Quantum Fluctuations around Bistable Solitons in the Cubic-Quintic nonlinear Schrödinger equation

A practice problem for Schr{ö}dinger transmission

We present the case of quantal transmission through a smooth, single-piece exponential potential, $V(x)=-V_0 e^{x/a}$, in contrast to the piece-wise continuous potentials, as a pedagogic model to demonstrate the analytic extraction of transmission (reflection) co-efficient.

Entanglement condition via su(2) and su(1,1) algebra using Schr{ö}dinger-Robertson uncertainty relation

The Schr{ö}dinger-Robertson inequality generally provides a stronger bound on the product of uncertainties for two noncommuting observables than the Heisenberg uncertainty relation, and as such, it can yield a stricter separability condition in conjunction with partial transposition. In this paper, using the Schr{ö}dinger-Robertson uncertainty relation, the separability condition previously derived from the su(2) and the su(1,1) algebra is made stricter and refined to a form invariant with respect to local phase shifts. Furthermore, a linear optical scheme is proposed to test this invariant se…

Wavefunction collapse induced by gravity in a relativistic Schr{\''o}dinger-Newton model

A relativistic version of the Schr{ö}dinger-Newton equation is analyzed within the recently proposed Grave de Peralta approach [L. Grave de Peralta, {\em Results Phys.} {\bf 18} (2020) 103318], which include relativistic effects by a parametrization of the non-relativistic hamiltonian, so as to impose that the average kinetic energy of the system coincide with its relativistic kinetic energy. The reliability of this method is tested for the particle in a box. By applying this method to the Schr{ö}dinger-Newton equation we shows that the characteristic length of the model [L. Di{ó}si, {\em Phys…

Web-Schrödinger: Program for the interactive solution of the time dependent and stationary two dimensional (2D) Schr{ö}dinger equation

Web-Schr{ö}dinger is an interactive client-server software for the solution of the time-dependent and time-independent (stationary) Schr{ö}dinger equation. The program itself runs on a server computer and can be used through the Internet with a simple Web browser. Nothing is installed on the user's computer. The user can load, run, and modify ready-made example files, or prepare her/his own configuration(s), which can be saved on her/his own computer for later use. Several users can access the program parallelly and each can have independent sessions. Typical run times are in the second, or mi…

Anderson localization in the quintic nonlinear Schrödinger equation

In the present paper we consider the quintic defocusing nonlinear Schrödinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The main result shows that Anderson localization requires a cutoff on the value of the parameter which controls the quintic nonlinearity, with the cutoff depending on the amplitude of the random potential.

对数薛定谔方程的小时间近似可控性

Small-time approximate controllability of the logarithmic Schr\''dinger equation

该论文证明了对数非线性薛定谔方程在双线性控制下的小时间全局近似可控性，通过结合相位控制和梯度流方法，并借助WKB分析处理非线性估计，为首个此类结果。