Engl Thomas, Urbina Juan Diego, Richter Klaus
Institut für Theoretische Physik, Universität Regensburg, Regensburg 93040, Germany
Institut für Theoretische Physik, Universität Regensburg, Regensburg 93040, Germany.
Philos Trans A Math Phys Eng Sci. 2016 Jun 13;374(2069). doi: 10.1098/rsta.2015.0159.
We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particle contributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.
我们提出了一种半经典方法，用于多体量子传播，该方法基于与相应经典非线性波动方程解相关的量子振幅的相干求和。这种方法充分描述了相互作用玻色子系统多体空间中的干涉效应。主要关注的量，即在动力学由单粒子贡献和大小相似的多体相互作用共同驱动时福克态之间的跃迁振幅，是按照古兹维勒从时间演化算符的路径积分表示推导范弗莱克传播子的精神非微扰构建的，但提升到了对称多体态空间。超出平均场的效应，这里代表理论的经典极限，通过干涉振幅进行半经典描述，其中经典解的作用和稳定性起作用。通过这种方式，由于时间反演相关的经典解之间的相干量子干涉，呈现出一种真正的多体回波现象，即福克空间中的相干背散射。
