Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential
نویسندگان
چکیده
We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique developed in [3], we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our works [5, 6] with a slightly different strategy.
منابع مشابه
Mean field limit for bosons and propagation of Wigner measures
We consider the N-body Schrödinger dynamics of bosons in the mean field limit with a bounded pair-interaction potential. According to the previous work [AmNi], the mean field limit is translated into a semiclassical problem with a small parameter ε → 0, after introducing an εdependent bosonic quantization. The limit is expressed as a push-forward by a nonlinear flow (e.g. Hartree) of the associ...
متن کاملMean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states
Contrary to the finite dimensional case, Weyl and Wick quantizations are no more asymptotically equivalent in the infinite dimensional bosonic second quantization. Moreover neither the Weyl calculus defined for cylindrical symbols nor the Wick calculus defined for polynomials are preserved by the action of a nonlinear flow. Nevertheless taking advantage carefully of the information brought by t...
متن کاملA two dimensional Simulation of crack propagation using Adaptive Finite Element Analysis
Finite element method (FEM) is one of the most famous methods which has many applications in varies studies such as the study of crack propagation in engineering structures. However, unless extremely fine meshes are employed, problem arises in accurately modelling the singular stress field in the singular element area around the crack tip. In the present study, the crack growth simulation has b...
متن کاملEuler-Lagrange equations and geometric mechanics on Lie groups with potential
Abstract. Let G be a Banach Lie group modeled on the Banach space, possibly infinite dimensional, E. In this paper first we introduce Euler-Lagrange equations on the Lie group G with potential and right invariant metric. Euler-Lagrange equations are natural extensions of the geodesic equations on manifolds and Lie groups. In the second part, we study the geometry of the mechanical system of a r...
متن کاملEffect of interactions on the integrability and level statistics of two particles in an infinite quantum well
We determine the energy spectrum of a system consisting of two particles which interact through a screened Coulomb potential. The spinless particles are confined in a one-dimensional infinite well. The integrable bouncing-ball limit and the bare potential cases, the latter one for different strengths, are considered. In both cases, the level of distribution for the integrable limits do not foll...
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:
دوره شماره
صفحات -
تاریخ انتشار 2011