Related papers: An Introduction to Breakdown Phenomena in Disorder…
We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with…
When magnets are fashioned into nanoscale elements, they exhibit a wide variety of phenomena replete with rich physics and the lure of tantalizing applications. In this topical review, we discuss some of these phenomena, especially those…
The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…
This paper investigates the effect of disorder on a ferromagnetic metal with repulsive interactions. We assume that, in the clean limit, the ferromagnetic state can be described by Stoner mean-field theory and study how disorder affects the…
We derive an efficient and unbiased method for computing order parameters in correlated electron systems with competing instabilities. Charge, magnetic and pairing fluctuations above the energy scale of spontaneous symmetry breaking are…
This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their…
In the scientific literature, the term emergent phenomena is invoked in the context of a collective behavior observed in a complex adaptive system that exhibits no correspondence with the behavior of the system constituents. Although this…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also…
We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…
The formation of breakdown pattern on an insulating surface under the influence of a transverse magnetic field is theoretically investigated. We have generalized the Dielectric Breakdown Model (DBM) for the case of external magnetic field.…
Spontaneous symmetry breaking is responsible for the rich phenomena in equilibrium physics. Driving a system out-of-equilibrium can significantly enrich the possibility of spontaneous symmetry breaking, which occurs not only in space, but…
The spin splitting caused by the terms linear in wavevector in the effective Hamiltonian containing can give rise to the new magneto-oscillation phenomena in two-dimensional systems. It is shown that the joint action of the spin-dependent…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
The conventional theory of combustion describes systems where all of the parameters are spatially homogeneous. On the other hand, combustion in disordered explosives has long been known to occur after local regions of the material, called…
This review provides a dynamical systems perspective on psychiatric symptoms and disease, and discusses its potential implications for diagnosis, prognosis, and treatment. After a brief introduction into the theory of dynamical systems, we…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random…