Integrable Lattice Systems and Markov Processes

Loschmidt echo of local dynamical processes in integrable and non integrable spin chains

The Loschmidt echo is investigated to track the effect of the local QDP. It is also quite sensitive to whether the background dynamics is integrable or not. For the integrable case, viz. the Heisenberg model, the Loschmidt echo depends on the parameters operators corresponding to the QDP as well as the time of QDP. The probability of reviving the system to its initial state is higher for incoherent QDPs occurring at large time intervals. Whereas each time coherent QDP occurs certain probability of reviving the state is always lost. For For the non-integrable case, viz. a kicked Harper model, i…

On the non-Markovianity of quantum semi-Markov processes

The non-Markovianity of the stochastic process called the quantum semi-Markov (QSM) process is studied using a recently proposed quantification of memory based on the deviation from semigroup evolution, that provides a unified description of divisible and indivisible channels. This is shown to bring out the property of QSM processes to exhibit memory effects even in the CP-divisible regime, in agreement with an earlier result. An operational meaning to the non-Markovian nature of semi-Markov processes is also provided.

On time-reversal and space-time harmonic processes for Markovian quantum channels

The time reversal of a completely-positive, nonequilibrium discrete-time quantum Markov evolution is derived via a suitable adjointness relation. Space-time harmonic processes are introduced for the forward and reverse-time transition mechanisms, and their role for relative entropy dynamics is discussed.

Operational Markov condition for quantum processes

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process, or the experimental falsifiability of a Markovian hypothesis.

Integrable Stochastic Ladder Models

A general way to construct ladder models with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These symmetric models give rise to series of integrable systems. It is shown that corresponding to these SU(2) symmetric integrable ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov processes with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.

双纠缠隐马尔可夫过程与常返性

Bi-Entangled Hidden Markov Processes and Recurrence

本文提出双纠缠隐马尔可夫过程概念，给出其联合期望公式，研究相关量子马尔可夫过程常返性，证明限制于交换子代数可恢复经典隐马尔可夫过程，仅考虑至多可数状态空间。