Related papers: Topology trivialization transition in random non-g…

We consider a nonlinear autonomous random dynamical system of $N$ degrees of freedom coupled by Gaussian random interactions and characterized by a continuous spectrum $n_{\mu}(\lambda)$ of real positive relaxation rates. Using Kac-Rice…

We study the landscapes of multi-species spherical spin glasses. Our results determine the phase boundary for annealed trivialization of the number of critical points, and establish its equivalence with a quenched strong topological…

Our goal is to discuss in detail the calculation of the mean number of stationary points and minima for random isotropic Gaussian fields on a sphere as well as for stationary Gaussian random fields in a background parabolic confinement.…

We consider large-dimensional dynamical systems involving a linear force and a random force comprising both potential and non-conservative contributions. Such systems are known to exhibit a topological trivialization phase transition as the…

We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such…

We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in…

We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades…

We develop a general compactification framework to facilitate analysis of nonlinear nonautonomous ODEs where nonautonomous terms decay asymptotically. The strategy is to compactify the problem: the phase space is augmented with a bounded…

We present an example for the phase transition between a topological non-trivial solid phase and a trivial solid phase in the quantum dimer model(QDM) on triangular lattice. Such a transition is beyond the Landau's paradigm of phase…

We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a…

We present a null model for single- and multi-layered complex systems constructed using homogeneous and isotropic random Gaussian maps. By means of a Kac-Rice formalism, we show that the mean number of fixed points can be calculated as the…

Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust…

Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size $2$-spin spherical model using both…

The transition from topologically nontrivial to a trivial state is studied by first-principles calculations on bulk zinc-blende type (Hg$_{1-x}$Zn$_x$)(Te$_{1-x}$S$_x$) disordered alloy series. The random chemical disorder was treated by…

A new theoretical approach to non-equilibrium statistical systems has recently been proposed by the author, a co-author and others. It is based on a variational principle which is associated with the discrepancy of a path through…

This paper presents the continuous and discrete variational formulations of simple thermodynamical systems whose configuration space is a (finite dimensional) Lie group. We follow the variational approach to nonequilibrium thermodynamics…

We investigate the response of a system of hard spheres to two classes of perturbations over a range of densities spanning the fluid, crystalline, and glassy regimes within a molecular dynamics framework. Firstly, we consider the relaxation…

We consider the Generalized Lotka-Volterra system of equations with all-to-all, random asymmetric interactions describing high-dimensional, very diverse and well-mixed ecosystems. We analyze the multiple equilibria phase of the model and…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

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…