Propagation of chaos for many-boson systems in one dimension with a point pair-interaction
نویسندگان
چکیده
We consider the semiclassical limit of nonrelativistic quantum many-boson systems with delta potential in one dimensional space. We prove that time evolved coherent states behave semiclassically as squeezed states by a Bogoliubov time-dependent affine transformation. This allows us to obtain properties analogous to those proved by Hepp and Ginibre-Velo ([Hep], [GiVe1, GiVe2]) and also to show propagation of chaos for Schrödinger dynamics in the mean field limit. Thus, we provide a derivation of the cubic NLS equation in one dimension. 2000 Mathematics subject classification: 81S30, 81S05, 81T10, 35Q55
منابع مشابه
Conservative chaotic flow generated via a pseudo-linear system
Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...
متن کاملFocusing Quantum Many-body Dynamics: the Rigorous Derivation of the 1d Focusing Cubic Nonlinear Schrödinger Equation
We consider the dynamics of N bosons in one dimension. We assume that the pair interaction is attractive and given by Nβ−1V (N ·) where ∫ V 6 0. We develop new techniques in treating the N−body Hamiltonian so that we overcome the diffi culties generated by the attractive interaction and establish new energy estimates. We also prove the optimal 1D collapsing estimate which reduces the regularity...
متن کاملTwo interacting particles in a disordered chain II: Critical statistics and maximum mixing of the one body states
For two particles in a disordered chain of length L with on-site interaction U , a duality transformation maps the behavior at weak interaction onto the behavior at strong interaction. Around the fixed point of this transformation, the interaction yields a maximum mixing of the one body states. When L ≈ L1 (the one particle localization length), this mixing results in weak chaos accompanied by ...
متن کاملChaotic Analysis and Prediction of River Flows
Analyses and investigations on river flow behavior are major issues in design, operation and studies related to water engineering. Thus, recently the application of chaos theory and new techniques, such as chaos theory, has been considered in hydrology and water resources due to relevant innovations and ability. This paper compares the performance of chaos theory with Anfis model and discusses ...
متن کاملSinglet scalar dark matter in noncommutative space
In this paper, we examine the singlet scalar dark matter annihilation to becoming the Standard Model particles in the non-commutative space. In the recent decades, many candidates of dark matter have been offered, but our information about the nature of dark matter is still limited. There are such particle candidates as scalar matetr, fermion, boson, gauge boson, etc.; however, they have nei...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Asymptotic Analysis
دوره 76 شماره
صفحات -
تاریخ انتشار 2012