Related papers: Mean field coupled dynamical systems: Bifurcations…
Subdiffusion is a generic feature of chaotic many-body dynamics with multipole conservation laws and subsystem symmetries. We numerically study this subdiffusive dynamics, using quantum automaton random unitary circuits, in a broad range of…
A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the…
We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate…
We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…
We define a Gaussian invariant measure for the two-dimensional averaged-Euler equation and show the existence of its solution with initial conditions on the support of the measure. An invariant surface measure on the level sets of the…
We review double field theory (DFT) with emphasis on the doubled spacetime and its generalized coordinate transformations, which unify diffeomorphisms and b-field gauge transformations. We illustrate how the composition of generalized…
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…
Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…
Decoherence in realistic quantum platforms motivates a mixed-state notion of topological phases of matter, including average symmetry-protected topological (ASPT) phases. Alongside this progress, generalized symmetries--notably…
Mean-field integro-differential equations are studied in an abstract framework, through couplings of the corresponding stochastic processes. In the perturbative regime, the equation is proven to admit a unique equilibrium, toward which the…
Assuming it preserves an orientation of its stable bundle, any three-dimensional partially hyperbolic diffeomorphism can be used to construct a four-dimensional partially hyperbolic diffeomorphism which is dynamically incoherent. Under the…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…
The Takens-Bogdanov bifurcation is a codimension two bifurcation that provides a key to the presence of complex dynamics in many systems of physical interest. When the system is translation-invariant in one spatial dimension with no…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We consider the multifractal analysis of the pointwise dimension for Gibbs measures on countable Markov shifts. Our paper analyses the set of non-analytic points or phase transitions of the multifractal spectrum. By Sarig's thermodynamic…
We introduce a solvable model of a measurement-induced phase transition (MIPT) in a deterministic but chaotic dynamical system with a positive Lyapunov exponent. In this setup, an observer only has a probabilistic description of the system…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It…
We propose experimentally feasible ways to probe universal features of absorbing phase transitions from two different approaches, both based on numerical validations. On one hand, we numerically study a probability distribution of…
We study theories breaking diffeomorphism (Diff) invariance down to the subgroup of transverse diffeomorphisms (TDiff), consisting of multiple scalar fields in a cosmological background. In particular, we focus on models involving a field…