量子Klein-Gordon模型色散关系的含时变分法研究

Time-dependent variational approach to dispersion relation of the quantum Klein-Gordon model

通过采用含时变分原理,在结合Hartree型多粒子试探波函数和Jackiw-Kerman型单粒子波函数的基础上,研究了带对称单阱非谐格点势的量子Klein-Gordon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,并以此得到了声子色散关系.结果表明:与经典模型相比,由于量子涨落的影响,量子模型中的有效格点势的二次方项系数增大,声子元激发的带隙变宽;二次方项系数和带隙随着量子涨落和格点势的四次方项系数的增大而增大.

The phonon dispersion relation of the quantum Klein-Gordon model with symmetric single-well anharmonic substrate potential is studied by means of the time-dependent variational principle combined with Hartreetype trial wavefunction for system and Jackiw-Kerman wavefunction for single particle. 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 coefficient of square term of the substrate potential is strengthened and the band gap is broadened due to the quantum fluctuations in comparison with those of the classical model. In addition, the coefficient of square term and the band gap increase with increasing the quantum fluctuations and the coefficient of quartic term of the substrate potential.