Scattering of a particle with internal structure from a single slit: exact numerical solutions

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 Greenʼs 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.

Diffraction of diatomic molecular beams: a model with applications to Talbot-Lau interferometry

“…By focusing on the initial state of energy E and recalling (15), we see that the propagator ( 16) has unbounded terms in the limit of short wavelengths replaced in (33):…”

“…Notable attempts have been made on the scattering analysis of classical and quantum-mechanical objects with internal structure or finite extension [14], [15]. In those precedents, important model simplifications such as the restriction of the center-of-mass motion to a line and the constraint of internal molecular motion to classical rigidity led to concrete theoretical results on the existence of resonances at a slit acting as a scatterer.…”

Feshbach resonances of nonzero partial waves at different collision energies

“…In this way, resonant positions at collision energies far above the threshold were measured accurately, and the classic Beutler-Fano profile was observed in the experiment [9,10]. Moreover, the effects of self-energy corrections have been observed over a range of collision energies and magnetic fields [10], and the energy-dependent self-energy describing the coupling between the open and closed channels has been studied [35][36][37][38].…”

Quantum mechanical scattering on time-dependent potentials using nonequilibrium Green's functions

“…More specifically, the integer index j has values in the interval (−∞, −1] for region I, [0, M ] for region II, and [M + 1, ∞) for region III. However, it can be shown [1,11] that it is sufficient to concentrate on the spatial domain where the potential is nonzero, i.e., on region II. (For constant potentials, simple matrix multiplication leads to this result, but it holds also in our case.)…”

“…This allows us to perform a Fourier transformation with respect to the time difference τ, the conjugate variable of which is the energy ( = 1). The retarded Green's function of a semi-infinite line segment in energy domain can be calculated e.g., by eigenfunction expansion and contour integration [1,11]. The result is…”