اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPower law eigenvalue density, scaling and critical random matrix ensembles
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.
قيم البحث
اقرأ أيضاً
The correlation length $xi$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to
the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.
We propose a generic scaling theory for critical phenomena that includes power-law and essential singularities in finite and infinite dimensional systems. In addition, we clarify its validity by analyzing the Potts model in a simple hierarchical netw
ork, where a saddle-node bifurcation of the renormalization-group fixed point governs the essential singularity.
We discuss shortest-path lengths $ell(r)$ on periodic rings of size L supplemented with an average of pL randomly located long-range links whose lengths are distributed according to $P_l sim l^{-xpn}$. Using rescaling arguments and numerical simulati
on on systems of up to $10^7$ sites, we show that a characteristic length $xi$ exists such that $ell(r) sim r$ for $r<xi$ but $ell(r) sim r^{theta_s(xpn)}$ for $r>>xi$. For small p we find that the shortest-path length satisfies the scaling relation $ell(r,xpn,p)/xi = f(xpn,r/xi)$. Three regions with different asymptotic behaviors are found, respectively: a) $xpn>2$ where $theta_s=1$, b) $1<xpn<2$ where $0<theta_s(xpn)<1/2$ and, c) $xpn<1$ where $ell(r)$ behaves logarithmically, i.e. $theta_s=0$. The characteristic length $xi$ is of the form $xi sim p^{- u}$ with $ u=1/(2-xpn)$ in region b), but depends on L as well in region c). A directed model of shortest-paths is solved and compared with numerical results.
We demonstrate a method to solve a general class of random matrix ensembles numerically. The method is suitable for solving log-gas models with biorthogonal type two-body interactions and arbitrary potentials. We reproduce standard results for a vari
ety of well-known ensembles and show some new results for the Muttalib-Borodin ensembles and recently introduced $gamma$-ensemble for which analytic results are not yet available.
We consider a broad class of Continuous Time Random Walks with large fluctuations effects in space and time distributions: a random walk with trapping, describing subdiffusion in disordered and glassy materials, and a Levy walk process, often used to
model superdiffusive effects in inhomogeneous materials. We derive the scaling form of the probability distributions and the asymptotic properties of all its moments in the presence of a field by two powerful techniques, based on matching conditions and on the estimate of the contribution of rare events to power-law tails in a field.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
