Related papers: Random Energy Model as a paradigm of complex syste…
A random fuse network, or equivalently a two-dimensional spring network with quenched disorder, is subjected to a constant load and thermal noise, and studied by means of numerical simulations. Rupture is thermally activated and the…
Astrophysical observations suggest that magnetic reconnection in relativistic plasmas plays an important role in the acceleration of energetic particles. Modeling this accurately requires numerical schemes capable of addressing large scales…
A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
The phase diagram and the thermodynamics of the random field Ising model (RFIM) defined on a family of diamond hierarchical lattices of arbitrary dimension and scaling factor $b=2$ is investigated. The phase diagram is studied considering…
We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In…
Special relativity combined with the stochastic vacuum flux impact model lead to an explicit interpretation of many of the phenomena of elementary quantum mechanics. We examine characteristics of a repetitively impacted submicroscopic…
In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a…
We examine SERS from two perspectives: as a phenomenon described by the Laplace Equation (the electrostatic or Rayleigh limit) and by the Helmholtz Equation (electrodynamic or Mie limit). We formulate the problem in terms of the scalar…
The physics of supersymmetry is reviewed from the perspective of physics at ever increasing energies. Starting from the minimal supersymmetric extension of the Standard Model at the electroweak scale, we proceed to higher energies seeking…
The energy spectrum of a system of $N_a$ atoms of $n$ levels interacting with a one-mode electromagnetic field is studied in the dipole and rotating wave approximations. We find that, under the resonant condition, it exhibits a mirror…
Spin-conserving and spin-flip opaque reflections of electrons from a potential barrier in heterostructures are described. An electric field of the barrier is considered to be the only source of energy spin splitting in the presence of…
Random-matrix eigenvalues have a well-known interpretation as a gas of like-charge particles. We make use of this to introduce a model of vortex dynamics by defining a time-dependent wave function as the characteristic polynomial of a…
We consider the spherical spin glass model defined by a combination of the pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian and the ferromagnetic Curie-Weiss Hamiltonian. In the large system limit, there is a two-dimensional phase…
An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle…
Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers.…
We analyze several ground state related properties of mesoscopic systems using the random interaction matrix model EGOE(1+2)-$\cs$ (or RIMM) for many fermion systems with spin degree of freedom and the Hamiltonian containing pairing and…
We study the effects of random fluctuations on quantum phase transitions by the energy gap analysis. For the infinite-ranged spin-glass models with a transverse field, we find that a strong sample-to-sample fluctuation effect leads to broad…
The phenomenon of resonant energization of a relativistic quantum particle, moving in unison with an intense ElectroMagnetic Wave, is demonstrated in a semiclassical calculation. The wave nature of the quantum particle is of essence because…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…