Publications Nadja Kutz

Math/Physics Publications Nadja Kutz

(9) "Discrete Curves in CP^1 and the Toda Lattice", T. Hoffmann, N. Kutz
preprint postscript copy: preprint math.DG/0208190
Stud. Appl. Math. Volume 113 Issue 1, 31-55 (2004)

(8) "Tri-hamiltonian Toda lattice and a canonical bracket for closed discrete curves" , N. Kutz
preprint postscript copy: preprint math.DG/0304083
published in Lett. Math. Phys. 64, Issue 3, 229-234 (2003) (2003)

(7) "Factorization dynamics and Coxeter-Toda lattices", T. Hoffmann, J. Kellendonk, N. Kutz and R. Reshetikhin
preprint postscript copy: Sfb288 preprint #420
published in Comm. Math. Phys. 212, Issue 2, 297-321 (2000)

(6) "Spectra of Quantum Integrals", J. Kellendonk, N. Kutz, R. Seiler
preprint (pdf)
published in "Discrete Integrable Geometry and Physics", ed. A. Bobenko, R. Seiler, Oxford Science Publications, Oxford 1999

(5) "Lagrangian description of discrete Sine-Gordon type models", N. Kutz>
preprint (pdf)
published in "Discrete Integrable Geometry and Physics", ed. A. Bobenko, R. Seiler, Oxford Science Publications, Oxford 1999

(4) "Free Massive Fermions Inside the Quantum Discrete sine-Gordon Model" , N. Kutz
postscript copy: Sfb288 preprint #231
published in Comm. Math. Phys. 204, 115-136 (1999)

(3) "Doubly discrete Lagrangian systems related to the Hirota and sine-Gordon equation", C. Emmrich, N. Kutz
postscript copy: Sfb288 preprint #138
published in Phys. Lett. A 201 no. 2/3 (1995) 156-160

(2) "On the spectrum of the Quantum Pendulum", N. Kutz
postscript copy: Sfb288 preprint #101
published in Phys. Lett. A 187 (1994) 365-372

(1) "The discrete quantum pendulum", A. Bobenko, N. Kutz, U. Pinkall
postscript copy: Sfb288 preprint #42
(the file has a missing titlepage and is partially without pictures)
published in Phys. Lett. A 177 (1993) 399-404

The content of this PhD thesis is centered around the sine-Gordon equation and in particular around a space and time ("doubly") discretized version of it, which arises in discrete analogs of surfaces with constant negative Gaussian curvature (socalled discrete K-surfaces). In the present work symplectic structures for a class of discrete spacetime systems which contain the sine-Gordon system are derived with methods from Lagrangian mechanics/symplectic geometry. The derived symplectic structures are used for quantizing the corresponding sine-Gordon system. The approach via differential geometry allows to show that central elements in some of the involved algebras arise from gauge freedoms of the corresponding differential geometric frame. Quantum integrals of motion are derived. A reduction of the quantized discrete sine-Gordon equation, the quantized discrete pendulum equation (a discrete version of the nonlinear harmonic oscillator) is investigated in detail, the spectrum of the corresponding quantum integral of motion (the "quantum pendulum hamiltonian") is described in terms of Bethe Ansatz equations. Some parts of this spectrum can be derived explicitly (the quantum pendulum hamiltonian is a square of the Hofstadter's butterfly, which is related to the quantum Hall effect). Finite dimensional representations of the corresponding algebras are constructed. Explicit constructions for the R-matrix at roots of unity are given. This allows to draw connections to models in statistical mechanics and in particular to free fermions on a lattice. Connections to the 2 dim billard in an ellipse and to other sytems are given, partially as an outlook on quantized versions of the underlying discrete surfaces and/or their normal maps (the normal map of K-surfaces provides a sigma model).

Other publications

- "Semantic web applications with regard to math and environment", 2012 unpublished
arxive.org abstract, see also Mimirix project webpage.

- "Testing new toy economies/political structures in MMOGs", slides of talk on Open Knowledge Conference July 2011, Berlin
slides on slideshare.net work in progress

- "On the need for a global academic internet platform", 2008 unpublished
arxive.org abstract

- "Nonverbale Kommunikation im virtuellen Raum und Körperlichkeit -- das Experiment "seidesein" ("Nonverbal communication in virtual space and physicality -- the experiment "seidesein") 2006, proceedings of the cinferene "Neue Medien und Technologien der Informationsgesellschaft", Academy of Sciences Berlin
german original (pdf)
slightly extended english version (pdf)

- "Poster werben fuer Mathematik", Andreas Frommer, Nadja Kutz, DMV-Mitteilungen 2/2000.