Klein paradox for bosons, wave packets and negative tunnelling times.

We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein-Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barrier's height is enhanced yet remains finite.

Reply to "comment on 'entanglement and chaos in the kicked top' ".

We reply to the preceding Comment that attempts to clarify the connection between chaos and entanglement exposed in our previous paper [Phys. Rev. E 83, 016207 (2011)PRESCM1539-375510.1103/PhysRevE.83.016207]. We present additional computations that show the argument exposed in the Comment to explain the entangling power of some regular states is not important in the present case. More fundamentally we argue that the example chosen in the Comment is not the most significant in order to understand why specific regular dynamics can entangle as efficiently as when the corresponding classical dynamics is chaotic.

Observing trajectories with weak measurements in quantum systems in the semiclassical regime.

We propose a scheme allowing us to observe the evolution of a quantum system in the semiclassical regime along the paths generated by the propagator. The scheme relies on performing consecutive weak measurements of the position. We show how "weak trajectories" can be extracted from the pointers of a series of devices having weakly interacted with the system. The properties of these weak trajectories are investigated and illustrated in the case of a time-dependent model system.

Entanglement and chaos in the kicked top.

The standard kicked top involves a periodically kicked angular momentum. By considering this angular momentum as a collection of entangled spins, we compute the bipartite entanglement dynamics as a function of the dynamics of the classical counterpart. Our numerical results indicate that the entanglement of the quantum top depends on the specific details of the dynamics of the classical top rather than depending universally on the global properties of the classical regime. These results are grounded on linking the entanglement rate to averages involving the classical angular momentum, thereby explaining why regular dynamics can entangle as efficiently as the classically chaotic regime. The findings are in line with previous results obtained with a two-particle top model, and we show here that the standard kicked top can be obtained as a limiting case of the two-particle top.

Diffraction and spectral statistics in systems with a multilevel scatterer.

A semiclassical framework to interpret the spectral rigidity of a system containing a scatterer with internal states is developed. Our prototype system is a scaled Rydberg molecule in an external magnetic field, where the core is a multilevel scatterer: the potential sheet in which the outer electron moves depends on the quantum state of the core. Thus the electron-core collision, interpreted in terms of the diffraction of the semiclassical waves associated with the outer electron on the core, can result in a change of the electron's dynamical regime. We examine the contribution of the diffraction to the spectral rigidity by obtaining the diffractive Green's function in the semiclassical limit. We concurrently determine this contribution from accurate quantum spectra and compare numerically the semiclassical and quantum results. Our findings indicate that, in a system with a multilevel scatterer, the diffractive contribution to the spectral rigidity cannot be accounted for by a simple universal expression, but rather depends on system specific nonuniversal terms: the quantum properties of the scatterer (reflected by the relative values of the phase shifts in the different channels) and the classical properties of the shortest periodic orbits in the different dynamical regimes.

Numerical construction of "optimal" nonoscillating amplitude and phase functions.

A numerical recipe for the construction of nonoscillating amplitude and phase functions for potentials with a single minimum is given. We give different examples illustrating the recipe, showing the usefulness of the procedure for the construction of basis functions in bound-state scattering processes, such as those described by quantum defect theory. The resulting amplitude and accumulated phase functions are coined as "optimal" nonoscillating (as a function of the space and energy variables) because they are the counterpart for the quantum problem of the classical action for the analog semiclassical problem.

Rydberg molecules in external fields: a semiclassical analysis.

We analyze the spectra of simple Rydberg molecules in static fields within the framework of closed/periodic-orbit theories. We conclude that in addition to the usual classical orbits one must consider classically forbidden diffractive paths. Further, the molecule brings in a new type of "inelastic" diffractive trajectory in addition to the usual "elastic" diffractive orbits encountered in systems with point scatterers. The relative importance of inelastic versus elastic diffraction is quantified by merging the usual closed orbit theory framework with molecular quantum defect theory.