Holger Hennig

The nature and perception of fluctuations in human musical rhythms

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.

Musical rhythms: The science of being slightly off

With a statistical understanding of our natural rhythmic imperfections, one can make computer-generated music sound more human.

Charge transfer driven by electron correlation: A non-Dyson propagator approach

A hole charge created in a molecular system, for instance, by ionization, can migrate through the system solely driven by electron correlation. This charge transfer due to electron correlation is referred to as charge migration. We introduce in this work a new ab initio method analyzing charge migration due to electron correlation in molecules. This method, a third-order non-Dyson propagator approach, aims in the long run, in particular, at the calculation of charge migration in relatively large molecules such as oligopeptides. First results of the new non-Dyson method are compared with a previously used propagator approach.

Transfer of Bose-Einstein condensates through discrete breathers in an optical lattice

We study the effect of discrete breathers (DBs) on the transfer of a Bose-Einstein condensate (BEC) in an optical lattice using the discrete nonlinear Schrodinger equation. In previous theoretical (primarily numerical) investigations of the dynamics of BECs in leaking optical lattices, collisions between a DB and a lattice excitation, e.g., a moving breather (MB) or phonon, were studied. These collisions led to the transmission of a fraction of the incident (atomic) norm of the MB through the DB, while the DB can be shifted in the direction of the incident lattice excitation. Here we develop an analytic understanding of this phenomenon, based on the study of a highly localized system--namely, a nonlinear trimer--which predicts that there exists a total energy threshold of the trimer, above which the lattice excitation can trigger the destabilization of the DB and that this is the mechanism leading to the movement of the DB. Furthermore, we give an analytic estimate of upper bound to the norm that is transmitted through the DB. We then show numerically that a qualitatively similar threshold exists in extended lattices. Our analysis explains the results of the earlier numerical studies and may help to clarify functional operations with BECs in optical lattices such as blocking and filtering coherent (atomic) beams.

Avalanches of Bose–Einstein condensates in leaking optical lattices

We study the decay of an atomic Bose–Einstein condensate (BEC) population N(τ) from the leaking boundaries of an optical lattice (OL). For a rescaled interatomic interaction strength Λ>Λb, discrete breathers (DBs) are created that prevent the atoms from reaching the leaking boundaries. Collisions of other lattice excitations with the outermost DBs result in avalanches, i.e. steps in N(τ), which for a whole range of Λ-values follow a scale-free distribution P(J=δN)~1/Jα. A theoretical analysis of the mixed phase space of the system indicates that 1

Nature of self-localization of Bose-Einstein condensates in optical lattices

We analyze the nature of a novel type of self-trapping transition called self-localization (SL) of Bose-Einstein condensates in one-dimensional optical lattices in the presence of weak local dissipation. SL has recently been observed in several studies based upon the discrete nonlinear Schrodinger equation (DNLS), however, its origin is hitherto an open question. We show that SL is based upon a self-trapping crossover in the system. Furthermore, we establish that the origin of the crossover is the Peierls-Nabarro barrier, an energy threshold describing the stability of self-trapped states. Beyond the mean-field description the crossover becomes even sharper which is also reflected by a sudden change of the coherence of the condensate. While we expect that the crossover can be readily studied in current experiments in deep optical lattices, our results allow for the preparation of robust and long-time coherent quantum states.

Dynamics of entanglement in a dissipative Bose-Hubbard dimer

We study the connection between the semiclassical phase space of the Bose-Hubbard dimer and inherently quantum phenomena in this model, such as entanglement and dissipation-induced coherence. Near the semiclassical self-trapping fixed points, the dynamics of Einstein-Podolski-Rosen (EPR) entanglement and condensatefractionconsistsofbeatsamongjustthreeeigenstates.SincepersistentEPRentangledstatesariseonly intheneighborhoodofthesefixedpoints,ouranalysisexplainsessentiallyalloftheentanglementdynamicsinthe system. We derive accurate analytical approximations by expanding about the strong-coupling limit; surprisingly, their realm of validity is nearly the entire parameter space for which the self-trapping fixed points exist. Finally, we show significant enhancement of entanglement can be produced by applying localized dissipation.

Global phase space of coherence and entanglement in a double-well Bose-Einstein condensate

Ultracold atoms provide an ideal system for the realization of quantum technologies, but also for the study of fundamental physical questions such as the emergence of decoherence and classicality in quantum many-body systems. Here, we study the global structure of the quantum dynamics of bosonic atoms in a double-well trap and analyze the conditions for the generation of many-particle entanglement and spin squeezing which have important applications in quantum metrology. We show how the quantum dynamics is determined by the phase space structure of the associated mean-field system and where true quantum features arise beyond this `classical approximation.

Fractal conductance fluctuations of classical origin

In mesoscopic systems, conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system, with either fully chaotic or mixed phase space, generically exhibits fractal conductance fluctuations unrelated to quantum interference. This might explain the unexpected dependence of the fractal dimension of the conductance curves on the (quantum) phase breaking length observed in experiments on semiconductor quantum dots.