Related papers: Passive and reciprocal linear time-and-space-invar…
We complexify a 1-d potential which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters becomes…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
Breaking Lorentz reciprocity was believed to be a prerequisite for nonreciprocal transmissions of light fields, so the possibility of nonreciprocity by linear optical systems was mostly ignored. We put forward a structure of three mutually…
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework…
Nonreciprocity is most commonly associated with a large difference in the transmitted energy when the locations of the source and receiver are interchanged. This energy bias is accompanied by a difference in the transmitted phase. We…
In recent years, studies of long-range interacting (LRI) systems have taken centre stage in the arena of statistical mechanics and dynamical system studies, due to new theoretical developments involving tools from as diverse a field as…
The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying…
Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…
Reciprocity is shown so far only when the scattering potential is either real or parity symmetric complex. We extend this result for parity violating complex potential by considering several explicit examples: (i) we show reciprocity for a…
Having in mind that physical systems have different levels of structure we develop the concept of external, internal and total improper Lorentz transformation (space inversion and time reversal). A particle obtained from the ordinary one by…
Reciprocity is fundamental to light transport and is a concept that holds also in rather complex systems. Yet, reciprocity can be switched off even in linear, isotropic and passive media by setting the material structure into motion. In…
The bulk conductivity of a two-dimensional system is studied assuming that quantum interference effects break time-reversal symmetry in the presence of strong spin-orbit interaction and strong lattice potential. The study is carried out by…
This work presents a mechanism by which non-reciprocal wave transmission is achieved in a class of gyric metamaterial lattices with embedded rotating elements. A modulation of the device's angular momentum is obtained via prescribed…
Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…
Topological theory predicts the necessary conditions for robust dimensional reduction in a host of quantum and classical systems. Models have recently been proposed for stochastic systems which describe many biological and chemical…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
Recently, there has been an increasing interest in employing rotational motion measurements for seismic source inversion, structural imaging and ambient noise analysis. We derive reciprocity and representation theorems for rotational…
We study state-feedback design for continuous-time LTI systems with a control input and an external input-output pair. Our objective is to determine feedback gains that render the closed-loop system (strictly) passive with respect to the…
Thermodynamic and dynamical properties of systems with long range pairwise interactions (LRI) which decay as 1/r^{d+\sigma} at large distances r in $d$ dimensions are reviewed in these Notes. Two broad classes of such systems are…
Onsager reciprocity $L_{ij}=L_{ji}$ is a cornerstone of near-equilibrium thermodynamics derived from microscopic time-reversal symmetry. We develop a geometric framework in which entropy-weighted reparameterization of thermodynamic response…