Flambaum V V, Izrailev F M
School of Physics, University of New South Wales, Sydney 2052, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Sep;64(3 Pt 2):036220. doi: 10.1103/PhysRevE.64.036220. Epub 2001 Aug 29.
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers, etc., can be considered as "chaotic" superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is due to a very high level density of many-body states that are easily mixed by a residual interaction between particles (quasiparticles). For such systems, we have derived simple analytical expressions for the time dependence of the energy width of wave packets, as well as for the entropy, number of principal basis components, and inverse participation ratio, and tested them in numerical experiments. It is shown that the energy width Delta(t) increases linearly and very quickly saturates. The entropy of a system increases quadratically, S(t) approximately t(2), at small times, and afterward can grow linearly, S(t) approximately t, before saturation. Correspondingly, the number of principal components determined by the entropy N(pc) approximately exp[S(t)] or by the inverse participation ratio increases exponentially fast before saturation. These results are explained in terms of a cascade model which describes the flow of excitation in the Fock space of basis components. Finally, the striking phenomenon of damped oscillations in the Fock space at the transition to equilibrium is discussed.
在诸如原子核、原子、量子点、自旋系统、量子计算机等量子系统中，高度激发的多粒子态可被视为平均场基态（斯莱特行列式、自旋或量子比特态的乘积）的“混沌”叠加。这是由于多体态的能级密度非常高，很容易被粒子（准粒子）之间的残余相互作用混合。对于此类系统，我们推导了波包能量宽度随时间变化的简单解析表达式，以及熵、主要基分量的数量和逆参与率的表达式，并在数值实验中对其进行了检验。结果表明，能量宽度Δ(t)呈线性增加且很快饱和。系统的熵在短时间内呈二次方增长，S(t)≈t²，之后在饱和之前可呈线性增长，S(t)≈t。相应地，由熵N(pc)≈exp[S(t)]或逆参与率确定的主要分量数量在饱和之前呈指数快速增加。这些结果用一个级联模型来解释，该模型描述了基分量福克空间中的激发流。最后，讨论了向平衡态转变时福克空间中阻尼振荡的显著现象。
