A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations
A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations
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DOI：
10.1063/1.5018725
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发表时间：
2018-01-07
影响因子：
4.4
通讯作者：
Cao, Jianshu
中科院分区：
文献类型：
--
作者：
Hsieh, Chang-Yu;Cao, Jianshu
我们扩展了一个标准的随机理论来研究开放的量子系统耦合到一个通用的量子环境。我们通过研究一个双线性耦合到三个基本类的非相互作用粒子：玻色子，费米子和自旋的二能级量子系统来扩展一般框架。在这种统一的随机方法中，广义随机刘维尔方程（SLE）正式捕获的确切的量子耗散时，噪声变量与适当的统计不同的浴模型。非高斯浴的非谐波效应被精确地编码在噪声变量必须满足的浴多时间相关函数中。从SLE出发，我们通过平均噪声变量设计了一族广义分层方程，并在正交函数的完全基中展开浴多时间相关函数。一般层次方程构成线性方程组，提供量子动力学的数值精确模拟。对于玻色子浴模型，我们的一般层次运动方程减少正是一个扩展版本的层次运动方程，允许有效的模拟任意的谱密度和温度制度。类似的效率和灵活性，可以实现在我们的形式主义的费米子浴模型。纺丝浴模型可以用两种互补的方法在本形式主义模拟。(I)它们可以被看作是非高斯浴模型的一个例子，并直接与一般的分层方程的方法给出了他们的多时间相关函数处理。(II)或者，每个浴自旋可以首先映射到一对费米子，并被视为费米子环境内本形式主义。出版社：AIP Publishing
We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism. Published by AIP Publishing.