Related papers: Bilinear quantum systems on compact graphs: well-p…
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…
In this paper, we study the control of a class of time-invariant linear ensemble systems whose natural dynamics are linear in the system parameter. This class of ensemble control systems arises from practical engineering and physical…
In this paper we study quantum star graphs with time-dependent bond lengths. Quantum dynamics is treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs. Time-dependence of the average kinetic energy…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
We present a conceptually new approach to describe state-of-the-art photonic quantum experiments using Graph Theory. There, the quantum states are given by the coherent superpositions of perfect matchings. The crucial observation is that…
A surrogate model for particle-in-cell plasma simulations based on a graph neural network is presented. The graph is constructed in such a way as to enable the representation of electromagnetic fields on a fixed spatial grid. The model is…
We theoretically investigate the spectrum of a single electron double quantum dot, defined by top gates in a graphene with a substrate induced gap. We examine the effects of electric and magnetic fields on the spectrum of localized states,…
We investigate the propagation of a massless scalar field on a star graph, modeling the junction of $n$ quantum wires. The vertex of the graph is represented by a point-like impurity (defect), characterized by a one-body scattering matrix.…
In this work, we investigate the small-time global controllability properties of a class of fourth-order nonlinear parabolic equations driven by a bilinear control posed on the one-dimensional torus. The controls depend only on time and act…
This work studies the Schr\"odinger bridge problem for the kinematic equation on a compact connected Lie group. The objective is to steer a controlled diffusion between given initial and terminal densities supported over the Lie group while…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the…
The mechanisms of optical activity and quantum transport of twisted bilayer graphene are studied. The formation of unique electron states in the bilayer systems is studied using an effective continuum model. Such states are shown to support…
We study quantum tunneling in an asymmetric double-well potential using a dynamical systems--based approach rooted in the Ehrenfest formalism. In this framework, the time evolution of a Gaussian wave packet is governed by a hierarchy of…
This work investigates the motion of a non-relativistic charged particle within the spacetime of a global monopole. We introduce the Schr\"odinger equation to describe the particle's motion with two interactions by considering the Kratzer…
We consider an explicitly solvable model (formulated in the Riemannian geometry terms) for a stationary wave process in a specific thin domain with the Dirichlet boundary conditions on the boundary of the domain. The transition from the…
We consider basic dynamical effects in settings based on a pair of local potential traps that may be effectively switched on and off, or suddenly displaced, by means of appropriate control mechanisms, such as the scanning tunneling…
We study the controllability of a linear KdV-Schr{\"o}dinger equation on the one-dimensional torus via purely imaginary bilinear controls. Considering controls spanning a suitable finite number of Fourier modes, we prove small-time global…
We consider the problem of controlling a partially-observed dynamic process on a graph by a limited number of interventions. This problem naturally arises in contexts such as scheduling virus tests to curb an epidemic; targeted marketing in…