Magnetotunnelling spectroscopy: an experimental tool for studying chaos in quantum transport

Resonant tunnelling spectroscopy is used to investigate the energy level spectrum of a wide potential well in the presence of a large magnetic field oriented at angles θ between 0° and 90° to the normal to the plane of the well. In the tilted field geometry, the current-voltage characteristics exhibit a large number of quasiperiodic resonant peaks even though the classical motion of electrons in the potential well is chaotic. The voltage range and spacing of the resonances both change dramatically with θ. We give a quantitative explanation for this behaviour by considering the classical period of unstable periodic orbits within the chaotic sea of the potential well.

Comment on "Acoustic chaos in a duct with two separate sound sources" [J. Acoust. Soc. Am. 110, 120-126 (2001)] (L)

In a paper published in this journal in 2001 by Dong [W. G. Dong, X. Y. Huang, and Q. L. Wo, J. Acoust. Soc. Am. 110, 120-126 (2001)] it was claimed that acoustic chaos was obtained experimentally by the nonlinear interaction of two acoustic waves in a duct. In this comment a simple experimental setup and an analytical model is used to show that the dynamics of such systems corresponds to a quasiperiodic motion, and not to a chaotic one. © 2008 Acoustical Society of America.

Molecular phylogenetics of the family Cyprinidae (Actinopterygii : Cypriniformes) as evidenced by sequence variation in the first intron of S7 ribosomal protein-coding gene: Further evidence from a nuclear gene of the systematic chaos in the family

The family Cyprinidae is the largest freshwater fish group in the world, including over 200 genera and 2100 species. The phylogenetic relationships of major clades within this family are simply poorly understood, largely because of the overwhelming diversity of the group; however, several investigators have advanced different hypotheses of relationships that pre- and post-date the use of shared-derived characters as advocated through phylogenetic systematics. As expected, most previous investigations used morphological characters. Recently, mitochondrial DNA (mtDNA) sequences and combined morphological and mtDNA investigations have been used to explore and advance our understanding of species relationships and test monophyletic groupings. Limitations of these studies include limited taxon sampling and a strict reliance upon maternally inherited mtDNA variation. The present study is the first endeavor to recover the phylogenetic relationships of the 12 previously recognized monophyletic subfamilies within the Cyprinidae using newly sequenced nuclear DNA (nDNA) for over 50 species representing members of the different previously hypothesized subfamily and family groupings within the Cyprinidae and from other cypriniform families as outgroup taxa. Hypothesized phylogenetic relationships are constructed using maximum parsimony and Basyesian analyses of 1042 sites, of which 971 sites were variable and 790 were phylogenetically informative. Using other appropriate cypriniform taxa of the families Catostomidae (Myxocyprinus asiaticus), Gyrinocheilidae (Gyrinocheilus aymonieri), and Balitoridae (Nemacheilus sp. and Beaufortia kweichotvensis) as outgroups, the Cyprinidae is resolved as a monophyletic group. Within the family the genera Raiamas, Barilius, Danio, and Rasbora, representing many of the tropical cyprinids, represent basal members of the family. All other species can be classified into variably supported and resolved monophyletic lineages, depending upon analysis, that are consistent with or correspond to Barbini and Leuciscini. The Barbini includes taxa traditionally aligned with the subfamily Cyprininae sensu previous morphological revisionary studies by Howes (Barbinae, Labeoninae, Cyprininae and Schizothoracinae). The Leuciscini includes six other subfamilies that are mainly divided into three separate lineages. The relationships among genera and subfamilies are discussed as well as the possible origins of major lineages. (c) 2008 Published by Elsevier Inc.

Entanglement dynamics and chaos in the Dicke model

We study dynamical properties of quantum entanglement in the Dicke model with and without the rotating-wave approximation. Specifically, we investigate the maximal entanglement and mean entanglement which reflect the underlying chaos in the system, and a good classical-quantum correspondence is found. We also show that the maximal linear entropy can be more sensitive to chaos than the mean linear entropy.

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.

Dynamical Instabilities and Deterministic Chaos in Ballistic Electron Motion in Semiconductor Superlattices

We consider the motion of ballistic electrons within a superlattice miniband under the influence of an alternating electric field. We show that the interaction of electrons with the self-consistent electromagnetic field generated by the electron current may lead to the transition from regular to chaotic dynamics. We estimate the conditions for the experimental observation of this deterministic chaos and discuss the similarities of the superlattice system with the other condensed matter and quantum optical systems.

Symmetry-breaking and chaos in electron transport in semiconductor superlattices

We study the motion of electrons in a single miniband of a semiconductor superlattice driven by THz electric field polarized along the growth direction. We work in the semiclassical balance-equation model, including different elastic and inelastic scattering rates, and incorporating the self-consistent electric field generated by electron motion. We explore regions of complex dynamics, which can include chaotic behaviour and symmetry-breaking. We estimate the magnitudes of dc current and dc voltage that spontaneously appear in regions of broken-symmetry for parameters characteristic of modern semiconductor superlattices. This work complements PRL 80(1998)2669 [ cond-mat/9709026 ].

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.