Related papers: Nonequilibrium Molecular Dynamics, Fractal Phase-S…

A phase-space formulation of non-stationary nonlinear dynamics including both Hamiltonian (e.g., quantum-cosmological) and dissipative (e.g., dissipative laser) systems reveals an unexpected affinity between seemly different branches of…

This is a study of the information evolution of complex systems by geometrical consideration. We look at chaotic systems evolving in fractal phase space. The entropy change in time due to the fractal geometry is assimilated to the…

Classically integrable approximants are here constructed for a family of predominantly chaotic periodic systems by means of the Baker-Hausdorff-Campbell formula. We compare the evolving wave density for the corresponding exact quantum…

We revisit a two-temperature Nos\'e-Hoover wanderer particle embedded in a two-dimensional periodic 2x2 cell with four smooth repulsive corners at $(x,y) = (\pm 1, \pm 1)$ to explore chaos with anisotropic thermostatting. The model employs…

Heterodimensional cycles are heteroclinic cycles that connect periodic orbits whose unstable manifolds have different dimensions. This is a source of nonhyperbolic dynamics and unstable dimension variability. For smooth invertible maps…

The non-equilibrium Fokker-Planck dynamics in an arbitrary force field $\vec f(\vec r)$ in dimension $N$ is revisited via the correspondence with the non-hermitian quantum mechanics in a scalar potential $V(\vec r)$ and a vector potential…

We further study the stochastic model discussed in Ref.[2] in which positive and negative particles diffuse in an asymmetric, CP invariant way on a ring. The positive particles hop clockwise, the negative counter-clockwise and…

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…

The extension of many-body quantum dynamics to the non-unitary domain has led to a series of exciting developments, including new out-of-equilibrium entanglement phases and phase transitions. We show how a duality transformation between…

If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…

In the first half of the paper, some recent advances in coupled dynamical systems, in particular, a globally coupled map are surveyed. First, dominance of Milnor attractors in partially ordered phase is demonstrated. Second, chaotic…

Aspects of the Nos\'e and Nos\'e-Hoover dynamics developed in 1983-1984 along with Dettmann's closely related dynamics of 1996, are considered. We emphasize paradoxes associated with Liouville's Theorem. Our account is pedagogical, focused…

An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…

We propose a generalization of the model of classical baker map on the torus, in which the images of two parts of the phase space do overlap. This transformation is irreversible and cannot be quantized by means of a unitary Floquet…

For spatially one-dimensional run-and-tumble dynamics with mass conservation we develop a coarse phase diagram, that discriminates between global decay to equidistributed constant states, existence of spatially non-trivial waves, and finite…

Infinitesimal volumes stretch and contract as they coevolve with classical phase space trajectories according to linearized dynamics. Unless these tangent-space dynamics are modified, chaotic evolution causes the volume spanned by evolving…

Time-local generators of open quantum systems are generically divergent at long times, even though the reduced dynamics remains regular. We construct, by analytic continuation, nonperturbative dynamical maps consistent with these…

Motivated by the study of reversal behaviour of myxobacteria, in this article we are interested in a kinetic model for reversal dynamics, in which particles with directions close to be opposite undergo binary collision resulting in…

The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability $p$ or disappears with probability $1\!-\!p$. It describes a stochastic dyadic Cantor set that…