Related papers: Global Level Number Variance in Integrable Systems
We study stability and distortions of liquid crystal nematic order in a cell with a random heterogeneous substrate. Modeling this system as a bulk xy model with quenched disorder confined to a surface, we find that nematic order is…
We continue here with previous investigations on the global behavior of general type non-linear wave equations for a class of small, scale-invariant initial data. The method is based on the use of a new set of Strichartz estimates for the…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
A class of Hamiltonian impact systems exhibiting smooth near integrable behavior is presented. The underlying unperturbed model investigated is an integrable, separable, 2 degrees of freedom mechanical impact system with effectively bounded…
We consider fluctuations in a perfect irrotational fluid coupled to gravity in an Einstein static universe background. We show that the homogeneous linear perturbations of the scalar and metric fluctuations in the Einstein static universe…
The full spectrum of transfer matrices of the general eight-vertex model on a square lattice is obtained by numerical diagonalization. The eigenvalue spacing distribution and the spectral rigidity are analyzed. In non-integrable regimes we…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
The spectra of Sinai microwave billiards and rectangular billiards with statistically distributed circular scatterers have been taken as a function of the position of one wall, and of one of the scatterers, respectively. Whereas in the…
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 consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
In this paper, we consider Anderson type operators on a separable Hilbert space where the random perturbations are finite rank and the random variables have full support on $\mathbb{R}$. We show that spectral multiplicity has a uniform…
Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the…
Pendulum-like dynamics is a universal motif across many areas of physics, underlying systems ranging from classical nonlinear oscillators to superconducting qubits and cold-atom tunneling platforms. Here we present an exact frequency-domain…
Formulating order metrics that sensitively quantify the degree of order/disorder in many-particle systems in $d$-dimensional Euclidean space $\mathbb{R}^d$ across length scales is an outstanding challenge in physics, chemistry, and…
Scale-invariance is a ubiquitous observation in the dynamics of large distributed complex systems. The computation of its scaling exponents, which provide clues on its origin, is often hampered by the limited available sampling data, making…
The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity…
Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level…
We investigate the system size scaling of the net defect number created by a rapid quench in a second-order quantum phase transition from an O(N) symmetric state to a phase of broken symmetry. Using a controlled mean-field expansion for…
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…