[Lecture notes]

Notes from lectures at the New York Institute for mathematics and mechanics?

Table générale du Recueil des traités de G. F. de Martens et de ses continuateurs, 1494-1874.

Pref. signed: J. Hopf.

Dr. J.M. Bechstein's Forstbotanik : oder, Vollständige Naturgeschichte der deutschen Holzgewächse und einiger fremden. Zur Selbsbelehrung für Oberförster, Förster und Forstgehülfen.

Pritzel (2nd ed.)

Ueber den germanischen erbadel. Beitrag zur geschichte des ursprungs der stände in Deutschland.

Mode of access: Internet.

Der Landprediger von Wakefield ...

Mode of access: Internet.

Böhmen in den jahren 1600 bis 1621; historischer roman nach Thibeaudeau.

Mode of access: Internet.

Komischer Volks-Kalender... Für 1853, Vou [!]

Illustrations by J. Peters.

Geschichte des dreissigjährigen Krieges /

Imprint varies, v. 2-5: Erfurt : Hennings und Hopf.

Die deutsche Krisis des Jahres 1866 : mit einem Anhang: Die sogenannte Braunschweigische Frage vorgeführt in Aktenstücken, Aufzeichnungen und quellenmässigen Darstellungen /

Cover title: Das Jahr 1866.

Die altorientalischen Teppiche; eine Studie über ihre Schönheitswerte.

Mode of access: Internet.

Concordanz der poetischen National-Literatur der Deutschen,

Mode of access: Internet.

Functionality, Robustness and Control of Nonlinear Network Dynamics: Modeling and Understanding the C. elegans Connectome

Thesis (Ph.D.)--University of Washington, 2016-06

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Braided m-Lie algebras

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of End(F)M, where M is a Yetter-Drinfeld module over B with dimB < infinity. In particular, generalized classical braided m-Lie algebras sl(q,f)(GM(G)(A),F) and osp(q,l)(GM(G)(A),M,F) of generalized matrix algebra GMG(A) are constructed and their connection with special generalized matrix Lie superalgebra sl(s,f)(GM(Z2)(A(s)),F) and orthosymplectic generalized matrix Lie super algebra osp(s,l) (GM(Z2)(A(s)),M-s,F) are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established.

Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.