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

Abstract

We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schrödinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. 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 ∆U , (ii) a resonant tunneling with |∆U | κ ω is realized for motion starting from upper minimum of asymmetric potential wells, but not for motion from lower minimum (κ = 0, 1, 2, · · · ; ω: oscillator frequency at minima), (iii) the reduction of the tunneling probability by an asymmetry is less significant for the Gaussian wavepacket with narrower width, and (iv) the uncertainty product δx 2 δp 2 in the resonant tunneling state is larger than that in the non-resonant tunneling state. The item (ii) is in contrast with the earlier study [Mugnai et al., Phys. Rev. A 38 (1987) 2182] which showed the symmetric result for motion starting from upper and lower minima.

Scaling and self-similarity for the dynamics of a particle confined to an asymmetric time-dependent potential well

“…In the classical case and considering time perturbations to the potential, the particles may exhibit chaotic motion leading to scaling invariance under the variation of control parameters whenever also the escape of particles from specific regions of the phase space can be considered [12,14]. To cite an application of the quantum case, the Gaussian wave-packet dynamics and quantum tunneling in asymmetric double-well systems were reported in [15].…”

Validity of the time-dependent variational approximation to the Gaussian wavepacket method applied to double-well systems

“…(2) Time dependences of expectation values of x and p , and the auto-correlation function The item (1) holds also in asymmetric DW systems [24]. The item (2) implies that the tunneling phenomenon characteristic in DW systems cannot be well accounted for in TDVA ( Fig.…”

“…where We expect that SM with N m = 30 adopted in our numerical calculations is fairly accurate [23,24]. Some results of SM have been cross-checked, by solving the Schrödinger equation with the use the MATHEMATICA resolver for the partial differential equation.…”

Bound states of the one-dimensional Dirac equation for scalar and vector double square-well potentials

“…shown that an asymmetry in the double-well potential yields interesting quantum phenomena [18,19]. An application of the Dirac equation to an asymmetric DSP is under consideration and results will be reported in a separate paper.…”