We study the time evolution of an integrable many-particle system, described by the $q$-boson Hamiltonian in the limit of strong interactions $q\to\infty$. It is shown that, for a particular class of pure initial states, the analytical calculation of certain observables simplifies considerably. Namely, we provide exact formulas for the calculation of the Loschmidt-echo and the emptiness formation probability, where the computational time scales polynomially with the particle number. Moreover, we construct a non-local mapping of the $q$-boson model to the XX spin chain, and show how this can be utilized to obtain the time evolution of various local bosonic observables for translationally invariant initial states. The results obtained via the bosonic and fermionic picture show perfect agreement. In the infinite volume and large time limits, we rigorously verify the prediction of the Generalized Gibbs Ensemble for homogeneous initial Fock states.
Dynamically generated correlations in a trapped bosonic gas via frequency quenches
Raman Research Institute（拉曼研究所）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究所国际理论科学中心）；LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay（巴黎南大学萨克雷大学法国国家科学研究中心理论与统计物理实验室）
Conserved quantities in a bosonic tight-binding chain with non-Hermitian quartic terms
The University of Tokyo（东京大学）；Institute for Physics of Intelligence, The University of Tokyo（东京大学智能物理研究所）；Trans-Scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
我们利用规范/重力对偶性来研究强耦合N=2* 规范理论的等离子体中的“热猝灭”。具体地说，我们考虑的响应下的玻色子或费米子质量的变化的理论的初始热平衡状态，以m/T<<1的领导秩序。当使质量随时间变化时，必须引入新的新的反项来重新正规化边界理论。我们考虑了从共形超杨-米尔斯理论到质量形变规范理论的跃迁以及相反的跃迁。通过构造，这些转变由特征时间尺度\calt控制，并且我们展示了系统的响应如何取决于该时间尺度与热时间尺度1/T的比率。该响应显示了有趣的标度行为，在T \calt < >1的快速猝灭极限下<1 and slow quenches with T \calt >。在T \calt \to \infty的极限下，我们观察到预期的绝热响应。对于快速淬火，放松到最终平衡控制的最低quasinormal模式的批量标量对偶淬火运营商。对于慢猝灭，系统松弛与（近）绝热响应，这是完全由后期的时间分布的质量。我们描述了新的重整化方案在定义规范不变观测量的理论与时间相关的耦合的歧义。
