Classically, rigid objects with elongated shapes can fit through apertures only when properly aligned. Quantum-mechanical particles which have internal structure (e.g. a diatomic molecule) also are affected during attempts to pass through small apertures, but there are interesting differences with classical structured particles. We illustrate here some of these differences for ultra-slow particles. Notably, we predict resonances that correspond to prolonged delays of the rotor within the aperture-a trapping phenomenon not found classically.

We consider an $N$ qubit system and show that in the symmetric subspace, $\mathbb{S}$ a state is not globally entangled, iff it is a coherent state. It is also proven that in the orthogonal complement $\mathbb{S}_{\bot}$ all states are globally entangled

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.

The scattering of a rod-like rotating object by a single slit on a screen is followed according to the laws of classical mechanics. We assume a free planar motion and a uniform rotation, except for the moments of collisions, causing discontinuous jumps in the velocity and the angular velocity of the object. The collisions, which are assumed to be ideally elastic, result in certain constrains and we show that the motion in the six-dimensional phase space of the problem can be mapped onto a 3D billiard. We simulate numerically the dynamics of the problem and find that the collision number shows a sensitive dependence on the initial conditions for certain regions of the phase space. This result forecasts the necessity of further caution in the quantum version of this problem, where entanglement of rotational and translational degrees of freedom should play a role.

We consider a quantum system consisting of N parts, each of which is a "quKit" described by a K dimensional Hilbert space. We prove that in the symmetric subspace, S, a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement S ⊥ all states are globally entangled.