Related papers: On System Operators with Variation Bounding Proper…
In the present note, we give two examples of bilinear quantum systems showing good agreement between the total variation of the control and the variation of the energy of solutions, with bounded or unbounded coupling term. The corresponding…
Systems whose variable are constrained to be positive allow computationally efficient control design. We generalize these results to linear systems which leave a cone invariant. This is a wider class of systems than positive systems. We…
The causality properties of linear time-varing systems under constant time lags are investigated based on the definition and use of the definitions of appropriate Hankel and Toeplitz causal and anticausal operators.
In various applications in the field of control engineering the estimation of the state variables of dynamic systems in the presence of unknown inputs plays an important role. Existing methods require the so-called observer matching…
Several continuous dynamical systems have recently been proposed as special-purpose analog computers designed to solve combinatorial optimization problems such as $k$-SAT or the Ising problem. While combinatorial optimization problems are…
Nonlinear dynamical systems possessing an invariant subspace can display interesting dynamical behavior, such as on-off intermittency and bubbling. This letter shows that a class of such systems have amazing features of (1) supersensitivity…
We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time…
We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that…
We develop a method to describe the temporal evolution of an interacting system of bosons, for which the field operator expansion is truncated after a finite number $M$ of modes, in a rigorously controlled manner. Using McLachlan's…
As we show in this paper, the prediction for output token $n+1$ of Transformer architectures without one of the mechanisms of positional encodings and causal attention is invariant to permutations of input tokens $1, 2, ..., n-1$. Usually,…
Noise is ubiquitous in nature, so it is essential to characterize its effects. Considering a fluctuating Hamiltonian, we introduce an observable, the stochastic operator variance (SOV), which measures the spread of different stochastic…
Scrambling is a key concept in the analysis of nonequilibrium properties of quantum many-body systems. Most studies focus on its characterization via out-of-time-ordered correlation functions (OTOCs), particularly through the early-time…
In this paper, a leader-following coordination problem of heterogeneous multi-agent systems is considered under switching topologies where each agent is subject to some local (unbounded) disturbances. While these unknown disturbances may…
Besides perturbation theory (which clearly requires the knowledge of the exact unperturbed solution), variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in quantum…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their…
A dynamical system is called contractive if any two solutions approach one another at an exponential rate. More precisely, the dynamics contracts lines at an exponential rate. This property implies highly ordered asymptotic behavior…
We consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport…
This paper presents a non-minimal order dynamics model for many analysis, simulation, and control problems of constrained mechanical systems with switching topology by making use of linear projection operator. The distinct features of this…
In this paper we present two different problems within the framework of shift-invariant theory. First, we develop a triangular form for shift-preserving operators acting on finitely generated shift-invariant spaces. In case of the normal…