Time-Minimal Control of Dissipative Two-level Quantum Systems: the Generic Case

Time-minimal control of dissipative two-level quantum systems: The Integrable case

The objective of this article is to apply recent developments in geometric optimal control to analyze the time minimum control problem of dissipative two-level quantum systems whose dynamics is governed by the Lindblad equation. We focus our analysis on the case where the extremal Hamiltonian is integrable.

Hamiltonian structure for dispersive and dissipative dynamical systems

We develop a Hamiltonian theory of a time dispersive and dissipative inhomogeneous medium, as described by a linear response equation respecting causality and power dissipation. The proposed Hamiltonian couples the given system to auxiliary fields, in the universal form of a so-called canonical heat bath. After integrating out the heat bath the original dissipative evolution is exactly reproduced. Furthermore, we show that the dynamics associated to a minimal Hamiltonian are essentially unique, up to a natural class of isomorphisms. Using this formalism, we obtain closed form expressions for t…

最小固有时间与确定性微观态：涌现的量子场与相对论时空

Minimal Proper Time and Deterministic Microstates: Emergent Quantum Fields and Relativistic Spacetime

从因果有序事件的确定性前几何基底出发，通过对微观历史粗粒化，在低能时导出有效量子动力学，给出最小固有时间步微观解释，红外极限恢复标准量子场论，还为涌现相对论时空几何提供自然框架。