Related papers: Universal shocks in the Wishart random-matrix ense…
Driven single-file motion, in which particles move unidirectionally along one-dimensional channels, sets the paradigm for wide variety of one-dimensional directed movements, ranging from intracellular transport and urban traffic to ant…
The Wigner-Gaudin-Mehta-Dyson conjecture asserts that the local eigenvalue statistics of large random matrices exhibit universal behavior depending only on the symmetry class of the matrix ensemble. For invariant matrix models, the…
We formulate Witten index problems for theories with two supercharges in a Majorana doublet, as in $d=3$ $\mathcal N=1$ theories and dimensional reduction thereof. Regardless of spacetime dimensions, the wall-crossing occurs generically, in…
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…
We derive a universal bound on the integrated total scattering cross-section at \emph{finite} energies, expressed in terms of a single low-energy coefficient constrained by the non-perturbative S-matrix Bootstrap. At high energies, the…
The origin of wall shear-stress fluctuations in wall turbulence was studied through energy dissipation at the wall. While confirming the universality in wall dissipation at small inner scales, the dissipation at larger scales is a…
We describe a new universality class for unitary invariant random matrix ensembles. It arises in the double scaling limit of ensembles of random $n \times n$ Hermitian matrices $Z_{n,N}^{-1} |\det M|^{2\alpha} e^{-N \Tr V(M)} dM$ with…
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving…
We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…
We reveal elegant relations between the shape dependence of the Casimir effects and Weyl anomaly in boundary conformal field theories (BCFT). We show that for any BCFT which has a description in terms of an effective action, the near…
Eugene Wigner's revolutionary vision predicted that the energy levels of large complex quantum systems exhibit a universal behavior: the statistics of energy gaps depend only on the basic symmetry type of the model. Simplified models of…
Heavy-tailed fluctuations and power law statistics pervade physics, finance, and economics, yet their origin is often ascribed to systems poised near criticality. Here we show that such behavior can emerge far from instability through a…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We adapt the one parameter scaling theory (OPT) to the context of quantum chaos. As a result we propose a more precise characterization of the universality classes associated to Wigner-Dyson and Poisson statistics which takes into account…
We study unitary random matrix ensembles in the critical case where the limiting mean eigenvalue density vanishes quadratically at an interior point of the support. We establish universality of the limits of the eigenvalue correlation…
As a rule, the shock compression controls the spectrum of diffusively accelerated particles. We argue that this is not so if the backreaction of these particles on the shock structure is significant. We present a self-similar solution in…
We investigate dissipative dynamical systems under the influence of an external driving with two or more frequencies. Our main quantities of interest are long-time averages of expectation values which turn out to exhibit universal features.…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
A discontinuous generalization of the standard map, which arises naturally as the dynamics of a periodically kicked particle in a one dimensional infinite square well potential, is examined. Existence of competing length scales, namely the…
A disorder-dependent Gaussian variational approach is applied to the problem of a $d$ dimensional polymer chain in a random medium (or potential). Two classes of variational solutions are obtained. For $d<2$, these two classes may be…