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arXiv 1201.0565cond-mat.stat-mech
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小量子系统在有限水浴中的响应

Responses of small quantum systems subjected to finite baths

Hideo Hasegawa

摘要:

利用正则变换结合Husimi方法研究了$N_B$-体相互作用谐振子系统的量子$(N_S+N_B)$模型在$N_S$-体相互作用谐振子浴中对外力的响应. Husimi,Prog. Theor. Phys.{\bf 9},381(1953)]。已经表明,对由哈密顿量表示的均匀力的响应:$H_f= -f(t) \sum_{k=1}^{N_S} Q_k$通常不与$N_S$成比例,除了没有系统-浴耦合之外,其中$f(t)$表示其时间依赖性,并且$Q_k$表示系统的$k$ th粒子的位置算子。我们还计算了对由$H_f= -f(t) \sum_{k=1}^{N_S} Q_k \: e^{i 2 πk u/N_S}$表示的空间和时间相关力的响应,其中波矢量$u$分别为均匀力和交错力的$u=0$和$u=-N_S/2$。研究了$Q_k$和$Q_{k+m}$的一对位置的空间相关性$Γ_m$作为$N_S$和温度的函数。我们的计算表明,在研究通常包含任意数量粒子的量子开放系统时,考虑有限$N_S$是重要的。

英文摘要:

We have studied responses to applied external forces of the quantum $(N_S+N_B)$ model for $N_S$-body interacting harmonic oscillator (HO) system subjected to $N_B$-body HO bath, by using canonical transformations combined with Husimi's method for a driven quantum HO [K. Husimi, Prog. Theor. Phys. {\bf 9}, 381 (1953)]. It has been shown that the response to a uniform force expressed by the Hamiltonian: $H_f= -f(t) \sum_{k=1}^{N_S} Q_k$ is generally not proportional to $N_S$ except for no system-bath couplings, where $f(t)$ expresses its time dependence and $Q_k$ denotes a position operator of $k$th particle of the system. We have calculated also the response to a space- and time-dependent force expressed by $H_f= -f(t) \sum_{k=1}^{N_S} Q_k \: e^{i 2 πk u/N_S}$, where the wavevector $u$ is $u=0$ and $u=-N_S/2$ for uniform and staggered forces, respectively. The spatial correlation $Γ_m$ for a pair of positions of $Q_k$ and $Q_{k+m}$ has been studied as functions of $N_S$ and the temperature. Our calculations have indicated an importance of taking account of finite $N_S$ in studying quantum open systems which generally include arbitrary numbers of particles.

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