The mean-field approximation and the non-linear Schrödinger functional for trapped Bose gases

Although semi-classical methods can be applied to many problems, we choose to remain quite close in this short presentation to the initial goals of the theory, that is the

Estimates in dimension d = 2 for constant magnetic fields Numerical results and the symmetry issue. 3 Magnetic rings: the one-dimensional periodic case Magnetic interpolation on

Regard- ing the Schr¨ odinger equation proper as a special case of the NLS equations, we argue that the results of this paper imply that the probabilistic interpretation of

Our aim is to prove that the limiting dynamics of the Schr¨ odinger evolution in a random potential under this scaling is governed by a heat equation.. Quantum correlations that

Wong and Stephen Yau, I gave a lower estimate of the gap of the first 2 eigenvalues of the Schr¨odinger operator in case the potential is convex.. In this note we note that the

Very recently, the author ([25] and [26]) established weighted norm inequalities for some Schr¨ odinger-type operators, which include commutators of Riesz transforms,

, On smoothing property of Schr¨ odinger propagators, in Functional- Analytic Methods for Partial Differential Equations (Tokyo, 1989 ), Lecture Notes in Math.. , Smoothing property

It is not a reliable guide, of course, because sometimes in similar situations critical bound states are absent [1], nevertheless, here we are able to demonstrate that discrete