论文标题
低温多体系统的绝热演变
Adiabatic Evolution of Low-Temperature Many-Body Systems
论文作者
论文摘要
我们考虑有限范围，多体效费晶格模型，并在引入弱且缓慢变化的时间依赖性扰动后研究其热平衡状态的演变。在适当的假设对外部驾驶的假设下，我们通过扰动中的收敛膨胀来得出局部可观察结果的平均值，以适应足够小的温度。收敛性适用于系统大小均匀的一系列参数。在对未扰动的哈密顿量的光谱差距假设下，收敛在温度下也均匀。作为一种应用，我们的扩展使我们能够在局部可观察物的期望下，在零温度下的期望，与扰动系统的瞬时吉布斯保持亲密关系。作为推论，我们还建立了线性响应的有效性。我们的策略是基于Wick旋转的严格版本，它使我们可以根据欧几里得相关功能来代表实时动态的Duhamel扩展，以使用费米子群集扩展证明了精确的衰减估计值。
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows us to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation, which allows us to represent the Duhamel expansion for the real-time dynamics in terms of Euclidean correlation functions, for which precise decay estimates are proved using fermionic cluster expansion.
