Related papers: Singularity spectrum of self-organized criticality
We investigate the two-point correlations in the band spectra of spatially periodic systems that exhibit chaotic diffusion in the classical limit. By including level pairs pertaining to non-identical quasimomenta, we define form factors…
We propose an analytical Landau-Ginzburg theory of the charge density waves coupled with lattice and electronic long-range order parameters. Examples of long-range order include electronic wave function of superconducting Cooper pairs,…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
Time-reversal symmetry is a prevalent feature of microscopic physics, including operational quantum theory and classical general relativity. Previous works have studied indefinite causal structure using the language of operational quantum…
We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a `simple' and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics,…
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the…
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of Galton-Watson trees.
The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…
We study the phenomena of energy concentration for the critical O(3) sigma model, also known as the wave map flow from R^{2+1} Minkowski space into the sphere S^2. We establish rigorously and constructively existence of a set of smooth…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
We consider the stochastic Ginzburg-Landau equation in a bounded domain. We assume the stochastic forcing acts only on high spatial frequencies. The low-lying frequencies are then only connected to this forcing through the non-linear…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We calculate perturbatively the multifractality spectrum of wave-functions in critical random matrix ensembles in the regime of weak multifractality. We show that in the leading order the spectrum is universal, while the higher order…
We propose to build a combinatorial invariant, called the spectral monodromy, from the spectrum of a single non-selfadjoint h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from…
We study the singularity probability of n*n random matrices with i.i.d. entries from highly biased discrete distributions. We obtain sharp non-asymptotic bounds for this probability and derive estimates on the least singular values. Our…
Spatial self-similarity is a hallmark of critical phenomena. We study the dynamic process of percolation, in which bonds are incrementally added to an initially empty lattice until the system becomes fully occupied. By tracking the gap --…
Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal…
We study the spectrum of Landau-Ginzburg theories in 1+1 dimensions using the truncated conformal space approach employing a compactified boson. We study these theories both in their broken and unbroken phases. We first demonstrate that we…
Simple field-theoretical approach to critical phenomena is described. In contrast to the Wilson's theory, a description in real 3-dimensions space is used. At the same time the described approach is not the same as Parisi's. Used…