Energy transfer in the Holstein approach for the interplay between periodic on-site and linear acoustic potentials

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-07-04 DOI:10.1016/j.wavemoti.2024.103382
Sergio Reza-Mejía , Luis A. Cisneros-Ake
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Abstract

We study the problem of a transferring electron along a lattice of phonons, in the continuous long wave limit, holding periodic on-site and linear longitudinal interactions in Holstein’s approach. We thus find that the continuum limit of our modeling produces an effective coupling between the linear Schrödinger and sine–Gordon equations. Then, we take advantage of the existence of trapped kink–anti kink solutions in the sine–Gordon equation to variationally describe traveling localized coupled solutions. We validate our variational findings by solving numerically the full coupled system. Very reasonable agreement is found between the variational and full numerical solutions for the amplitude evolution of both profiles; the wave function and the trapped kink–anti kink. Our results show the significance of permitting longitudinal interactions in the Holstein’s approach to hold trapped localized solutions. It is actually found a critical ratio between longitudinal and on-site interactions, as depending on the velocity of propagation, from where coupled localized solutions exist.

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霍尔施泰因方法中周期性现场和线性声势相互作用的能量转移
我们研究了在连续长波极限下,在霍尔施泰因方法中保持周期性现场和线性纵向相互作用的情况下,电子沿着声子晶格转移的问题。因此,我们发现建模的连续极限在线性薛定谔方程和正弦-戈登方程之间产生了有效耦合。然后,我们利用正弦-戈登方程中存在的被困扭结-反扭结解,对行进的局部耦合解进行变分描述。我们通过对完整耦合系统进行数值求解来验证我们的变分结论。在波函数和陷波-反陷波这两个剖面的振幅演化方面,我们发现变分求解和全数值求解之间存在非常合理的一致性。我们的结果表明,在霍尔施泰因方法中允许纵向相互作用对于保持陷波局部解具有重要意义。实际上,我们发现了纵向相互作用与现场相互作用之间的临界比率,该比率取决于传播速度,在该比率下存在耦合局部解。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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