Escape from quantum lattice billiards

Uktam Salomov, D. U. Matrasulov, F. C. Khanna +1 more

Rafael A. Molina

Advances in Quantum Chaotic Scattering: From (Non-) Linear Waves to Few-Body Systems, Dresden, Germany 9 - 13 September 2013. \nhttp://www.mpipks-dresden.mpg.de/~aqcs13/

Igor V. Zozoulenko, Torbjörn Blomquist

We perform numerical studies of wave packet propagation through open quantum billiards whose classical counterparts exhibit regular and chaotic dynamics. We show that for $t\ensuremath{\lesssim}{\ensuremath{\tau}}_{H}({\ensuremath{\tau}}_{H}$ being the Heisenberg time), the features in the transmitted and reflected currents are directly related to specific classical trajectories connecting the billiard leads. When $t\ensuremath{\gtrsim}{\ensuremath{\tau}}_{H},$ the calculated quantum-mechanical current starts to deviate from its classical counterpart, with the decay rate obeying a power law that depends on the number of decay channels. In a striking contrast to the classical escape from chaotic and regular systems (exponentially fast ${e}^{\ensuremath{-}\ensuremath{\gamma}t}$ for the former versus power-law ${t}^{\ensuremath{-}\ensuremath{\xi}}$ for the latter), the asymptotic decay of the corresponding quantum systems does not show a qualitative difference.

Peter Schmelcher, F. Lenz, Davron U. Matrasulov +2 more

Alejandro Puga, Bruce N. Miller

Many systems of interest at the forefront of technological development, for example, in quantum computation, consist of weakly interacting elements that obey quantum mechanics. A challenge for modern theoretical physics is to develop a systematic methodology for approaching these “open” quantum systems. In particular, applied mathematicians have formulated the method of transparent boundary conditions (TBCs) to model interacting quantum systems of infinite extent. Here, we consider a particular application of TBCs to the escape of a particle from a one-dimensional infinite well when one of the bounding barriers is extinguished. We analytically obtain the exact time-dependent wave function by a Green's function method and then show that a numerical solution based on the TBC method is in excellent agreement. This work was motivated by an experiment carried out at the University of Texas on escape from a gravitational wedge billiard. Physicists have used billiards to understand and explore both classical and quantum chaos. Although the original experiment was carried out in the classical regime, current work is probing lower temperatures, where a quantum mechanical formulation is required.