Quantum quench of the trap frequency in the harmonic Calogero model
Quantum quench of the trap frequency in the harmonic Calogero model
复制标题
谐波 Calogero 模型中陷波频率的量子淬灭
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
S. Sotiriadis
中科院分区：
文献类型：
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作者：
M. Rajabpour;S. Sotiriadis
我们考虑通过平方反比势相互作用并限制在谐波陷阱（谐波卡洛杰罗模型）中的玻色子系统中陷阱频率的量子淬灭。我们根据淬火后本征态准确确定初始状态，并推导出简单物理可观测量的时间演化。由于该模型拥有无限的运动积分 (IoM) 集合，可以实现精确解，因此可以提出广义吉布斯系综 (GGE)，即考虑所有 IoM 守恒的统计系综，以描述失超后很久的局部物理可观测值。尽管由于陷阱的存在，物理可观测量并不表现出平衡而是周期性演化，这样的 GGE 仍然可以正确描述它们的时间平均值。我们通过分析检查局部玻色子密度，发现 GGE 猜想在热力学极限内确实有效。
We consider a quantum quench of the trap frequency in a system of bosons interacting through an inverse-square potential and confined in a harmonic trap (the harmonic Calogero model). We determine exactly the initial state in terms of the post-quench eigenstates and derive the time evolution of simple physical observables. Since this model possesses an infinite set of integrals of motion (IoM) that allow its exact solution, a generalised Gibbs ensemble (GGE), i.e. a statistical ensemble that takes into account the conservation of all IoM, can be proposed in order to describe the values of local physical observables long after the quench. Even though, due to the presence of the trap, physical observables do not exhibit equilibration but periodic evolution, such a GGE may still describe correctly their time averaged values. We check this analytically for the local boson density and find that the GGE conjecture is indeed valid, in the thermodynamic limit.