Hidden variables in quantum mechanics: Generic models, set-theoretic forcing, and the emergence of probability

Set theoretical forcing in quantum mechanics and AdS/CFT correspondence

We show unexpected connection of Set Theoretical Forcing with Quantum Mechanical lattice of projections over some separable Hilbert space. The basic ingredient of the construction is the rule of indistinguishability of Standard and some Nonstandard models of Peano Arithmetic. The ingeneric reals introduced by M. Ozawa will correspond to simultaneous measurement of incompatible observables. We also discuss some results concerning model theoretical analysis of Small Exotic Smooth Structures on topological 4-space. Forcing appears rather naturally in this context and the rule of indistinguishabil…

Zero forcing, linear and quantum controllability for systems evolving on networks

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a connection between the quantum (Lie theoretic) property of controllability and the linear systems (Kalman) controllability condition. We investigate how the graph theoretic concept of a zero forcing set impacts the controllability property. In particular, we prove that if a set of vertices is a zero forcing set, the associated dynamical system is controllable…

载流量子点模拟器中电荷时间晶体的涌现与动力学稳定性

Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator

本文从理论上证明可在量子点阵列模拟的无自旋Hubbard梯子电荷电流中直接测量时间晶体性，并展示通过动态调出再调回时间晶体相验证其对外部扰动的鲁棒性。