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arXiv 1201.0477quant-ph
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量子随机和动力学映射的相互作用以识别马尔可夫和非马尔可夫跃迁

Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions

A. R. Usha Devi, A. K. Rajagopal, Sudha, R. W. Rendell

摘要:

已知系统的动力学演化,从系统和环境的初始张量积状态到任意两个随后的时间t1,t2(t2> t1),都是完全正的(CP),但在t1和t2之间的中间时间不一定是CP。这揭示了中间动力学的马尔可夫(如果是CP)和非马尔可夫(如果不是CP)化身的关键。这是在这里提出的量子随机映射A和相关的动力学映射B-不诉诸主方程的方法。我们用四个具有完全不同的物理起源的例子来研究这些特征:(i)具有时间相关噪声参数的两量子比特Werner状态映射;(ii)最近关于光子偏振的开放系统演化的光学实验(Nature Physics,7,931(2011))的现象学模型。(iii)哈密顿动力学的量子位耦合到浴的$N$量子位和(iv)两个量子位酉动力学的约旦等。等人(Phys.Rev.A70,052110(2004))中描述的方法,其中初始产物状态为量子位。在所有这些模型中,证明了中间时间动态B映射的特征值的正/负性决定了动态B映射的马尔可夫/非马尔可夫性质.

英文摘要:

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if it is not CP) avataras of the intermediate dynamics. This is brought out here in terms of the quantum stochastic map A and the associated dynamical map B -- without resorting to master equation approaches. We investigate these features with four examples which have entirely different physical origins (i) a two qubit Werner state map with time dependent noise parameter (ii) Phenomenological model of a recent optical experiment (Nature Physics, 7, 931 (2011)) on the open system evolution of photon polarization. (iii) Hamiltonian dynamics of a qubit coupled to a bath of $N$ qubits and (iv) two qubit unitary dynamics of Jordan et. al. (Phys. Rev. A 70, 052110 (2004)) with initial product states of qubits. In all these models, it is shown that the positivity/negativity of the eigenvalues of intermediate time dynamical B map determines the Markov/non-Markov nature of the dynamics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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