Related papers: Random matrix universality in dynamical correlatio…
An isolated quantum system is said to thermalize if ${\rm Tr} (A \rho(t)) \to {\rm Tr} (A \rho_{\rm eq})$ for time $t \to \infty$. Here $\rho(t)$ is the time-dependent density matrix of the system, $\rho_{\rm eq}$ is the time-independent…
We report the study of a model of a two-level system interacting in a non-diagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random…
We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential $W(H)$, we (i) find the joint distribution functions of the eigenvalues of…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Multitime correlation functions provide useful probes for the ensembles of trajectories underlying the stochastic dynamics of complex systems. These can be obtained by measuring their optical response to sequences of ultrashort optical…
The leading correction to the smoothed connected energy density-density correlation function is obtained for the large energy difference, within the context of the Gaussian Random Matrix Theory. In order to achieve this result, the…
We present a systematic study of dynamical heterogeneity in a model for permanent gels, upon approaching the gelation threshold. We find that the fluctuations of the self intermediate scattering function are increasing functions of time,…
We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…
We consider Random Hopping Time (RHT) dynamics of the Sherrington - Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature we prove that, on time scales that are sub-exponential in…
The expected root-mean-square value of a matrix element $A_{\alpha\beta}$ in a classically chaotic system, where $A$ is a smooth, $\hbar$-independent function of the coordinates and momenta, and $\alpha$ and $\beta$ label different energy…
We study the aging behavior of a truncated version of the Random Energy Model evolving under Metropolis dynamics. We prove that the natural time-time correlation function defined through the overlap function converges to an arcsine law…
The Eigenstate Thermalization Hypothesis (ETH) explains emergence of the thermodynamic equilibrium by assuming a particular structure of observable's matrix elements in the energy eigenbasis. Schematically, it postulates that off-diagonal…
We derive the Eigenstate Thermalization Hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by J. M. Deutsch [Phys. Rev. A 43, 2046 (1991)]. We approximate the coupling between a subsystem and a many-body…
We study fluctuation properties of embedded random matrix ensembles of non-interacting particles. For ensemble of two non-interacting particle systems, we find that unlike the spectra of classical random matrices, correlation functions are…
Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized…
Financial markets are prominent examples for highly non-stationary systems. Sample averaged observables such as variances and correlation coefficients strongly depend on the time window in which they are evaluated. This implies severe…
In this work we use the random matrix theory (RMT) to correctly describethe behavior of spectral statistical properties of the sea surface temperatureof oceans. This oceanographic variable plays an important role in theglobalclimate system.…
Scaling behavior is studied of several dominant eigenvalues of spectra of Markov matrices and the associated correlation times governing critical slowing down in models in the universality class of the two-dimensional Ising model. A scheme…