### 論文 "On amplification of quantum harmonic oscillators under time-periodic perturbations" のアブストラクト

In this paper, we study the amplification phenomenon of a one dimensional quantum harmonic oscillator Hamiltonian $p^2/2+\omega^2x^2/2$ under a time-periodic perturbation $-\chi_{I_0}(t)\omega^2x^2/2$, where $\omega>0$, $T>0$ is the period of this perturbation, $I_0=\bigcup_{n\in\boldsymbol{Z}}[nT+T_\omega,(n+1)T)$ for some $T_\omega$ such that $0<T_\omega<T$, and $\chi_{I_0}(t)$ is the characteristic function of $I_0$. We see that if $(\cos(\omega T_\omega)-\omega(T-T_\omega)\sin(\omega T_\omega)/2)^2-1>0$, then the exponential amplification phenomenon occurs for this time-periodic quantum system; while, if $(\cos(\omega T_\omega)-\omega(T-T_\omega)\sin(\omega T_\omega)/2)^2-1=0$, then the linear amplification phenomenon occurs.