Related papers: Dynamics in a kinetic model of oriented particles …
We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…
We propose a mean-field theory for nonequilibrium phase transitions to a periodically oscillating state in spin models. A nonequilibrium generalization of the Landau free energy is obtained from the join distribution of the magnetization…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the…
We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: Firstly we…
We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [16]. We provide several criteria for existence and uniqueness of…
We uncover a finite-time dynamical phase transition in the thermal relaxation of a mean-field magnetic model. The phase transition manifests itself as a cusp singularity in the probability distribution of the magnetisation that forms at a…
A modeling framework for the internal conformational dynamics and external mechanical movement of single biological macromolecules in aqueous solution at constant temperature is developed. Both the internal dynamics and external movement…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
We consider critical one dimensional quantum systems initially prepared in their groundstate and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the…
We present the first example of a phase transition in a nonequilibrium steady-state that can be argued analytically to be first order. The system of interest is a two-species reaction-diffusion problem whose control parameter is the total…
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
We investigate the effect of self-propulsion on a mean-field order-disorder transition. Starting from a $\varphi^4$ scalar field theory subject to an exponentially correlated noise, we exploit the Unified Colored Noise Approximation to map…
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously…
We study the dynamics of a system of coupled oscillators of distributed natural frequencies, by including the features of both thermal noise, parametrized by a temperature, and inertial terms, parametrized by a moment of inertia. For a…
This article investigates an energy balance model coupled to the primitive equations by a dynamic boundary condition with and without noise on the boundary. It is shown that this system is globally strongly well-posed both in the…
We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes…
Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In…
We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns…
We get fractional symmetric Fokker - Planck and Einstein - Smoluchowski kinetic equations, which describe evolution of the systems influenced by stochastic forces distributed with stable probability laws. These equations generalize known…