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We study a zero-range process where the jump rates do not only depend on the local particle configuration, but also on the size of the system. Rigorous results on the equivalence of ensembles are presented, characterizing the occurrence of…
We study abrupt changes in the dynamics and/or steady state of fermionic dissipative systems produced by small changes of the system parameters. Specifically, we consider open fermionic systems whose dynamics is described by master…
We consider a dynamical system, possibly infinite dimensional or non-autonomous, with fast and slow time scales which is oscillatory with high frequencies in the fast directions. We first derive and justify the limit system of the slow…
Discontinuous quantum phase transitions and the associated metastability play central roles in diverse areas of physics ranging from ferromagnetism to false vacuum decay in the early universe. Using strongly-interacting ultracold atoms in…
The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional…
The properties of the first-order phase transition in a set of plasma models with common feature - absence of individual correlations between charges of op-posite sign, have been studied. Predicted discontinuities in equilibrium non-uniform…
An asymmetric generalization of the zero-temperature Glauber model on a lattice is introduced. The dynamics of the particle-density and specially the large-time behavior of the system is studied. It is shown that the system exhibits two…
We consider turbulence in the Gross-Pitaevsky model and study the creation of a coherent condensate via an inverse cascade originated at small scales. The growth of the condensate leads to a spontaneous breakdown of symmetries of…
Many systems in nature exhibit transitions between fluid-like states and solid-like states, or "jamming transitions". There is a strong theoretical foundation for understanding equilibrium phase transitions that involve solidification, or…
At a finite temperature, the stable equilibrium states of a coupled two-component superfluid with the same mass in both non-rotating and rotating cases can be obtained by studying its real time dynamics via holography, the equilibrium state…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
The occurrence of abrupt dynamical transitions in the macroscopic state of a system has received growing attention. We present experimental evidence for abrupt transition via explosive synchronization in a real-world complex system, namely…
The exploration of the rich dynamics of electrons is a frontier in fundamental nano-physics. The dynamical behavior of electrons is dominated by random and chaotic thermal motion with ultrafast ($\approx$ ps) and nanoscale scatterings. This…
We consider the nonlinear extension of the Kuramoto model of globally coupled phase oscillators where the phase shift in the coupling function depends on the order parameter. A bifurcation analysis of the transition from fully synchronous…
We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of…
Microcanonical statistics can be well applied to non-extensive systems like nuclei, atomic clusters and systems at phase transitions of first order with inhomogeneous configurations like phase separation. No thermodynamic limit has to be…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
The unconstrained ensemble describes completely open systems in which energy, volume and number of particles fluctuate. Here we show that not only equilibrium states can exist in this ensemble, but also that completely open systems can…
A two dimensional self-gravitating Hamiltonian model made by $N$ fully-coupled classical particles exhibits a transition from a collapsing phase (CP) at low energy to a homogeneous phase (HP) at high energy. From a dynamical point of view,…
Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…