Engl Thomas, Urbina Juan Diego, Richter Klaus
Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062907. doi: 10.1103/PhysRevE.92.062907. Epub 2015 Dec 8.
We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number N. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, nonperturbative solutions of the, typically nonlinear, wave equation of the classical (mean-field) limit. To this end, we construct the semiclassical approximation for both the smooth and oscillatory parts of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects such as vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommensurable frequencies, our formulas are generically valid also in the free-field case of noninteracting bosons.
我们考虑在大粒子数(N)的半经典极限下晶格上相互作用的玻色子量子场的多体谱。我们表明，多体态密度可以表示为对由经典（平均场）极限下典型非线性波动方程的周期性、非微扰解给出的振荡长波贡献的相干求和。为此，我们从多体正交态之间传播子的精确路径积分形式出发，根据迹公式构建多体态密度的光滑部分和振荡部分的半经典近似。因此，我们避免了使用相干态表示特有的复化经典极限。虽然精确考虑了真空涨落和规范不变性等量子效应，但我们的半经典方法捕捉了量子干涉，因此在朴素的量子 - 经典对应关系失效的埃伦费斯特时间之外也有效。值得注意的是，由于具有不可公度频率的谐振系统的一个特殊特征，我们的公式在非相互作用玻色子的自由场情况下通常也有效。
