声子库的量子态对介观电路量子特性影响的研究

Study on the influence of quantum state for phonon bath on the quantum behavior of mesoscopic circuit

考虑电子与声子间相互作用,研究了两种声子库纯初始态(正则系综与粒子数态)下耗散介观电路的动力学特性.长时间极限下(t→∞):当环境处于热平衡态时,电路系统中的电流和电荷的平均值只与电路所处初始量子态中的平均值有关,与环境无关;环境初态为粒子数态时,电荷与电流平均值随时间的演化特性与环境初始处于热平衡态下时完全一样,表明介观电路中的电荷与电流的平均值与环境量子态的某组占有数无关.电路中电流和电荷的量子涨落不仅与系统的初态有关,还与系统所处环境的量子态及温度有关.一般地说,电路系统与环境的纠缠会导致系统量子态的纯度下降,只有当环境在极低温下且处于热平衡态时,介观电路保持在一个量子纯态.

Taking into account the interaction between electrons and phonons, we study the dynamical behavior of a mesoscopic dissipative circuit for two classes of pure initial states （grand canonical ensemble and number state） of phonon bath modes. In the long time limit t→∞： when the environment is initially at thermal equilibrium, the average values of current and charge in the circuit system will only depend on the average values of the circuit in initial quantum state, and they are not related with the environment ; when the environment is initially in number state, the time evolution of the average values of current and charge are just the same as that in thermal equihbrium, which indicates that the average values of current and charge are related to certain set of occupied numbers. The quantum fluctuations of current and charge in the circuit not only depend on the initial state of the system but also depend on the quantum state and temperature of the environment. Generally, the entanglement between the circuit system and environment will lead to the reduction of the purity of the quantum state. The mesoscopic circuit will remain in a pure quantum state only when the environment is at very low temperature and at thermal equilibrium.