量子FPU模型的声子色散关系的含时变分法研究  

Time-dependent variational approach to the phonon dispersion relation of the quantum FPU model

作　　者：钟红伟[1] 黄乒花[2] 孙小军[3] 

机构地区：[1]广西工学院信息与计算科学系,广西柳州545006 [2]成都电子科技大学物理电子学院,四川成都610054 [3]广西师范大学物理与电子工程学院,广西桂林541004

出　　处：《广西工学院学报》2008年第1期1-4,共4页Journal of Guangxi University of Technology

基　　金：国家自然科学基金(No.10547005)资助;广西工学院硕士基金(No.070237)资助

摘　　要：采用含时变分法并结合Hartree型多粒子试探波函数和冻结的Jackiw-Kerman型单粒子波函数,研究了量子FPU模型的声子色散关系。在满足最小测不准关系的条件下,导出了粒子的期望值所满足的运动方程,并用以得到了声子色散关系。结果表明:与经典FPU模型相比,由于量子涨落的影响,量子FPU模型的简谐耦合强度增强了,声子元激发的带宽变宽了;并且简谐耦合强度和声子元激发的带宽随着量子涨落和四次方耦合强度的增大而增大。The phonon dispersion relation of the quantum FPU model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the harmonically coupling strength is strengthened and the width of the phonon band is broadened due to the quantum fluctuations in comparison with those of the classical FPU model. In addition, the harmonically coupling strength and the width of the phonon band increase with increasing the quantum fluctuations and quartic coupling strength.

关 键 词：FPU模型 声子色散关系 含时变分法 Jackiw-Kerman波函数 量子涨落 

分 类 号：O415[理学—理论物理]