Related papers: Global Level Number Variance in Integrable Systems
A new numerical framework, based on the use of a simple first order strongly hyperbolic evolution equations, is introduced and tested in case of 4-dimensional spherically symmetric gravitating systems. The analytic setup is chosen such that…
This article is the second one in a series on the use of scaling invariance in finance. In the first article (cond-mat/9906048), we introduced a new formalism for the pricing of derivative securities, which focusses on tradable objects…
We study spectral statistics of lattice modes in a disordered crystal and in a crystal with a complex unit cell. The correlations of the eigenmode frequencies of a block of a disordered solid is found to obey the GOE Wigner-Dyson…
Nonperturbative, in inverse Thouless conductance 1/g, corrections to distributions of level velocities and level curvatures in quasi-one-dimensional disordered conductors with a topology of a ring subject to a constant vector potential are…
We construct large families of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. A Riemann-Hilbert problem approach is used to recast the governing equations…
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory.…
I survey physics theories involving parallel universes, arguing that they form a natural four-level hierarchy of multiverses allowing progressively greater diversity. Level I: A generic prediction of inflation is an infinite ergodic…
The level dynamics across the many body localization transition is examined for XXZ-spin model with a random magnetic field. We compare different scenaria of parameter dependent motion in the system and consider measures such as level…
Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical system of…
The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences. The first corresponds to states for which…
In complex network-coupled dynamical systems, two questions of central importance are how to identify the most vulnerable components and how to devise a network making the overall system more robust to external perturbations. To address…
In a variety of systems which exhibit aging, the two-time response function scales as $R(t,s)\approx s^{-1-a} f(t/s)$. We argue that dynamical scaling can be extended towards conformal invariance, obtaining thus the explicit form of the…
The global financial system is highly complex, with cross-border interconnections and interdependencies. In this highly interconnected environment, local financial shocks and events can be easily amplified and turned into global events.…
Disordered viscoelastic materials are ubiquitous and exhibit fascinating invariant scaling properties. In a companion article, we have presented comprehensive new results for the critical behavior of the dynamic susceptibility of disordered…
We study level number variance in a two-dimensional random matrix model characterized by a power-law decay of the matrix elements. The amplitude of the decay is controlled by the parameter b. We find analytically that at small values of b…
The level-spacing distribution of a spin 1/2 XXZ chain is numerically studied under random magnetic field. We show explicitly how the level statistics depends on the lattice size L, the anisotropy parameter $\Delta$, and the mean amplitude…
This is the third in a series of papers which considers first-order gauge-invariant and covariant gravitational perturbations to locally rotationally symmetric (LRS) class II space-times. In this paper we complete our analysis of the…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed retarded and neutral delays. The…
We discuss the appearance of oscillatory and standing wave states in second-order oscillator networks showing that it is a special case of a more general mechanism involving secondary synchronized clusters induced by inertia. Using a…
We consider discrete random fractal surfaces with negative Hurst exponent $H<0$. A random colouring of the lattice is provided by activating the sites at which the surface height is greater than a given level $h$. The set of activated sites…