Tunneling and the Vacuum Zero-Point Radiation

Abstract

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non null escape rate over the potential barrier at low temperatures (T → 0). It is found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results.

Quantum dynamics of wave packets in a non-stationary parabolic potential and the Kramers escape rate theory

“…This thesis is well illustrated by the Kramers model of escape out of a potential well modified with account of ZPO energy [3], according to which the strength of the Gaussian white noise is determined by a synergetic action of thermal and quantum fluctuations, as described by eq. ( 2).…”

“…the ground state energy of the harmonic oscillator, is the Plank constant, b k is the Boltzmann constant and T is the temperature. It is quite natural to use the noise strength (2) in the calculation of the Kramers escape rate of the potential well, which results in a non-vanishing escape rate even if 0 T  [3]. At sufficiently high temperatures, the noise strength becomes equal to B kT, and the Kramers rate (1) provides a theoretical basis for the Arrhenius law, whereas at low temperatures, significant deviations from this low are predicted due to quantum effects.…”