论文标题
确切的主方程，用于量子布朗运动，概括到动量依赖性系统 - 环境耦合
Exact Master Equation for Quantum Brownian Motion with Generalization to Momentum-Dependent System-Environment Couplings
论文作者
论文摘要
在本文中，我们将量子布朗尼运动推广到包括动量依赖的系统 - 环境耦合。常规的QBM模型对应于空间案例$ W_K = V_K $。广义QBM更为复杂，但有必要进行概括。这是因为系统和环境之间的粒子过渡和对产生的两个非常不同的物理过程，通常不能具有相同的耦合强度。因此，在实际量子物理世界中，几乎没有实现在经典层面上明确定义的常规QBM模型。我们讨论了不同物理系统中广义QBM的物理实现，并为初始解耦状态和初始相关状态提供了其确切的主方程。常规QBM模型的Hu-Paz-Zhang主方程被复制为一种特殊情况。我们发现，追溯所有环境状态自然诱发了动量依赖性电位后，重新归一化的布朗粒子汉密尔顿人，这也表明了在QBM Hamiltonian中包括动量依赖性耦合的必要性。在Hu-Paz-Zhang主方程中，这种重新归一化的电位被放错了位置，因此尚未找到正确的重态化Hamiltonian。对于初始解耦和初始相关状态的确切主方程式，有关初始震动的问题，这是HU-PAZ-ZHANG MASTER方程中一个长期问题的问题。我们发现，所谓的“初始震动”被认为是人为的效应，这是由于使用初始解耦系统 - 环境状态，与初始解耦状态无关。广义QBM的新的精确主方程也具有光子量子计算的潜在应用。
In this paper, we generalize the quantum Brownian motion to include momentum-dependent system-environment couplings. The conventional QBM model corresponds to the spacial case $W_k = V_k$. The generalized QBM is more complicated but the generalization is necessary. This is because the particle transition and the pair production between the system and the environment represent two very different physical processes, and usually cannot have the same coupling strengths. Thus, the conventional QBM model, which is well-defined at classical level, is hardly realized in real quantum physical world. We discuss the physical realizations of the generalized QBM in different physical systems, and derive its exact master equation for both the initial decoupled states and initial correlated states. The Hu-Paz-Zhang master equation of the conventional QBM model is reproduced as a special case. We find that the renormalized Brownian particle Hamiltonian after traced out all the environmental states induced naturally a momentum-dependent potential, which also shows the necessity of including the momentum-dependent coupling in the QBM Hamiltonian. In the Hu-Paz-Zhang master equation, such a renormalized potential is misplaced so that the correct renormalization Hamiltonian has not been found. With the exact master equation for both the initial decoupled and and initial correlated states, the issues about the initial jolt which is a long-stand problem in the Hu-Paz-Zhang master equation is also re-examined. We find that the so-called "initial jolt", which has been thought to be an artificial effect due to the use of the initial decoupled system-environment states, has nothing do to with the initial decoupled state. The new exact master equation for the generalized QBM also has the potential applications to photonics quantum computing.
