Related papers: Nonlinear Filtering of Classical and Quantum Spin …

Starting from the von Neumann-Maxwell equations for the Wigner quasi-probability distribution and for the self-consistent electric field, the quantum analog of the classical single-wave model has been derived. The linear stability of the…

We examine the classical limit of a fairly general nonlinear semiclassical hybrid system within a MaxEnt framework. The consistency of the hybrid dynamics requires algebraic constraints on quantum operators and smoothness conditions for the…

Hybrid inverse problems are mathematical descriptions of coupled-physics (also called multi-waves) imaging modalities that aim to combine high resolution with high contrast. The solution of a high-resolution inverse problem, a first step…

In this paper I developed a classical model of elementary particle that is associated with a membrane of finite size, surrounded by non-linear electromagnetic field. The form of local interaction which lead to bounded states of finite…

Using a modified version of Weinstein's argument for constrained minimization in nonlinear dispersive equations, we prove existence of solitary waves in fully nonlocally nonlinear equations, as long as the linear multiplier is of positive…

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific…

Nonlinear extensions of the Kalman filter (KF), such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are indispensable for state estimation in complex dynamical systems, yet the conditions for a nonlinear KF to…

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given…

We address quantum metrology in critical spin chains with anisotropy and Dzyaloshinskii-Moriya (DM) interaction, and show how local and quasi-local measurements may be exploited to characterize global properties of the systems. In…

We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…

Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…

The work concerns about multiscale McKean-Vlasov stochastic systems. First of all, we prove an average principle for these systems in the $L^2$ sense. Moreover, a convergence rate is presented. Then we define the nonlinear filtering of…

Static, cylindrically symmetric solutions to nonlinear scalar-Einstein equations are considered. Regularity conditions on the symmetry axis and flat or string asymptotic conditions are formulated in order to select soliton-like solutions.…

No quantum measurement can give full information on the state of a quantum system; hence any quantum feedback control problem is neccessarily one with partial observations, and can generally be converted into a completely observed control…

A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \]…

The measurement problem dates back to the dawn of quantum mechanics. Here, we measure a quantum dot electron spin qubit through off-resonant coupling with thousands of redundant nuclear spin ancillae. We show that the link from quantum to…

Correlated classical and quantum many-particle systems out of equilibrium are of high interest in many fields, including dense plasmas, correlated solids, and ultracold atoms. Accurate theoretical description of these systems is challenging…

This paper deals with the Newton--Wigner position observable for Poincar\'e-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton--Wigner theorem in the quantum…

Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the…