相关论文: Relaxation systems and cyclic monotonicity

In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…

There is an abundance of evidence that some relaxation dynamics, e.g., exponential decays, are much more common in nature than others. Recently, there have been attempts to trace this dominance back to a certain stability of the prevalent…

We investigate the property for an input-output system to map unimodal inputs to unimodal outputs. As a first step, we analyse this property for linear time-invariant (LTI) systems, static nonlinearities, and interconnections of those. In…

In this brief, an algorithm for controlling chaotic systems using small, continuous time perturbations is presented. Stabilisation is achieved by self controlling feedback using low order LTI filters. The algorithm alleviates the need of…

We explore the dynamics of the entanglement entropy near equilibrium in highly-entangled pure states of two quantum-chaotic spin chains undergoing unitary time evolution. We examine the relaxation to equilibrium from initial states with…

The presence of symmetries can lead to nontrivial dynamics of operator entanglement in open quantum many-body systems, which characterizes the cost of an matrix product density operator (MPDO) representation of the density matrix in the…

We define a Lax operator as a monic pseudodifferential operator $L(\partial)$ of order $N\geq 1$, such that the Lax equations $\dfrac{\partial L(\partial)}{\partial t_k}=[(L^{\frac kN}(\partial))_+,L(\partial)]$ are consistent and non-zero…

The relaxation dynamics in mixed chaotic systems are believed to decay algebraically with a universal decay exponent that emerges from the hierarchical structure of the phase space. Numerical studies, however, yield a variety of values for…

We introduce a new simple hierarchically constrained model of slow relaxation. The configurational energy has a simple form as there is no coupling among the spins defining the system; the associated stationary distribution is an…

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

A logarithmic oscillator has the outstanding property that the expectation value of its kinetic energy is constant for all stationary states [1]. Recently the ansatz that this property can be used to define a Hamiltonian thermostat has been…

A quantum mechanical explanation of the relaxation to equilibrium is shown for macroscopic systems for nonintegrable cases and numerically verified. The macroscopic system is initially in an equilibrium state, subsequently externally…

A truncated Toeplitz operator is the compression of a classical Toeplitz operator on the Hardy space to a model space. A truncated Hankel operator is the compression of a Hankel operator on the Hardy space to the orthogonal complement of a…

In many computational tasks and dynamical systems, asynchrony and randomization are naturally present and have been considered as ways to increase the speed and reduce the cost of computation while compromising the accuracy and convergence…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

Consider a state of a system with several subsystems. The entropies of the reduced state on different subsystems obey certain inequalities, provided there is an equivalence relation, and a function measuring volumes or weights of…

Here we investigate specifically the transient of a synchronizing system, considering synchronization as a relaxation phenomenon. The stepwise establishment of synchronization is studied in the system of dynamically coupled maps introduced…

We study the classical dynamics of resonantly modulated large-spin systems in a strong magnetic field. We show that these systems have special symmetry. It leads to characteristic nonlinear effects. They include abrupt switching between…

The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time t_w. Two types of response have been…

Slowing down of the relaxation of the fluctuations around equilibrium is investigated both by stochastic simulations and by analysis of Master equation of reversible reaction networks consisting of resources and the corresponding products…