广西师范大学学报（自然科学版） ›› 2012, Vol. 30 ›› Issue (3): 77-82.

• • 上一篇    下一篇

Fermi-Pasta-Ulam模型中量子涨落对包络孤子的耗散效应

曾上游, 张争珍, 曾绍稳, 周黎明, 王榕峰, 唐文艳, 房新荷, 梁丹   

  1. 广西师范大学电子工程学院,广西桂林541004
  • 收稿日期:2012-05-26 出版日期:2012-09-20 发布日期:2018-12-04
  • 通讯作者: 曾上游(1974—),男,湖南双峰人,广西师范大学教授,博士。E-mail:zsy@mailbox.gxnu.edu.cn
  • 作者简介:曾上游,男,湖南双峰人,中共预备党员,留美博士,广西师范大学电子工程学院教授。
  • 基金资助:
    国家自然科学基金资助项目(11065003);广西自然科学基金资助项目(2011GXNSFA018129);广西教育厅科研基金资助项目(201012MS026)

Dissipation Effect of Quantum Fluctuation on Envelope Soliton in Fermi-Pasta-Ulam Model

ZENG Shang-you, ZHANG Zheng-zhen, ZENG Shao-wen, ZHOU Li-ming, WANG Rong-feng, TANG Wen-yan, FANG Xin-he, LIANG Dan   

  1. College of Electronic Engineering,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2012-05-26 Online:2012-09-20 Published:2018-12-04

摘要： 本文应用含时变分法原理研究一维Fermi-Pasta-Ulam模型,链中粒子的运动方程由含时变分法原理导出,在这个半量子研究中所考虑的量子效应是量子涨落。对于单个粒子,我们采用Jackiw-Kerman波函数。研究结论表明量子涨落能够发散、模糊化甚至破坏Fermi-Pasta-Ulam模型的非线性激发:包络孤子,量子涨落效应与有效普朗克常数有准指数关系。我们进一步发现与有效普朗克常数耦合,非谐耦合强度对量子耗散有联合效应,这种特有的联合效应可能是由Fermi-Pasta-Ulam模型独特的哈密顿量所导致。

关键词: Fermi-Pasta-Ulam模型, 含时变分法原理, Jackiw-Kerman波函数, 量子涨落

Abstract: In this paper,the time-dependent variational principle (TDVP) is applied to study the one-dimensional Fermi-Pasta-Ulam (FPU) model,and the dynamic equation of particles in the chain is obtained by TDVP.In thesemi-quantal study,the considered quantum effect is quantum fluctuation.The Jackiw-Kerman wave function is used for the single particle.The research results show that quantum fluctuation can disperse,blur and even destroy the nonlinear excitation of FPU model,envelope soliton.The effect of quantum fluctuation has thequasi-exponentional relationship with the effective Plank constant.Furthermore,it is found that coupling the effective Plank constant the anharmonic couplingstrength has the joint effect on quantum dissipation.The uniquely joint effect may be induced by the unique Hamiltonian of the FPU chain.

Key words: Fermi-Pasta-Ulam model, quantum fluctuation, time-dependent variational principle

中图分类号: 

  • O415.6
[1] REMOISSENET M.Low-amplitude breather and envelope solitons in quasi-one-dimensional physical models[J].Phys Rev B,1986,33:2386-2392.
[2] FLACH S,WILLS C R.Discrete breathers[J].Phys Rep,1998,295:181-264.
[3] 徐权,田强.准一维单原子非线性晶格振动的扭结孤子解和反扭结孤子解[J].中国科学:G辑,2004,34(6):648-654.
[4] 庞小峰.非线性系统中微观粒子的特性和非线性量子力学[J].中国基础科学,2005,5:43-46.
[5] 甘星洋.一维FPU晶格中的经典和量子孤立子[D].湘潭:湘潭大学,2010.
[6] KONOTOP V V,TAKENO S.Quantization of weakly nonlinear lattices:envelope solitons[J].Phys Rev E,2001,63:066606.
[7] NEUHAUSER D,BAER R,KOSLOFF R.Quantum soliton dynamics in vibrational chains:comparison of fully correlated,mean field,and classical dynamics[J].JChem Phys,2003,118:5729.
[8] JACKIW R,KERMAN A.Time-dependent variational principle and the effective action[J].Phys Lett A,1979,71:158-162.
[9] HO C L,CHOU C I.Simple variational approach to quantum Frenkel-Kontorova model[J].Phys Rev E,2000,63:016203.
[10] TSUE Y,FUJIWARA Y.Time-dependent variational approach in termsof squeezed coherent states[J].Prog Theor Phys,1991,86:443-467.
[11] SAUERZAPF A,WAGNER M.Quantum decay of self-localized modes in anharmonic systems[J].Physica B,1999,263:723-726.
[12] VITALI D,BONCI L,MANNELLA R,et al.Localization breakdown as a joint effect of nonlinear and quantum dissipation[J].Phys Rev A,1992,45:2285-2293.
[13] ZHONG Hong-wei,TANG Yi.Time-dependent variational approach to the phonon dispersion relation of the commensurate quantum frenkel—kontorova model[J].ChinPhys Lett,2006,23(8):1965-1968.
[14] LIU Yang,DENG Lei,YANG Zhi-zong,et al.Semi-quantal method approach to small-amplitude nonlinear localized modes in a one-dimensional Klein-Gordon monatomic chain[J].Phys Scr,2011,83(1):015601.
[15] HUANG Guo-xiang,SHI Zhu-pei,XU Zai-xin.Asymmetric intrinsic localized in a homogeneous lattice with cubic and quartic anharmonicity[J].Phys Rev B,1993,47(21):14561-14564.
[16] 刘洋.一维非线性晶格模型中的量子孤子研究[D].湘潭:湘潭大学,2008.
[1] 杨浦, 付喆. 发放脉冲在化学耦合神经环路的周期传播稳定性[J]. 广西师范大学学报（自然科学版）, 2015, 33(4): 96-102.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发