Related papers: Phase of Nonlinear Systems
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
We assume that a system at a mesoscopic scale is described by a field $\phi(x,t)$ that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter $1/\sqrt{\Omega}$. The system stationary state…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
The stationary points of the Hamiltonian H of the classical XY chain with power-law pair interactions (i.e., decaying like r^{-{\alpha}} with the distance) are analyzed. For a class of "spinwave-type" stationary points, the asymptotic…
In this report we deal with the problem of global output feedback stabilization of a class of $n$-dimensional nonlinear positive systems possessing a one-dimensional unknown, though measured, part. We first propose our main result, an…
Passivity theory is one of the cornerstones of control theory, as it allows one to prove stability of a large-scale system while treating each component separately. In practice, many systems are not passive, and must be passivized in order…
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
The semiring of discrete dynamical systems is a simple algebraic model for modularity in deterministic systems. The objects of the semiring are finite transformations (viewed as directed graphs and regarded up to isomorphism), the sum of…
The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by…
In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an…
The paper studies the structure of high-order adiabatic approximation of a wave function for slowly changing Hamiltonians. A constructive technique for explicit separation of fast and slow components of the wave function is developed. The…
We consider a dissipative vector field which is represented by a nearly-integrable Hamiltonian flow to which a non symplectic force is added, so that the phase space volume is not preserved. The vector field depends upon two parameters,…
For the driven-dissipative system of two coupled bosonic modes in a nonlinear cavity resonator, we demonstrate a sequence of phase transitions from a trivial steady state to two distinct dissipative time crystalline phases. These effects…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The latter is described by a spin model whose main feature is that it possesses a…
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.