Thermalization in 2D critical quench and UV/IR mixing
Thermalization in 2D critical quench and UV/IR mixing
复制标题
二维临界淬火和 UV/IR 混合中的热化
DOI：
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发表时间：
2015
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通讯作者：
Nilakash Sorokhaibam
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作者：
G. Mandal;S. Paranjape;Nilakash Sorokhaibam
我们考虑了自由标量和费米子模型中的量子猝灭，其一般的随时间变化的质量m（t）从m0到零。我们证明了，正如MSS [1]中所预期的那样，后淬火动力学可以用广义Calabrese-Cardy形式的状态来描述|n = exp[−κ2H − ∑n >2∞κnWn]| Bd. Wn（n = 2，3，. . ., W2 = H）这里表示守恒的W∞电荷，|Bd表示共形边界态。无论预猝灭态是基态还是压缩态，我们的结果都成立，并且不需要像MSS中那样在κn中进行微扰展开。我们计算精确的时间依赖于一些特定的淬火协议m（t）。该热力学函数明确地显示了广义吉布斯系综（GGE）的热化，其逆温度β = 4κ2，化学势μn = 4κn。在预猝灭状态是基态的情况下，可以通过应用逆散射技术从最终GGE中检索精确的猝灭协议m（t）。另一个值得注意的结果，我们解释为UV/IR混合，是一些散射子的长距离和长时间（IR）行为关键取决于所有κn，尽管它们在通常的RG用语中是高度不相关的耦合。这表明微妙的RG参数时，适用于非平衡动力学。
A bstractWe consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass m(t) that goes from m0 to zero. We prove that, as anticipated in MSS [1], the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form |ψ〉 = exp[−κ2H − ∑n >2∞κnWn]|Bd〉. The Wn (n = 2, 3, . . ., W2 = H) here represent the conserved W∞ charges and |Bd〉 represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the κn’s as in MSS. We compute exact time-dependent correlators for some specific quench protocols m(t). The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature β = 4κ2, and chemical potentials μn = 4κn. In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol m(t) from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all κn’s, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.