324 research outputs found
Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity
In this paper, we establish the unconditional uniqueness of solutions to the
cubic Gross-Pitaevskii hierarchy on in a low regularity Sobolev
type space. More precisely, we reduce the regularity down to the currently
known regularity requirement for unconditional uniqueness of solutions to the
cubic nonlinear Schr\"odinger equation ( if and
if ). In such a way, we extend the recent work of
Chen-Hainzl-Pavlovi\'c-Seiringer.Comment: 26 pages, 1 figur
Cascaded Entanglement Enhancement
We present a cascaded system consisting of three non-degenerate optical
parametric amplifiers (NOPAs) for the generation and the enhancement of quantum
entanglement of continuous variables. The entanglement of optical fields
produced by the first NOPA is successively enhanced by the second and the third
NOPAs from -5.3 to -8.1 below the quantum noise limit. The dependence
of the enhanced entanglement on the physical parameters of the NOPAs and the
reachable entanglement limitation for a given cascaded NOPA system are
calculated. The calculation results are in good agreement with the experimental
measurements.Comment: 5 pages, 4 figure
Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy
In this paper, we study solutions to the three-dimensional quintic
Gross-Pitaevskii hierarchy. We prove unconditional uniqueness among all small
solutions in the critical space (which corresponds to on
the NLS level). With slight modifications to the proof, we also prove
unconditional uniqueness of solutions to the Hartree hierarchy without
smallness condition. Our proof uses the quantum de Finetti theorem, and is an
extension of the work by Chen-Hainzl-Pavlovi\'c-Seiringer \cite{CHPS}, and our
previous work \cite{UniqueLowReg}.Comment: 1 figure, 24 page
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From quantum many body systems to nonlinear Schrödinger Equations
textThe derivation of nonlinear dispersive PDE, such as the nonlinear Schrödinger (NLS) or nonlinear Hartree equations, from many body quantum dynamics is a central topic in mathematical physics, which has been approached by many authors in a variety of ways. In particular, one way to derive NLS is via the Gross-Pitaevskii (GP) hierarchy, which is an infinite system of coupled linear non-homogeneous PDE. In this thesis we present two types of results related to obtaining NLS via the GP hierarchy. In the first part of the thesis, we derive a NLS with a linear combination of power type nonlinearities in R[superscript d] for d = 1, 2. In the second part of the thesis, we focus on considering solutions to the cubic GP hierarchy and we prove unconditional uniqueness of low regularity solutions to the cubic GP hierarchy in R[superscript d] with d ≥ 1: the regularity of solution in our result coincides with known regularity of solutions to the cubic NLS for which unconditional uniqueness holds.Mathematic
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