Related papers: Stability and control of a 1D quantum system with …
We consider the stability of position control of traveling waves in reaction-diffusion system as proposed in {[}J. L\"ober, H. Engel, arXiv:1304.2327{]}. Instead of analyzing the controlled reaction-diffusion system, stability is studied on…
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
We study a non-interacting quantum particle, moving on a one-dimensional lattice, which is subjected to repetitive measurements. We investigate the consequence when such motion is interrupted and restarted from the same initial…
We study a quantum computer with fixed and permanent interaction of diagonal type between qubits. It is controlled only by one-qubit quick transformations. It is shown how to implement Quantum Fourier Transform and to solve Shroedinger…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
The problem of the time of arrival of a quantum system in a specified state is considered in the framework of the repeated measurement protocol and in particular the limit of continuous measurements is discussed. It is shown that for a…
This study presents a numerical simulation of a quantum electron confined in a 10 nm potential well, using the Crank-Nicolson numerical technique to solve the time-dependent Schrodinger equation. The results capture the evolution of the…
In this article we consider a 2-D quantum particle confined a disc whose radius can be deformed continuously in time. We study the problem of controllability of such a quantum particle via deformations of the initial disc, i.e., when we set…
We investigate the long time behavior of a passive particle evolving in a one-dimensional diffusive random environment, with diffusion constant $D$. We consider two cases: (a) The particle is pulled forward by a small external constant…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities…
The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of…
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous localizations in space. We prove global existence and…
In this paper we consider quantum Hamiltonians with time-dependent interaction strengths, and following the recently formulated generalized Bethe ansatz framework [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)], we show that constraints…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of…
In quantum mechanics, a classical particle is raised to a wave-function, thereby acquiring many more degrees of freedom. For instance, in the semi-classical regime, while the position and momentum expectation values follow the classical…
In this paper, a nonlinear Schr\"odinger equation with an attractive (focusing) delta potential and a repulsive (defocusing) double power nonlinearity in one spatial dimension is considered. It is shown, via explicit construction, that both…