Entropy Distance: New Quantum Phenomena

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology and information geometry. This research is motivated by a theory of info-max principles, where we contribute by computing first order optimality conditions of the entropy distance.Comment: 34 pages, 5 figure

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

On the Form Factor for the Unitary Group

We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary ensemble.Comment: 35 page

Widespread Treponema pallidum Infection in Nonhuman Primates, Tanzania

We investigated Treponema pallidum infection in 8 nonhuman primate species (289 animals) in Tanzania during 2015–2017. We used a serologic treponemal test to detect antibodies against the bacterium. Infection was further confirmed from tissue samples of skin-ulcerated animals by 3 independent PCRs (polA, tp47, and TP_0619). Our findings indicate that T. pallidum infection is geographically widespread in Tanzania and occurs in several species (olive baboons, yellow baboons, vervet monkeys, and blue monkeys). We found the bacterium at 11 of 14 investigated geographic locations. Anogenital ulceration was the most common clinical manifestation; orofacial lesions also were observed. Molecular data show that nonhuman primates in Tanzania are most likely infected with T. pallidum subsp. pertenue–like strains, which could have implications for human yaws eradication

Double exponential stability of quasi-periodic motion in Hamiltonian systems

We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus. We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable. Our results hold true for real-analytic but more generally for Gevrey smooth systems

VICA, a visual counseling agent for emotional distress

We present VICA, a Visual Counseling Agent designed to create an engaging multimedia face-to-face interaction. VICA is a human-friendly agent equipped with high-performance voice conversation designed to help psychologically stressed users, to offload their emotional burden. Such users specifically include non-computer-savvy elderly persons or clients. Our agent builds replies exploiting interlocutor\u2019s utterances expressing such as wishes, obstacles, emotions, etc. Statements asking for confirmation, details, emotional summary, or relations among such expressions are added to the utterances. We claim that VICA is suitable for positive counseling scenarios where multimedia specifically high-performance voice communication is instrumental for even the old or digital divided users to continue dialogue towards their self-awareness. To prove this claim, VICA\u2019s effect is evaluated with respect to a previous text-based counseling agent CRECA and ELIZA including its successors. An experiment involving 14 subjects shows VICA effects as follows: (i) the dialogue continuation (CPS: Conversation-turns Per Session) of VICA for the older half (age &gt; 40) substantially improved 53% to CRECA and 71% to ELIZA. (ii) VICA\u2019s capability to foster peace of mind and other positive feelings was assessed with a very high score of 5 or 6 mostly, out of 7 stages of the Likert scale, again by the older. Compared on average, such capability of VICA for the older is 5.14 while CRECA (all subjects are young students, age &lt; 25) is 4.50, ELIZA is 3.50, and the best of ELIZA\u2019s successors for the older (&gt; 25) is 4.41

Beyond the periodic orbit theory

The global constraints on chaotic dynamics induced by the analyticity of smooth flows are used to dispense with individual periodic orbits and derive infinite families of exact sum rules for several simple dynamical systems. The associated Fredholm determinants are of particularly simple polynomial form. The theory developed suggests an alternative to the conventional periodic orbit theory approach to determining eigenspectra of transfer operators.Comment: 29 pages Latex2

Chaotic eigenfunctions in momentum space

We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally applications and generalizations are discussed.Comment: 30 pages. The figures are included in low resolution only. For a version with figures in high resolution see http://www.physik.uni-ulm.de/theo/qc/ulm-tp/tp99-2.htm