 120B5B22, digital print, 2000
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 120B5B4, digital print, 2000
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Artist's Statement A pendulum is one of the most basic physical systems. The corresponding pendulum equation is a good model for describing all sorts of oscillations. If one watches the pendulum with a stroboscope, i.e. in discrete time steps, then one sees a socalled discrete pendulum.
At the beginning of the 20th century it was found out that enlarging the pendulum model to a socalled quantized pendulum model produces the right description of the radiation of a black body (imagine a dark tube with a little hole). In particular that discovery was one of the strongest arguments that lead to the development of quantum mechanics itself.
As a result of soliton theory (a theory that describes e.g. shallow water waves), whose development started in the 1970âs, the pendulum equation was revisited also for high energy values (physical pendulum) and many further fascinating facts connected with the pendulum were found. Among such was the description of a discrete quantum pendulum (1993).
If one marks out the various positions and the corresponding velocites of the oscillator, then for low energies one ends up with concentric ellipses . The size of the ellipses indicates the energy. For high energies (e.g. when the pendulum starts looping) the ellipses turn into a kind of fish shaped object. In the shown pictures, quantized versions of the above ellipses can be seen - they are the blurred light ellipses forcing the color patterns into shape. The three pictures should be seen as a series of rising energy levels.
The artistic process for the prints in Digital'01 involved the use of a scientific mathematical software in order to reflect the physical or mathematical reality in an appropriate way.
For physicists/mathematicians: Let | a> be a coherent state, let B and S be discrete position and momentum operators (here unitary idempotent matrices of size p), let | n> be an energy eigenstate of the quantum pendulum hamiltonian, then in the pictures the function
i,k -> < n | Bi Sk a > as a map from a p times p square grid to the complex numbers is displayed. p is 30, 45, 60 and 120 in the pictures. For details see ãThe discrete quantum pendulumä, A. Bobenko, N. Kutz, U. Pinkall, Phys. Lett. A 177 (1993) 399-404. In the pictures the argument of a complex number is encoded in brightness and saturation, its phase in the hue.
Nadja Kutz
nadja@daytar.de
www.daytar.de
Nadja Kutz has been trained as a mathematical physicist (Ph.D.1996, TU Berlin). Parallely in her freetime she has been doing arts since many years and even passed several classes at professional art schools (like sculpture class, Yoshimi Hashimoto 1997/98, HDK Berlin) or art related schools (like computer graphics, David Zeltzer, Media Lab, MIT 1987/88).
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