论文标题
插值碰撞模型形式主义
Interpolated Collision Model Formalism
论文作者
论文摘要
开放量子系统的动力学（即，与不受控制的环境相互作用的量子系统的动力学）构成了从量子热力学到量子计算的许多活跃研究领域的基础。建模开放量子系统的一种方法是通过碰撞模型。例如，人们可以将环境建模为由许多小量子系统（Ancillas）组成，这些系统（Ancillas）在一系列“碰撞”中依次与目标系统相互作用。在这篇论文中，我将讨论一种新的方法，用于从任何此类碰撞模型给出的离散时间动力学中构建连续时间主方程。这种新方法可用于任何相互作用持续时间，$ΔT$，通过插值时间点之间的动力学$ t = n \，Δt$。我将与以前仅在连续限制（$ΔT\至0 $）中使用的方法进行对比。此外，我将表明，除非以某种方式进行微调，否则任何基于连续的基于限制的方法都将始终产生统一动力。例如，通常在相互作用强度（$ g $）中采用（我会争辩的）差异（我会争辩说非物理上的差异），从而在连续限制中找到非单身动力学，以便$ g^2Δt$是$Δt\ to $Δt\ to 0 $。
The dynamics of open quantum systems (i.e., of quantum systems interacting with an uncontrolled environment) forms the basis of numerous active areas of research from quantum thermodynamics to quantum computing. One approach to modeling open quantum systems is via a Collision Model. For instance, one could model the environment as being composed of many small quantum systems (ancillas) which interact with the target system sequentially, in a series of "collisions". In this thesis I will discuss a novel method for constructing a continuous-time master equation from the discrete-time dynamics given by any such collision model. This new approach works for any interaction duration, $δt$, by interpolating the dynamics between the time-points $t = n\,δt$. I will contrast this with previous methods which only work in the continuum limit (as $δt\to 0$). Moreover, I will show that any continuum-limit-based approach will always yield unitary dynamics unless it is fine-tuned in some way. For instance, it is common to find non-unitary dynamics in the continuum limit by taking an (I will argue unphysical) divergence in the interaction strengths, $g$, such that $g^2 δt$ is constant as $δt \to 0$.
