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Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates…
We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states.…
We evaluate the localization length of the wave solution of a random potential characterized by an arbitrary autocorrelation function. We go beyond the Born approximation to evaluate the localization length using a non-linear approximation…
A general model-independent discussion of mesonic correlation functions is given. We derive new inequalities, including one stronger than Weingarten's inequality. Mesonic correlation functions are calculated in the random instanton vacuum…
The energy-energy correlation function of the two-dimensional Ising model with weakly fluctuating random bonds is evaluated in the large scale limit. Two correlation lengths exist in contrast to one correlation length in the pure 2D Ising…
We study numerically the effects of short- and long-range correlations on the localization properties of the eigenstates in a one-dimensional disordered lattice characterized by a random non-Hermitian Hamiltonian, where the imaginary part…
In [1] we gave a precise holographic calculation of chaos at the scrambling time scale. We studied the influence of a small perturbation, long in the past, on a two-sided correlation function in the thermofield double state. A similar…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
The angular and frequency correlation functions of the transmission coefficient for light propagation through a strongly scattering amplifying medium are considered. It is found that just as in the case of an elastic scattering medium the…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression…
A one-dimensional diagonal tight binding electronic system with correlated disorder is investigated. The correlation of the random potential is exponentially decaying with distance and its correlation length diverges as the concentration of…
The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…
Correlated structures are intimately connected to intriguing phenomena exhibited by a variety of disordered systems such as soft colloidal gels, bio-polymer networks and colloidal suspensions near a shear jamming transition. The universal…
Particle-particle correlation functions in ionic systems control many of their macroscopic properties. In this work, we use stochastic density functional theory to compute these correlations, and then we analyze their long-range behavior.…
Vortex lines in type-II superconductors display complicated relaxation processes due to the intricate competition between their mutual repulsive interactions and pinning to attractive point or extended defects. We perform extensive Monte…
We have studied numerically the dynamics of a directed elastic string in a two-dimensional array of quenched random impurities. The string is driven by a constant transverse force and thermal fluctuations are neglected. There is a…
This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the…
The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to…
Instanton crystal is a fascinating phase which is encountered when the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in the form of a chain of alternating instantons and…
The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and…