Related papers: A probability-conserving dissipative Schr\"odinger…
Exact analytic solutions to the Schr\"odinger equation for an electron moving in three dimensional potentials have been studied. These solutions can correspond to metals, semiconductors, or insulators. We show that there is an efficient…
The projection formalism for calculating effective Hamiltonians and resonances is generalized to the nonlocal and/or nonhermitian case, so that it is applicable to the reduction of relativistic systems (Bethe-Salpeter equations), and to…
We are interested in the behavior of solutions to the damped inhomogeneous nonlinear Schr\"odinger equation $ i\partial_tu+\Delta u+\mu|x|^{-b}|u|^{\alpha}u+iau=0$, $\mu \in\mathbb{C} $, $b>0$, $a \in \mathbb{C}$ such that $\Re…
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schr\"odinger equations, perturbed by bounded noise acting on only two Fourier modes. To tackle the lack of smoothing effect, we introduce…
The modified discrete nonlinear Schr\"odinger equation is used to study the formation of stationary localized states in a one-dimensional lattice with a single impurity and an asymmetric dimer impurity. A periodically modulated and a…
We calculate the reduced density matrix for a system of coupled harmonic oscillators in a bosonic heat bath using the Born-Markov approximation and show that the expectation values of position and momentum evolve like classical quantities.…
We represent the method of dynamic diffusion for the approximate solution of Shroedinger equation with decoherence. Decoherence shows as the divergency of exact solution from the dynamics of diffusion swarm, which arises when the total…
We study the asymptotics of the Schr\"odinger equation with time-dependent potential in dimension one. Assuming that the potential decays sufficiently rapidly as $|x| \to \infty$, we prove that the solution can be written as the sum of a…
We analyze the chaotic dynamics of a one-dimensional discrete nonlinear Schr\"odinger equation. This nonintegrable model, ubiquitous in several fields of physics, describes the behavior of an array of coupled complex oscillators with a…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the step-like input (photonic dam) into a pair of oppositely propagating…
We study the dynamics of entanglement in a two-qubit system interacting with a squeezed thermal bath via a dissipative system-reservoir interaction with the system and reservoir assumed to be in a separable initial state. The resulting…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation,…
We are interested in the scattering problem for the cubic 3D nonlinear defocusing Schr\"odinger equation with variable coefficients. Previous scattering results for such problems address only the cases with constant coefficients or assume…
The higher-order nonlinear Schrodinger equation (Dysthe's equation in the context of water-waves) models the time evolution of the slowly modulated amplitude of a wave-packet in dispersive partial differential equations (PDE). These…
We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as…
We present a theory for the dissipation of electronic spins trapped in quantum dots due to their coupling to the host lattice acoustic phonon modes. Based on the theory of dissipative two level systems for the spin dynamics, we derive a…
A stochastic Schr\"odinger equation is presented to describe simultaneous continuous measurement of the position and momentum of a non-relativistic particle. The equation is solved to yield a state localised in position and momentum…
A method is proposed to transform any analytic solution of the Bloch equation into an analytic solution of the Landau-Lifshitz-Gilbert equation. This allows for the analytical description of the dynamics of a two level system with damping.…