Related papers: Topology trivialization transition in random non-g…
The objective of the work summarised here has been to exploit and extend ideas from plasma physics and accelerator dynamics to formulate a unified description of collisionless relaxation that views violent relaxation, Landau damping, and…
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a…
Topologically ordered quantum systems have robust physical properties, such as quasiparticle statistics and ground-state degeneracy, which do not depend on the microscopic details of the Hamiltonian. We consider topological phase…
Slow relaxation and glassiness have been the focus of extensive research attention, along with popular and technological interest, for many decades. While much understanding has been attained through mean-field and mode-coupling models,…
When compressed, certain lattices undergo phase transitions that may allow nuclei to gain significant kinetic energy. To explore the dynamics of this phenomenon, we develop a framework to study Coulomb coupled N-body systems constrained to…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…
We start from the Theory of Random Point Processes to derive n-point coupled master equations describing the continuous dynamics of discrete variables in random graphs. These equations constitute a hierarchical set of approximations that…
We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
In this paper, we introduce a fictitious dynamics for describing the only fast relaxation of a stiff ordinary differential equation (ODE) system towards a stable low-dimensional invariant manifold in the phase-space (slow invariant manifold…
High-dimensional random landscapes underlie phenomena as diverse as glassy physics and optimization in machine learning, and even their simplest toy models already display extraordinarily rich behavior. This thesis aims to deepen our…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…
Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSSs) whose lifetime increases with system size. With reference to the Hamiltonian Mean Field (HMF) model, we here show that a maximum…
At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass",…
We study rough high-dimensional landscapes in which an increasingly stronger preference for a given configuration emerges. Such energy landscapes arise in glass physics and inference. In particular we focus on random Gaussian functions, and…
We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the…
The two dimensional O(3) sigma model, just as quantum chromodynamics, is an asymptotically free theory with a mass gap. Therefore, it is an interesting and simple toy model to investigate algorithms for Markov Chain Monte Carlo simulations…
Typicality of the orthogonal dynamics (TOD) is established as a generic feature of temporal relaxation processes in isolated many-body quantum systems. The basic idea in the simplest case is that the transient non-equilibrium behavior is…
Topological phenomena are commonly studied in phases of matter which are separated from a trivial phase by an unavoidable quantum phase transition. This can be overly restrictive, leaving out scenarios of practical relevance -- similar to…