Related papers: Passive systems with a normal main operator and qu…

We study here the behavior of the solutions to a $2\times 2$ semi-linear cooperative system involving Schr\" odinger operators (considered in its variational form): $$LU:=(-\Delta + q(x))U = AU+\mu U + F(x,U) \quad{\rm in}\ \mathbb{R}^N$$…

Passive imaging is a new technique which has been proved to be very efficient, for example in seismology: the correlation of the noisy fields, computed from the fields recorded at different points, is strongly related to the Green function…

This is a survey of the basic results on the behavior of the number of the eigenvalues of a Schr\"odinger operator, lying below its essential spectrum. We discuss both fast decaying potentials, for which this behavior is semiclassical, and…

Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past decade. They include systems of high interest to physicists and mathematicians such…

This work continues \cite{bib1} where the construction of Hamiltonian $H$ for the system of three quantum particles is considered. Namely the system consists of two fermions with mass $1$ and another particle with mass $m>0$. In the present…

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…

Quantum states that can yield work in a cyclical Hamiltonian process form one of the primary resources in the context of quantum thermodynamics. Conversely, states whose average energy cannot be lowered by unitary transformations are called…

An operator $T$ on a Hilbert space $\mathcal H$ is called expansive, if $\|Tx\|\geq \|x\|$ ($x\in\mathcal H$). Expansive operators $T$ quasisimilar to the unilateral shift $S_N$ of finite multiplicity $N$ are studied. It is proved that…

We introduce the notion of Quasi-Stationary State (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation…

In this note, it is shown that the stochastic Airy operator, which is the "Schr\"odinger operator" on the half-line whose potential term consists of Gaussian white noise plus a linear term tending to $+\infty$, can naturally be defined as a…

Deep selective State-Space Models (SSMs), whose state-space parameters are modulated online by a selection signal, offer significant expressive power but pose challenges for stability analysis, especially under discontinuous gating. We…

This paper presents an analysis of the passivity condition for discrete-time bilateral teleoperation systems. Considering discrete-time controllers for a master-slave teleoperation system can simplify its implementation. Varieties of…

Let $A$ and $B$ be almost commuting (i.e, $AB-BA\in\bS_1$) self-adjoint operators. We construct a functional calculus $\f\mapsto\f(A,B)$ for $\f$ in the Besov class $B_{\be,1}^1(\R^2)$. This functional calculus is linear, the operators…

A resistor-network picture of transitions is appropriate for the study of energy absorption by weakly chaotic or weakly interacting driven systems. Such "sparse" systems reach a novel non-equilibrium steady state (NESS) once coupled to a…

A nonadiabatic-transition system which exhibits ``quantum chaotic'' behavior [Phys. Rev. E {\bf 63}, 066221 (2001)] is investigated from quasi-classical aspects. Since such a system does not have a naive classical limit, we take the mapping…

We investigate the effect of slowly-varying parameter on the energy transfer in a system of weakly coupled nonlinear oscillators, with special attention to a mathematical analogy between the classical energy transfer and quantum…

Here we explore, in a series of articles, semiclassical quasimodes u(h,b), approximative solutions P(h)u(h,b)\sim 0, depending on $0<h<1$, and on b, the subprincipal symbol. We study a pseudodifferential operator with transversal…

We study transient patterns appearing in a class of SPDE using the framework of quasi-stationary and quasi-ergodic measures. In particular, we prove the existence and uniqueness of quasi-stationary and quasi-ergodic measures for a class of…

For a large class of dynamical problems from mathematical physics the skew-selfadjointness of a spatial operator of the form $A=\left(\begin{array}{cc} 0 & -C^{*}\\ C & 0 \end{array}\right)$, where $C:D\left(C\right)\subseteq H_{0}\to…

The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be…