Regularization of tunneling rates in quantum chaotic systems

Igor Filikhin, S.G. Matinyan, Branislav Vlahović

J. K. Breslin

Louis M. Pecora, Hoshik Lee, Dong-Ho Wu +3 more

Quantum tunneling rates through a barrier separating two-dimensional, symmetric, double-well potentials are shown to depend on the classical dynamics of the billiard trajectories in each well and, hence, on the shape of the wells. For shapes that lead to regular (integrable) classical dynamics the tunneling rates fluctuate greatly with eigenenergies of the states sometimes by over two orders of magnitude. Contrarily, shapes that lead to completely chaotic trajectories lead to tunneling rates whose fluctuations are greatly reduced, a phenomenon we call regularization of tunneling rates. We show that a random-plane-wave theory of tunneling accounts for the mean tunneling rates and the small fluctuation variances for the chaotic systems.

Rachel Owen, John Rodgers

Acknowledgments For two-dimensional, symmetric double well potentials separated by a tunneling barrier, it has been shown theoretically that quantum mechanical tunneling rates are dependent on the shape of the well in the limit of small quantum wavelength. Shapes that support chaotic wave functions produce statistically smaller fluctuations in the tunneling rate than classical (integrable) wells. This effect is called “regularization” of tunneling rates and can be analyzed by examining the splitting in energy level between symmetric and antisymmetric wave functions. Utilizing the similarity in the wave natures of a quantum mechanical particle in a symmetric double well and transverse electromagnetic waves in a 2-D cavity, we investigate chaos regularization in coupled microwave cavities both numerically and experimentally. The difference between the antisymmetric and symmetric eigenstate frequencies squared and evanescent electromagnetic wave propagation in a cutoff tunnel is shown to be analogous to energy splitting and quantum mechanical tunneling, respectively. This analogy allows investigation of regularization in various microwave cavities and, by extension to a lab-scale model, the behavior of complex quantum mechanical systems.

Giulio Casati, Robert Graham, Italo Guarneri +1 more

Niall D. Whelan