普适性与两体损耗：从两粒子有效非厄米动力学中得到的启示
Universality and two-body losses: lessons from the effective non-Hermitian dynamics of two particles
AI总结：
本研究针对一维受限两粒子的两体损耗晚期动力学，通过可解析的非厄米哈密顿量，在全参数空间得到普适衰减幂律及晶格下的对数修正，揭示了连续与晶格体系的动力学共性。
摘要：
我们研究了被限制在一维空间、受两体损耗作用的两个粒子的晚期动力学。该动力学可由一个非厄米哈密顿量精确描述，该哈密顿量在连续体系和晶格体系中均可解析研究。我们在该问题的全参数空间内精确计算了渐近衰减率以及粒子数衰减的普适幂律形式。当初始态中两个粒子相距较远时，体系中的平均粒子数随时间$t$以$t^{-1/2}$的规律衰减；而当初始态中两个粒子交叠时，则会呈现出$t^{-3/2}$的不同幂律。这些结果在连续体系和晶格体系中均成立，但在晶格体系中会出现对数修正项。
英文摘要：
We study the late-time dynamics of two particles confined in one spatial dimension and subject to two-body losses. The dynamics is exactly described by a non-Hermitian Hamiltonian that can be analytically studied both in the continuum and on a lattice. The asymptotic decay rate and the universal power-law form of the decay of the number of particles are exactly computed in the whole parameter space of the problem. When in the initial state the two particles are far apart, the average number of particles in the setup decays with time $t$ as $t^{-1/2}$; a different power law, $t^{-3/2}$, is found when the two particles overlap in the initial state. These results are valid both in the continuum and on a lattice, but in the latter case a logarithmic correction appears.
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