Related papers: Hidden Harmonic Structure, Universal Damping, and …

Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…

We consider a set of non-linear interactions between dark matter and dark energy which comprises couplings proportional to products of (powers of) the energy densities of both dark components and of the total energy. We demonstrate that…

We investigate the role of relaxation mechanisms in the driven response of elastic disordered interfaces in finite dimensions, focusing on the interplay between dimensionality and interaction range. Through extensive numerical simulations,…

Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…

A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

Starting from the geometric description of quantum systems, we propose a novel approach to time-independet dissipative quantum processes according to which the energy is dissipated but the coherence of the states is preserved. Our proposal…

For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…

The heat conduction behavior of one dimensional momentum conserving lattice systems with asymmetric interparticle interactions is numerically investigated. It is found that with certain degree of interaction asymmetry, the heat conductivity…

Non-Hermitian models describe the physics of ubiquitous open systems with gain and loss. One intriguing aspect of non-Hermitian models is their inherent topology that can produce intriguing boundary phenomena like resilient higher-order…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

We develop a unified geometric framework for dissipative mechanical systems based on uniform $q$-contact manifolds, which provide an extended phase space equipped with multiple contact $1$-forms. Within this setting, we construct both…

Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…

While non-Hermitian systems are normally constructed through incoherent coupling to a larger environment, recent works have shown that under certain conditions coherent couplings can be used to similar effect. We show that this new paradigm…

In this paper we study vakonomic dynamics on contact systems with nonlinear constraints. In order to obtain the dynamics, we consider a space of admisible paths, which are the ones tangent to a given submanifold. Then, we find the critical…

We present an overdamped continuum description of oriented active solids in which interactions respect the symmetries of space but do not obey the principle of action and reaction. Taking position and orientation as kinematic variables, we…

This paper analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODEs with constant coeffcients. The novel part of this research is that the…

We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…

We study long-time dynamics of a class of abstract second order in time evolution equations in a Hilbert space with the damping term depending both on displacement and velocity. This damping represents the nonlinear strong dissipation…

In this paper we address the problem of identifying contracting systems among dynamical systems appearing in mechanics. First, we introduce a sufficient condition to identify contracting systems in a general Riemannian manifold. Then, we…