A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency $\nu$. We prove that up to a quasi-exponential time $\tau_* \sim e^{c \frac{\nu}{\log^3 \nu}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $\tau_*$, and hence this effective Hamiltonian is a conserved quantity up to $\tau_*$. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction $U$ is much larger than the hopping $J$. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time $\tau_*$ that is (almost) exponential in $U/J$.Comment: 21 pages, file updated to match published versio

Local Cyber-physical Attack with Leveraging Detection in Smart Grid

A well-designed attack in the power system can cause an initial failure and then results in large-scale cascade failure. Several works have discussed power system attack through false data injection, line-maintaining attack, and line-removing attack. However, the existing methods need to continuously attack the system for a long time, and, unfortunately, the performance cannot be guaranteed if the system states vary. To overcome this issue, we consider a new type of attack strategy called combinational attack which masks a line-outage at one position but misleads the control center on line outage at another position. Therefore, the topology information in the control center is interfered by our attack. We also offer a procedure of selecting the vulnerable lines of its kind. The proposed method can effectively and continuously deceive the control center in identifying the actual position of line-outage. The system under attack will be exposed to increasing risks as the attack continuously. Simulation results validate the efficiency of the proposed attack strategy.Comment: Accepted by IEEE SmartGridComm 201