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Title: Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems

Abstract

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

Authors:
ORCiD logo [1];  [2];  [3];  [3];  [3];  [4];  [3]
  1. Univ. of Science and Technology of China, Anhui (China); Luoyang Electronic Equipment Testing Center, Luoyang (China)
  2. Univ. of Science and Technology of China, Anhui (China); Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab.
  3. Univ. of Science and Technology of China, Anhui (China)
  4. Univ. of Science and Technology Beijing, Beijing (China)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1420776
Grant/Contract Number:  
51477182; 11575185; 11575186; 2015GB111003; QYZDB-SSW-SYS004
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 349; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Schrödinger–Maxwell equations; Symplectic structure; Discrete Poisson bracket; Geometric algorithms; First-principle simulation

Citation Formats

Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, and Wang, Yulei. Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems. United States: N. p., 2017. Web. https://doi.org/10.1016/j.jcp.2017.08.033.
Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, & Wang, Yulei. Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems. United States. https://doi.org/10.1016/j.jcp.2017.08.033
Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, and Wang, Yulei. Thu . "Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems". United States. https://doi.org/10.1016/j.jcp.2017.08.033. https://www.osti.gov/servlets/purl/1420776.
@article{osti_1420776,
title = {Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems},
author = {Chen, Qiang and Qin, Hong and Liu, Jian and Xiao, Jianyuan and Zhang, Ruili and He, Yang and Wang, Yulei},
abstractNote = {An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.},
doi = {10.1016/j.jcp.2017.08.033},
journal = {Journal of Computational Physics},
number = C,
volume = 349,
place = {United States},
year = {2017},
month = {8}
}

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Cited by: 3 works
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Works referenced in this record:

Relativistic laser-matter interaction: from attosecond pulse generation to fast ignition
journal, November 2007


Attosecond physics
journal, February 2009


Multiple absorption of laser photons by atoms
journal, April 1973


Free-Free Transitions Following Six-Photon Ionization of Xenon Atoms
journal, April 1979


Effect of an intense electromagnetic field on a weakly bound system
journal, November 1980


Multiphoton absorptions above the ionisation threshold
journal, April 1980

  • Gontier, Y.; Poirier, M.; Trahin, M.
  • Journal of Physics B: Atomic and Molecular Physics, Vol. 13, Issue 7
  • DOI: 10.1088/0022-3700/13/7/013

Studies of multiphoton production of vacuum-ultraviolet radiation in the rare gases
journal, January 1987

  • McPherson, A.; Gibson, G.; Jara, H.
  • Journal of the Optical Society of America B, Vol. 4, Issue 4
  • DOI: 10.1364/JOSAB.4.000595

Above-Threshold Ionization in Low-Frequency Limit
journal, November 1988


Above-threshold ionization
journal, June 1991


Stabilization of atomic hydrogen in superintense, high-frequency laser fields of circular polarization
journal, November 1990


High-order harmonic generation from atoms and ions in the high intensity regime
journal, June 1992

  • Krause, Jeffrey L.; Schafer, Kenneth J.; Kulander, Kenneth C.
  • Physical Review Letters, Vol. 68, Issue 24
  • DOI: 10.1103/PhysRevLett.68.3535

Atomic Stabilization by Super-Intense Lasers
journal, November 1993


Plasma perspective on strong field multiphoton ionization
journal, September 1993


Theory of high-harmonic generation by low-frequency laser fields
journal, March 1994


Lagrange Equilibrium Points in Celestial Mechanics and Nonspreading Wave Packets for Strongly Driven Rydberg Electrons
journal, September 1994


Rescattering effect in above-threshold ionization processes
journal, March 1996

  • Bao, D.; Chen, S. G.; Liu, J.
  • Applied Physics B Laser and Optics, Vol. 62, Issue 3
  • DOI: 10.1007/BF01080962

Generation of Coherent X-rays in the Water Window Using 5-Femtosecond Laser Pulses
journal, October 1997


Feynman's Path-Integral Approach for Intense-Laser-Atom Interactions
journal, May 2001


Atomic transient recorder
journal, February 2004

  • Kienberger, R.; Goulielmakis, E.; Uiberacker, M.
  • Nature, Vol. 427, Issue 6977
  • DOI: 10.1038/nature02277

High-harmonic generation by resonant plasmon field enhancement
journal, June 2008

  • Kim, Seungchul; Jin, Jonghan; Kim, Young-Jin
  • Nature, Vol. 453, Issue 7196
  • DOI: 10.1038/nature07012

High harmonic interferometry of multi-electron dynamics in molecules
journal, July 2009

  • Smirnova, Olga; Mairesse, Yann; Patchkovskii, Serguei
  • Nature, Vol. 460, Issue 7258
  • DOI: 10.1038/nature08253

Quantitative rescattering theory for high-order harmonic generation from molecules
journal, July 2009


Real-time observation of valence electron motion
journal, August 2010

  • Goulielmakis, Eleftherios; Loh, Zhi-Heng; Wirth, Adrian
  • Nature, Vol. 466, Issue 7307
  • DOI: 10.1038/nature09212

Numerical study of two-photon ionization of helium using an ab initio numerical framework
journal, June 2010


Stabilization of Helium in Intense xuv Laser Fields
journal, April 2010


Bright Coherent Ultrahigh Harmonics in the keV X-ray Regime from Mid-Infrared Femtosecond Lasers
journal, June 2012


Extremely high-intensity laser interactions with fundamental quantum systems
journal, August 2012


Theories of photoelectron correlation in laser-driven multiple atomic ionization
journal, July 2012


Multiphoton Above Threshold Effects in Strong-Field Fragmentation
journal, October 2012


Photoionization of helium by attosecond pulses: Extraction of spectra from correlated wave functions
journal, May 2013


Scaling of the Low-Energy Structure in Above-Threshold Ionization in the Tunneling Regime: Theory and Experiment
journal, January 2013


Theoretical Analysis of High-Harmonic Generation in Solids
journal, August 2014


Keldysh theory of strong field ionization: history, applications, difficulties and perspectives
journal, October 2014


Ultraviolet surprise: Efficient soft x-ray high-harmonic generation in multiply ionized plasmas
journal, December 2015


Generation of bright phase-matched circularly-polarized extreme ultraviolet high harmonics
journal, December 2014


Extreme ultraviolet high-harmonic spectroscopy of solids
journal, May 2015

  • Luu, T. T.; Garg, M.; Kruchinin, S. Yu.
  • Nature, Vol. 521, Issue 7553
  • DOI: 10.1038/nature14456

Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering
journal, March 2015


Optical attosecond pulses and tracking the nonlinear response of bound electrons
journal, February 2016


Recollision physics
journal, March 2011


Time-dependent multiconfiguration methods for the numerical simulation of photoionization processes of many-electron atoms
journal, January 2014

  • Hochstuhl, D.; Hinz, C. M.; Bonitz, M.
  • The European Physical Journal Special Topics, Vol. 223, Issue 2
  • DOI: 10.1140/epjst/e2014-02092-3

Time-dependent generalized-active-space configuration-interaction approach to photoionization dynamics of atoms and molecules
journal, December 2014


Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media
journal, May 1966


Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations
journal, November 1981


A perfectly matched layer for the absorption of electromagnetic waves
journal, October 1994


Symplectic splitting operator methods for the time-dependent Schrödinger equation
journal, June 2006

  • Blanes, Sergio; Casas, Fernando; Murua, Ander
  • The Journal of Chemical Physics, Vol. 124, Issue 23
  • DOI: 10.1063/1.2203609

Accurate time propagation for the Schrödinger equation with an explicitly time-dependent Hamiltonian
journal, May 2008

  • Kormann, Katharina; Holmgren, Sverker; Karlsson, Hans O.
  • The Journal of Chemical Physics, Vol. 128, Issue 18
  • DOI: 10.1063/1.2916581

High-order symplectic FDTD scheme for solving a time-dependent Schrödinger equation
journal, March 2013

  • Shen, Jing; Sha, Wei E. I.; Huang, Zhixiang
  • Computer Physics Communications, Vol. 184, Issue 3
  • DOI: 10.1016/j.cpc.2012.09.032

Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
journal, August 2012

  • Squire, J.; Qin, H.; Tang, W. M.
  • Physics of Plasmas, Vol. 19, Issue 8
  • DOI: 10.1063/1.4742985

A variational multi-symplectic particle-in-cell algorithm with smoothing functions for the Vlasov-Maxwell system
journal, October 2013

  • Xiao, Jianyuan; Liu, Jian; Qin, Hong
  • Physics of Plasmas, Vol. 20, Issue 10
  • DOI: 10.1063/1.4826218

Variational symplectic particle-in-cell simulation of nonlinear mode conversion from extraordinary waves to Bernstein waves
journal, September 2015

  • Xiao, Jianyuan; Liu, Jian; Qin, Hong
  • Physics of Plasmas, Vol. 22, Issue 9
  • DOI: 10.1063/1.4930118

Explicit high-order non-canonical symplectic particle-in-cell algorithms for Vlasov-Maxwell systems
journal, November 2015

  • Xiao, Jianyuan; Qin, Hong; Liu, Jian
  • Physics of Plasmas, Vol. 22, Issue 11
  • DOI: 10.1063/1.4935904

Hamiltonian time integrators for Vlasov-Maxwell equations
journal, December 2015

  • He, Yang; Qin, Hong; Sun, Yajuan
  • Physics of Plasmas, Vol. 22, Issue 12
  • DOI: 10.1063/1.4938034

Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations
journal, December 2015


Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
journal, September 2016

  • He, Yang; Sun, Yajuan; Qin, Hong
  • Physics of Plasmas, Vol. 23, Issue 9
  • DOI: 10.1063/1.4962573

Structure and structure-preserving algorithms for plasma physics
journal, April 2017


Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
journal, November 2016

  • Xiao, Jianyuan; Qin, Hong; Morrison, Philip J.
  • Physics of Plasmas, Vol. 23, Issue 11
  • DOI: 10.1063/1.4967276

Dynamics of an atomic electron and its electromagnetic field in a cavity
journal, March 2005


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    Symmetries and local conservation laws of variational schemes for the surface plasmon polaritons
    journal, April 2019

    • Chen, Qiang; Hao, Xiaojun; Wang, Chuanchuan
    • Physics of Plasmas, Vol. 26, Issue 4
    • DOI: 10.1063/1.5086236

    Optoelectronic Device Simulations Based on Macroscopic Maxwell–Bloch Equations
    journal, June 2019

    • Jirauschek, Christian; Riesch, Michael; Tzenov, Petar
    • Advanced Theory and Simulations, Vol. 2, Issue 8
    • DOI: 10.1002/adts.201900018