Related papers: The parabolic Anderson model on the hypercube
We consider a population dynamics model coupling cell growth to a diffusion in the space of metabolic phenotypes as it can be obtained from realistic constraints-based modelling. In the asymptotic regime of slow diffusion, that coincides…
In this study, we employ analytical and numerical techniques to examine a phase transition model with moving boundaries. The model displays two relevant spatial scales pointing out to a macroscopic phase and a microscopic phase, interacting…
We study the crossing of the quantum phase transition in the transverse-field Ising model after modulating the magnetic field at an arbitrary rate, exploring the critical dynamics from the slow to the sudden quench regime. We do so by…
We study a continuous time model for the frequency distribution of an infinitely large asexual population in which both beneficial and deleterious mutations occur and the fitness is additive. When beneficial mutations are ignored, the exact…
We numerically analyze the energy level statistics of the Anderson model with Gaussian site disorder and constant hopping. The model is realized on different two-dimensional lattices, namely, the honeycomb, the kagom\'e, the square, and the…
We consider the solution to the parabolic Anderson model with homogeneous initial condition in large time-dependent boxes. We derive stable limit theorems, ranging over all possible scaling parameters, for the rescaled sum over the solution…
We consider parabolic partial differential equations of Lotka-Volterra type, with a non-local nonlinear term. This models, at the population level, the darwinian evolution of a population; the Laplace term represents mutations and the…
We study the two-dimensional paramagnetic Anderson-Hubbard model using an extension of dynamical mean-field theory that allows us to treat disorder and strong electronic correlations on equal footing. We investigate the scaling of the…
The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction…
One dimensional pinning models have been widely studied in the physical and mathematical literature, also in presence of disorder. Roughly speaking, they undergo a transition between a delocalized phase and a localized one. In mathematical…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We continue our study of intermittency for the parabolic Anderson equation $\partial u/\partial t = \kappa\Delta u + \xi u$, where $u\colon \Z^d\times [0,\infty)\to\R$, $\kappa$ is the diffusion constant, $\Delta$ is the discrete Laplacian,…
We study the long-range, long-time behavior of the reactive-telegraph equation and a related reactive-kinetic model. The two problems are equivalent in one spatial dimension. We point out that the reactive-telegraph equation, meant to model…
Within the framework of population genetics we consider the evolution of an asexual haploid population under the effect of a rapidly varying natural selection (microevolution). We focus on the case in which the environment exerting…
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynamics of a variety of large systems of interacting particles.…
The concept of quantum revivals is extended to many-body systems and the implications of traversing a quantum phase transition are explored. By analyzing two different models, the vibron model for the bending of polyatomic molecules and the…
We investigate steady states of a quasilinear first order hyperbolic partial integro-differential equation. The model describes the evolution of a hierarchical structured population with distributed states at birth. Hierarchical…
We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
The eigenvalue problem of quantum many-body systems is a fundamental and challenging subject in condensed matter physics, since the dimension of the Hilbert space (and hence the required computational memory and time) grows exponentially as…