Research of Dr. Holger Then

Summary of research interests

My main interest is computing and applying arithmetic spectra to problems in mathematics and physics. The applications include analytic number theory, ergodic theory, quantum chaos, and cosmology.

If you wonder what the connections between arithmetic spectra and cosmology are: I am fascinated that the Universe might be multiply connected and seek answers to its large scale geometry and topology by using harmonic analysis and inverse spectral geometry, complemented with electromagnetic field symmetries and information-rich radio astronomy.

For a while, I did some research in non-equilibrium statistical mechanics, but do no longer follow this.

List of Publications

• H. Then, Large sets of consecutive Maass forms and fluctuations in the Weyl remainder, submitted.
• J. Jorgenson, L. Smajlovic & H. Then, On the distribution of eigenvalues of Maass forms on certain moonshine groups, submitted.
• A. R. Booker, A. Strömbergsson & H. Then, Bounds and algorithms for the K-Bessel function of imaginary order, to appear in LMS J. Comp. Math.
• H. Then, The rate of quantum ergodicity. In U. Bunke, S. Nonnenmacher & R. Schubert (editors), Quantum Ergodicity, OWR Report 49/2011, Mathematisches Forschungsinstitut Oberwolfach, 2011, pp. 2813–2817.
• R. Aurich, F. Steiner & H. Then, Numerical computation of Maass waveforms and an application to cosmology. In J. Bolte & F. Steiner (editors), Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology, Volume 397 of LMS Lecture Note Series, Cambridge University Press, 2011, pp. 229–269.
• B. Thidé, J. Lindberg, H. Then & F. Tamburini, Linear and angular momentum of electromagnetic fields generated by an arbitrary distribution of charge and current densities at rest, arXiv:1001.0954.
• A. M. Hahn & H. Then, Measuring the convergence of Monte Carlo free-energy calculations, Phys. Rev. E 81, 041117 (2010).
• A. M. Hahn & H. Then, Characteristic of Bennett's acceptance ratio method, Phys. Rev. E 80, 031111 (2009).
• J. T. Mendonça, B. Thidé & H. Then, Stimulated Raman and Brillouin backscattering of collimated beams carrying orbital angular momentum, Phys. Rev. Lett. 102, 185005 (2009).
• A. M. Hahn & H. Then, Using bijective maps to improve free-energy estimates, Phys. Rev. E 79, 011113 (2009).
• H. Then, B. Thidé, J. T. Mendonça, T. D. Carozzi, J. Bergman, W. A. Baan, S. Mohammadi & B. Eliasson, Detecting orbital angular momentum in radio signals, arXiv:0805.2735.
• J. T. Mendonça, B. Thidé, J. E. S. Bergman, S. M. Mohammadi, B. Eliasson, W. Baan & H. Then, Photon orbital angular momentum in a plasma vortex, arXiv:0804.3221.
• H. Then & B. Thidé, Mechanical properties of the radio frequency field emitted by an antenna array, arXiv:0803.0200.
• H. Then & A. Engel, Computing the optimal protocol for finite-time processes in stochastic thermodynamics, Phys. Rev. E. 77, 041105 (2008).
• B. Thidé, H. Then, J. Sjöholm, K. Palmer, J. Bergman, T. D. Carozzi, Y. N. Istomin, N. H. Ibragimov & R. Khamitova, Utilization of photon orbital angular momentum in the low-frequency radio domain, Phys. Rev. Lett. 99, 087701 (2007).
• R. Aurich, S. Lustig, F. Steiner & H. Then, CMB alignment in multi-connected universes, Class. Quantum Grav. 24, 1879–1894 (2007).
• H. Then, Spectral resolution in hyperbolic orbifolds, quantum chaos, and cosmology. In TSLELS5 Computational Physical Sciences 2006, Universiti Putra, Malaysia, 24 pages.
• H. Then, Foreground contamination of the WMAP CMB maps from the perspective of the matched circle test, Month. Not. Roy. Astron. Soc. 373, 139–145 (2006).
• H. Then, Arithmetic quantum chaos of Maass waveforms. In P. Cartier, B. Julia, P. Moussa & P. Vanhove (editors), Frontiers in Number Theory, Physics, and Geometry I, Springer, 2006, pp. 183–212.
• B. Thidé, H. Then, Y. Istomin, N. Ibragimov, J. Bergman & R. Karlsson, The use of electromagnetic field symmetries in radio physics. In XXVIIIth URSI General Assembly, New Delhi, India, 2005.
• B. Thidé, H. Then, J. Bergman, Y. Istomin & N. Ibragimov, On the use of conserved EM field quantities in radio studies of space. In RVK05, Swedish National URSI Conference, Linköping, Sweden, 2005.
• R. Aurich, S. Lustig, F. Steiner & H. Then, Indications about the shape of the universe from the WMAP data, Phys. Rev. Lett. 94, 021301 (2005).
• H. Then, Maass cusp forms for large eigenvalues, Math. Comp. 74, 363–381 (2005).
• R. Aurich, S. Lustig, F. Steiner & H. Then, Hyperbolic universes with a horned topology and the CMB anisotropy, Class. Quant. Grav. 21, 4901–4925 (2004).
• H. Then, Fluctuations in the CMB and the topology of the universe, PhD thesis, Universität Ulm, Germany (2003), (Monograph, 158 pages).
• H. Then, Bifurcations of periodic orbits in Hamiltonian systems with symmetries, Diploma thesis, Universität Ulm, Germany (1999). (Monograph, 111 pages).