excellent agreement, confirming the correctness of the first order finite size expression.
The geometry of multi-parameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert-sp
ace geometry of eigenstates of parameter-dependent random-matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian Unitary Ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature. We discuss relations to Levy stable distributions and compare our results to numerical simulations of random-matrix ensembles as well as electrons in a random magnetic field.
We analyze the scattering properties of a periodic one-dimensional system at criticality represented by the so-called power-law banded random matrix model at the metal insulator transition. We focus on the scaling of Wigner delay times $tau$ and reso
nance widths $Gamma$. We found that the typical values of $tau$ and $Gamma$ (calculated as the geometric mean) scale with the system size $L$ as $tau^{tiny typ}propto L^{D_1}$ and $Gamma^{tiny typ} propto L^{-(2-D_2)}$, where $D_1$ is the information dimension and $D_2$ is the correlation dimension of eigenfunctions of the corresponding closed system.
* ACTIVATED RANDOM WALK MODEL * This is a conservative particle system on the lattice, with a Markovian continuous-time evolution. Active particles perform random walks without interaction, and they may as well change their state to passive, then sto
pping to jump. When particles of both types occupy the same site, they all become active. This model exhibits phase transition in the sense that for low initial densities the system locally fixates and for high densities it keeps active. Though extensively studied in the physics literature, the matter of giving a mathematical proof of such phase transition remained as an open problem for several years. In this work we identify some variables that are sufficient to characterize fixation and at the same time are stochastically monotone in the models parameters. We employ an explicit graphical representation in order to obtain the monotonicity. With this method we prove that there is a unique phase transition for the one-dimensional finite-range random walk. Joint with V. Sidoravicius. * BROKEN LINE PROCESS * We introduce the broken line process and derive some of its properties. Its discrete version is presented first and a natural generalization to the continuum is then proposed and studied. The broken lines are related to the Young diagram and the Hammersley process and are useful for computing last passage percolation values and finding maximal oriented paths. For a class of passage time distributions there is a family of boundary conditions that make the process stationary and reversible. One application is a simple proof of the explicit law of large numbers for last passage percolation with exponential and geometric distributions. Joint with V. Sidoravicius, D. Surgailis, and M. E. Vares.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
