Quantum Tunnelling in Condensed Media

Henk T. C. Stoof

A. Kh. Rotaru, K. V. Shura

We present a theoretical study of the ultrashort nonlinear dynamics of bosonic quasiparticles in condensed media participating in two-photon quantum transitions. In the resonance approximation we obtain exact solutions in the form of elliptic functions. We show that allowing for antiresonant terms in the Hamiltonian of the interaction of the electromagnetic field and the quasiparticles leads to an entirely new phenomenon: the development of ultrashort chaos. The dynamical stochasticity of the quasiparticles is due to the disintegration of constants of motion of the system. Finally, we predict the effect of nonlinear tunneling from one potential well to another.

Joachim Ankerhold

Antonio Defendi, Marco Roncadelli

Alexey Kuznetsov

The nonadiabatic-tunneling probability of heavy particles is calculated while allowing for a dependence of the resonance integral on the vibrational coordinates. It is shown that quantum fluctuations of the tunneling species in a transverse direction can be of distinct importance in preparing the barrier for tunneling. In the model of harmonic vibrations, expressions are obtained for the transition probability which include the contribution from excited vibrational states of the tunneling particle as well as the changes in their vibrational frequency and equilibrium coordinates which occur as the system moves toward the transition configuration.

N. Emir Anuar

We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the Hamiltonian, we quantize canonically the classical particle in a viscous media. We study the free quantum particle in a viscous media and the dissipative quantum tunnelling. It is found that the dissipation influences tunnelling probability by a factor that closely resembles the result of Caldeira and Leggett.