Quantum effect in the diffusion along a potential barrier (原子核の複雑さと散逸)

Lyudvig Dmitrievich Faddeev, O. Yakubovskiĭ

D. Boosé, J. Richert, Uzy Smilansky

Quantum tunnelling induces transitions not only through potential barriers, but also through energy barriers of dynamical origin. The coupling to a noisy environment introduces dissipation which affects tunnelling. This effect is studied by an analytic non-perturbative solution of a problem involving tunnelling through a dynamical barrier in the presence of a noisy environment. The accessibility to the classically forbidden energy region above the dynamical barrier is reduced (enhanced) by the friction(diffusion) effect. The occupation of each level above the dynamical barrier is characterized by the succession in time of two different regimes. The transition between both regimes is ruled by an energy criterion which is discussed.

Alex E. Bernardini, Stefano De Leo, PIETRO P. ROTELLI

The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct solution, confirmed by numerical calculations is the creation of multiple peaks as a consequence of multiple reflections. Lessons concerning the use of the stationary phase method are drawn.

Sushanta Dattagupta, Sanjay Puri

Michele Battezzati, Valerio Magnasco

This article shows that the asymptotic quantum mechanical exchange energies and wave functions in a bistable potential can be obtained by computing the complex-valued first-passage time across the potential barrier from a transient state endowed with Smoluchowski boundary conditions, whose probability density is concentrated on one side of the barrier. This interpretation is validated by one of the authors’ previous work on diffusion in a random field, showing that this model yields a diffusion equation equivalent to quantum mechanical equations.

S. Mizutori, Søren Berg