相关论文: Degenerate Dynamical Systems

The dynamics of strongly disordered systems becomes extremely slow or glassy at low temperatures, which results in a characteristic aging scenario. This means that the outcome of measurements strongly depends on the history of the system…

The properties of one-dimensional superconductors are strongly influenced by topological fluctuations of the order parameter, known as phase slips, which cause the decay of persistent current in superconducting rings and the appearance of…

The basic mathematical assumptions for autonomous linear kinetic equations for a classical system are formulated, leading to the conclusion that if they are differential equations on its phase space $M$, they are at most of the 2nd order.…

Apart from not having crystallized, supercooled liquids can be considered as being properly equilibrated and thus can be described by a few thermodynamic control variables. In contrast, glasses and other amorphous solids can be arbitrarily…

Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field…

We use Langevin dynamics simulations to study dynamical behaviour of a dense planar layer of active semi-flexible filaments. Using the strength of active force and the thermal persistence length as parameters, we map a detailed phase…

A system's invariance under Galilean transformation implies three locally conserved densities. Including them as variables, the thermodynamics is rendered explicitly frame independent, dissipative mass currents are shown to vanish, and…

We study properties of domain walls in the symmetron model, in which the scalar gravitational degree of freedom decouples from matter in regions of high density, and exhibits a spontaneously broken $Z_2$ symmetry at low densities. The…

Based on the dissipative Landau-Lifshitz equation, the spatiotemporal structure formation problem is investigated in the region far above the transverse ferromagnetic resonance instability. Apart from the external fields, the model contains…

We study the dynamics of an elastic body whose shape and position evolve due to the gravitational forces exerted by a pointlike planet. The main result is that, if all the deformations of the satellite dissipate some energy, then under a…

Recently, several studies involving open quantum systems which possess a strong symmetry have observed that every individual trajectory in the Monte Carlo unravelling of the master equation will dynamically select a specific symmetry sector…

We study the dynamics of domain walls in a double-field model in which the U(1) symmetry is broken both spontaneously and explicitly. The global U(1) symmetry of the system is restored when the symmetry breaking parameter $\epsilon$ is set…

In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only…

We consider a one-dimensional family of rational surfaces with automorphisms. In a degeneration of this family, the limiting map is the identity map on a special fiber. We check that the map on the total space of the family has…

In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…

For Hamitonian systems with 3/2 degrees of freedom close to nonlinear integrable and for symplectic maps of the cylinder, bifurcations in degenerate resonance zones are discussed.

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and…

The spontaneous breaking of an approximate discrete symmetry is considered, with the resulting protodomains of true and false vacuum being separated by domain walls. Given a strong, symmetric Yukawa coupling of the real scalar field to a…