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We have studied responses to applied external forces of the quantum$(N_S+N_B)$ model for $N_S$-body interacting harmonic oscillator (HO) systemsubjected to $N_B$-body HO bath, by using canonical transformations combinedwith 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 forceexpressed by the Hamiltonian: $H_f= -f(t) \sum_{k=1}^{N_S} Q_k$ is generallynot 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 $k$thparticle of the system. We have calculated also the response to a space- andtime-dependent force expressed by $H_f= -f(t) \sum_{k=1}^{N_S} Q_k \: e^{i 2\pi k u/N_S}$, where the wavevector $u$ is $u=0$ and $u=-N_S/2$ for uniform andstaggered forces, respectively. The spatial correlation $\Gamma_m$ for a pairof positions of $Q_k$ and $Q_{k+m}$ has been studied as functions of $N_S$ andthe temperature. Our calculations have indicated an importance of takingaccount of finite $N_S$ in studying quantum open systems which generallyinclude arbitrary numbers of particles.

Responses of small quantum systems subjected to finite baths