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Tuesday, July 28, 2020 | History

5 edition of Wigner measure and semiclassical limits of nonlinear Schrodinger equations found in the catalog.

Wigner measure and semiclassical limits of nonlinear Schrodinger equations

Ping Zhang

Wigner measure and semiclassical limits of nonlinear Schrodinger equations

by Ping Zhang

  • 225 Want to read
  • 19 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Schrödinger equation,
  • WKB approximation,
  • Differential equations, Nonlinear,
  • Nonlinear theories

  • Edition Notes

    Includes bibliographical references.

    StatementPing Zhang.
    SeriesCourant lecture notes -- 17
    Classifications
    LC ClassificationsQC174.26.W28 Z43 2008
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL16958793M
    ISBN 109780821847015
    LC Control Number2008028025

      Firstly, based on the small-signal analysis theory, the nonlinear Schrodinger equation (NLSE) with fiber loss is solved. It is also adapted to the NLSE with the high-order dispersion terms. Furthermore, a general theory on cross-phase modulation (XPM) intensity fluctuation which adapted to all kinds of modulation formats (continuous wave, non-return-to-zero wave, and return-zero pulse wave) . The quantum effect on the Wigner time-delay and distribution for the polarization scattering in a semiclassical dense plasma is explored. The partial wave analysis is applied for a partially ionized dense plasma to derive the phase shift for the polarization interaction. The Wigner time-delay and the Wigner distribution are derived for the electron–atom polarization interaction including.

    Home» MAA Publications» MAA Reviews» Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations. Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations. Ping Zhang. Partial Differential Equations. Log in to post comments; Dummy View - NOT TO BE DELETED. MAA Publications. The Bloch decomposition plays a fundamental role in the study of quantum mechanics and wave propagation in periodic media. Most of the homogenization theory developed for the study of high frequency or semi-classical limit for these problems assumes no crossing of the Bloch bands, resulting in a classical Liouville equation in the limit along each Bloch band.

    2 Discrete Dynamics in Nature and Society The DFNLS has infinitely many conservation laws see, e.g., 1–3, two of which are ∂ tρ ∂ xJ 0, ∂ tJ ∂ x J2 ρ 1 2 ∂ x 2. corrections. Note that we avoid the frequently used term “semiclassical limit” for → 0; in particular since in solid state physics the term “semiclassical equation” is reserved for () as a “crystal” version of the Vlasov equation. The limit from a Schrödinger equation with a periodic potential, which yields the “semiclassical.


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Wigner measure and semiclassical limits of nonlinear Schrodinger equations by Ping Zhang Download PDF EPUB FB2

Abstract: This book is based on a course entitled “Wigner measures and semiclassical limits of nonlinear Schrödinger equations,” which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of Get this from a library.

Wigner measure and semiclassical limits of nonlinear Schrödinger equations. [Ping Zhang] -- "This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrodinger equations," which the author taught.

Get this from a library. Wigner measure and semiclassical limits of nonlinear Schrödinger equations. [Ping Zhang] -- This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrödinger equations," which the author taught at.

The WKB Approximation to Nonlinear Schrodinger Equation 5 References and Remarks 10 Chapter 2. Wigner Measure 11 Semiclassical Pseudodifferential Operators and the FBI Transform 11 Wigner Measure 14 Semiclassical Limit of the Linear Schrodinger Equation 30 References and Remarks 34 Chapter 3.

() Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain. Archive for Rational Mechanics and Analysis() Convergence of Nonlinear Schrödinger–Poisson Systems to the Compressible Euler by: Wigner Measure and the Semiclassical Limit of Schrödinger--Poisson Equations.

Related Databases. On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit. SIAM Journal on Numerical AnalysisAsymptotic limit of nonlinear Schrödinger-Poisson system with general initial by: Wigner Measure and Semiclassical Limits of Nonlinear Schrödinger Equations Ping Zhang Publication Year: ISBN ISBN.

How we measure 'reads' well-posedness and semiclassical limit of nonlinear Schrodinger-Poisson system. of the linear Schrodinger equation based on the Wigner transform is well suited for. This case is referred as the semiclassical limit or supercritical nonlinear optics limit and is usually studied by expanding the functions A and φ in Taylor series in ε similar to (), the.

The Gaussian semiclassical soliton ensemble and numerical methods for the focusing nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena, Vol. Issue. 21, p.

‘ Wigner measure and the semiclassical limit of Schrödinger On Fourier Time-Splitting Methods for Nonlinear Schrödinger Equations in the Semiclassical Limit. Abstract. In this paper, we study the semiclassical limit of the Gross-Pitaevskii equation (a cubic nonlinear Schrödinger equation) with the Neumann boundary condition in an exterior domain.

We consider the semiclassical limit of nonlinear Schrödinger equations with wavepacket initial data. We recover the Wigner measure of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum.

Wigner measures have been used to create effective models for wave propagation in random media, quantum molecular. Semiclassical limit for nonlinear Schrödinger equation with potential. II Article type: Research Keywords: Schrödinger equation, ground state, stability, semiclassical limit, Wigner measure, WKB method.

Journal: Asymptotic Analysis, vol. 47, no permissions, book requests, submissions and proceedings, contact the Amsterdam office. Uses the so-called Wigner measure approach. Figalli, Ligabò, Paul Modern approach to Wigner measures, dealing with rough potentials.

Infinite dimensional phase space (bosonic QFT) Ginibre and Velo Extension of the work of Hepp to infinite dimensions. Ammari and Nier Infinite dimensional Wigner measures. On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime P. Markowich, P.

Pietra, C. Pohl, and, H. Stimming, A Wigner-Measure Analysis of the Dufort-Frankel Scheme for the Schrödinger Equation, preprint.

Google Scholar. P.D. Miller, S. KamvissisOn the semiclassical limit of the focusing. The construction of Wigner measures in T is somewhat similar to the one in Rn, with the Fourier transform being replaced by Fourier series.

In this section we also present some applications to the study of semiclassical limit of stationary states for the Schrodinger equation. Next, in section 4, we formulate in terms of Wigner mea.

We apply Wigner transform techniques to the analysis of the Dufort--Frankel difference scheme for the Schrödinger equation and to the continuous analogue of the scheme in the case of a small (scaled) Planck constant (semiclassical regime). Abstract. This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrödinger equations," which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of Author: Ping Zhang.

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets).

We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum.

The first is Whitham’s averaging method, which gives the modulation equations governing the evolution of multi-phase solutions. The second is the Wigner transform, a convenient tool to derive the semiclassical limit equation in the phase space—the Vlasov equation—for the linear Schrödinger equation.

Recently, coupled systems of nonlinear Schrödinger equations have been used extensively to describe a double condensate, i.e. a binary mixture of Bose-Einstein condensates. In a double condensate, an interface and shock waves may occur due to large intraspecies and interspecies scattering lengths.

To know the dynamics of an interface and assure the existence of shock waves in .Another convenient tool to study the semiclassical limit of the Schrödinger equation (and many other problems) is the Wigner distribution [18,27,34,43], which gives, in the semiclassical limit, the Vlasov (or Liouville) equation in the phase space.

Since the Vlasov equation is a linear kinetic equation, it naturally unfolds the caustics and gives.Semiclassical Limit for the Schrödinger-Poisson Equation in a Crystal. By Norbert J.

Mauser. Abstract. Wigner transform Topics: nonlinear Schrödinger equations, Schrödinger-Poisson, Vlasov-Poisson, classical limit, semiclassical equations, Wigner measure, Wigner transform, Wigner Bloch series.

XI–1 semiclassical equations, Wigner.