Related papers: On "Universal" Correlations in Disordered and Chao…
Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-d integrable model with the $1/r^2$ interaction (the Calogero-Sutherland-Moser system), and…
A Value-at-Risk based model is proposed to compute the adequate equity capital necessary to cover potential losses due to operational risks, such as human and system process failures, in banking organizations. Exploring the analogy to a…
The $M$-dimensional scattering matrix $S(E)$ which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of…
The paper examines a class of first order linear hyperbolic systems, proposed as a generalization of the Goldstein-Kac model for velocity-jump processes and determined by a finite number of speeds and corresponding transition rates. It is…
We present the results of a detailed study of energy correlations at steady state for a 1-D model of coupled energy and matter transport. Our aim is to discover -- via theoretical arguments, conjectures, and numerical simulations -- how…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align…
The statistical description of oscillator strengths for systems like hydrogen in a magnetic field is developed by using the supermatrix nonlinear $\sigma$-model. The correlator of oscillator strengths is found to have a universal parametric…
The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation…
We investigate the effects of randomness in a strongly correlated electron model in one-dimension at half-filling. The ground state correlation functions are exactly written by products of 3$\times$3 transfer matrices and are evaluated…
Networks where each node has one or more associated numerical values are common in applications. This work studies how summary statistics used for the analysis of spatial data can be applied to non-spatial networks for the purposes of…
This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived.…
Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…
While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement -- analogous to the one used in quantum optics -- we show how to…
A framework for developing new approximate electronic structure methods is presented, in which the correlation energy of a many-electron system in the ground state is computed as in the single-reference second-order many-body perturbation…
We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We consider a Hamiltonian $H$ which is the sum of a deterministic part $H_0$ and of a random potential $V$. For finite $N \times N$ matrices, following a method introduced by Kazakov, we derive a representation of the correlation functions…
Spectra of the geometric collective model of atomic nuclei are analyzed to identify chaotic correlations among nonrotational states. The model has been previously shown to exhibit a high degree of variability of regular and chaotic…