1302.4110 (Hideo Hasegawa)

Gaussian wavepacket dynamics and quantum tunneling in asymmetric
double-well systems    [PDF]

Hideo Hasegawa

We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, solving Schr\"{o}dinger equation by using two kinds of spectral methods for a given initial Gaussian wavepacket. Time dependences of wavefunction, averages of position and momentum, the auto-correlation function, an uncertainty product and the tunneling probability have been calculated. Our calculations have shown that (i) the tunneling probability is considerably reduced by a potential asymmetry $\Delta U$, (ii) a resonant tunneling at $| \Delta U | \simeq \hbar \omega$ is not realized for a motion starting from the lower minimum of potential wells ($\omega$: oscillator frequency at minima), (iii) the reduction of the tunneling probability by an asymmetry is less significant for an initial Gaussian wavepacket with narrower width, and (iv) the uncertainty product $<\delta x^2 > < \delta p^2 >$ in the tunneling state is larger than that in the weak tunneling state. The item (i) is consistent with previous studies and items (ii)-(iv) are new findings in the present study.

View original: http://arxiv.org/abs/1302.4110