اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNonlinear Schrodinger equations with a multiple-well potential and a Stark-type perturbation
156
0
0.0
(
0
)
تأليف
Andrea Sacchetti
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A Bose-Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross-Pitaevskii equation. Here we prove that such an equation can be reduced, in the semiclassical limit and in the case of a lattice with a finite number of wells, to a finite-dimensional discrete nonlinear Schrodinger equation. Then, by means of numerical experiments we show that the BECs center of mass exhibits an oscillating behavior with modulated amplitude; in particular, we show that the oscillating period actually depends on the shape of the initial wavefunction of the condensate as well as on the strength of the nonlinear term. This fact opens a question concerning the validity of a method proposed for the determination of the gravitational constant by means of the measurement of the oscillating period.
قيم البحث
اقرأ أيضاً
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $Tgg1$ is the adiabat
ic evolution time. A generalization of the Berry phase of the linear Schrodinger equation is formulated for the Hartree type equation. For the solutions constructed, the Berry phases are found in explicit form.
In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear equation b
ecome a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.
Considering symmetric strictly convex potentials, a local relationship is inferred from the virial theorem, based on which a real log-concave function can be constructed. Using this as a weight function and in such a way that the virial theorem can s
till be verified, parameter-free ansatze for the eigenfunctions of the associated Schrodinger equation are built. To illustrate the process, the technique is successfully tested against the harmonic oscillator, in which it leads to the exact eigenfunctions, and against the quartic anharmonic oscillator, which is considered the paradigmatic testing ground for new approaches to the Schrodinger equation.
Based on the ideology of the Maslovs complex germ theory, a method has been developed for finding an exact solution of the Cauchy problem for a Hartree-type equation with a quadratic potential in the class of semiclassically concentrated functions. T
he nonlinear evolution operator has been obtained in explicit form in the class of semiclassically concentrated functions. Parametric families of symmetry operators have been found for the Hartree-type equation. With the help of symmetry operators, families of exact solutions of the equation have been constructed. Exact expressions are obtained for the quasi-energies and their respective states. The Aharonov-Anandan geometric phases are found in explicit form for the quasi-energy states.
Quantum trajectories are Markov processes that describe the time-evolution of a quantum system undergoing continuous indirect measurement. Mathematically, they are defined as solutions of the so-called Stochastic Schrodinger Equations, which are nonl
inear stochastic differential equations driven by Poisson and Wiener processes. This paper is devoted to the study of the invariant measures of quantum trajectories. Particularly, we prove that the invariant measure is unique under an ergodicity condition on the mean time evolution, and a purification condition on the generator of the evolution. We further show that quantum trajectories converge in law exponentially fast towards this invariant measure. We illustrate our results with examples where we can derive explicit expressions for the invariant measure.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
