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Chinese Physics Letters

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel-Kontorova Model

钟红伟, T. J. Yi

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

同量的量 Frenkel-Kontorovamodel 的声子分散关系借助于变化途径为粒子与 Hartree-typemany-body 试用波浪功能相结合的时间家属被学习。单个粒子的状态被拿是 frozenJackiw 苏格兰教会会员波浪功能。在最小的不确定性的条件下面，为粒子期望价值的运动的方程被导出获得声子分散关系。底层潜力和声子刺激差距的力量古典模型与那些比较由于量变化被减少，这被显示出。我们也把我们的结果与使用路径积分以前获得的那些作比较分子的动力学。

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同量的量 Frenkel-Kontorovamodel 的声子分散关系借助于变化途径为粒子与 Hartree-typemany-body 试用波浪功能相结合的时间家属被学习。单个粒子的状态被拿是 frozenJackiw 苏格兰教会会员波浪功能。在最小的不确定性的条件下面，为粒子期望价值的运动的方程被导出获得声子分散关系。底层潜力和声子刺激差距的力量古典模型与那些比较由于量变化被减少，这被显示出。我们也把我们的结果与使用路径积分以前获得的那些作比较分子的动力学。
地面状态阶段转变和量双井模型的声子分散关系借助于变化途径与 Hartree 类型许多身体试用波浪功能相结合的时间依赖者被学习。单个粒子的状态被拿是冻结的 Jackiw 苏格兰教会会员波浪功能。在最小的不确定性关系的条件下面，我们为粒子的期望价值为运动的系统和方程获得有效古典 Hamiltonian。到一个对称的单个井的潜力的从一个对称的双井潜力的有效底层潜力运输，和地面说，这被显示出作为增加量变化的力量从一个破对称阶段展出转变到一个恢复对称阶段。我们也在二个阶段获得声子分散关系和声子差距。
The phonon dispersion relation of the commensurate quantum Frenkel–Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw–Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.
We present a simple and complete variational approach to the one-dimensional quantum Frenkel-Kontorova model. Dirac's time-dependent variational principle is adopted together with a Hartree-type many-body trial wave function for the atoms. The single-particle state is assumed to have the Jackiw-Kerman form. We obtain an effective classical Hamiltonian for the system, which is simple enough for a complete numerical solution for the static ground state of the model. Numerical results show that our simple approach captures the essence of the quantum effects first observed in quantum Monte Carlo studies.