Localization phenomena in nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities: Theory and applications to Bose-Einstein condensates |
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| Authors: | Ví ctor M. Pé rez-Garcí a,Rosa Pardo |
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| Affiliation: | a Departamento de Matemáticas, E. T. S. I. Industriales and Instituto de Matemática Aplicada a la Ciencia y la Ingeniería, Edificio Politécnico, Avenida de Camilo José Cela, 3, Universidad de Castilla-La Mancha 13071 Ciudad Real, Spain
b Departamento de Matemática Aplicada, Facultad de Ciencias Químicas, Universidad Complutense, Avda. Complutense s/n, 28040 Madrid, Spain |
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| Abstract: | We study the properties of the ground state of nonlinear Schrödinger equations with spatially inhomogeneous interactions and show that it experiences a strong localization on the spatial region where the interactions vanish. At the same time, tunneling to regions with positive values of the interactions is strongly suppressed by the nonlinear interactions and as the number of particles is increased it saturates in the region of finite interaction values. The chemical potential has a cutoff value in these systems and thus takes values on a finite interval. The applicability of the phenomenon to Bose-Einstein condensates is discussed in detail. |
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| Keywords: | 03.75.Lm 05.45.Yv 42.65.Tg |
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