Abstract
Scattering of a quantum particle with internal structure is fundamentally different from that of a point particle and shows quantum effects such as the modification of transmission due to tunnelling and trapping of the particle. As in a preceding paper (Shore et al 2014 New J. Phys. 17 013046) we consider a model of a symmetric, rigid rotor travelling through an aperture in a thin but impenetrable screen which is perpendicular to both the direction of motion and the rotation axis. We determine the quantum mechanical properties of this two-dimensional geometrical model using a quasi one-dimensional scattering problem with unconventional boundaries. Our calculations rely on finding the Green's function, which has a direct connection to the scattering matrix. Evaluated on a discrete lattice the Hamiltonian is ‘dressed’ by a self-energy correction that takes into account the open boundary conditions in an exact way. We find that the passage through the aperture can be suppressed or enhanced as a result of the rotational motion. These effects manifest themselves through resonances in the transmission probability as a function of incident energy and symmetry of the incident wavefunction. We determine the density-of-states to reveal the mode structure of resonant states and to exhibit the lifetimes of temporary trapping within the aperture.
Highlights
In a previous article [1], referred hereafter as article I, we have considered the motion of a structured particle, idealized as a symmetric rigid rotor, passing through an aperture whose size is comparable to the particle
In order to bring out the similarities and differences between classical and quantum mechanical scattering, we consider an ensemble of non-rotating classical particles far away from the aperture, all with fixed initial energy ε and with an orientation angle φ distributed evenly on the interval −π 2 ⩽ φ ⩽ π 2
The calculations were carried out by a numerical method based on the Greens function of the problem in a discrete lattice representation
Summary
Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USA 5 Author to whom any correspondence should be addressed.
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