09:00 - 09:45 |
Igor Jex: Photons walking the line ↓ Light is a fascinating medium. It is interesting on its own but is equally well suited to be the tool for mimicking other physical systems. Recently considerable attention was given to processes called quantum walks. The quantum walk [1-2] is an excellent tool for modeling, simulating and testing a wide range of physical processes and effects. Quantum walks are defined as specific generalizations of classical (random) walks. The simplest model of a walk-the one dimensional discrete quantum walk (on a line)-is based on the combination of the dynamics of the internal degree of freedom defined by the coin operator and the conditioned shift in position space (step operator). The evolution of the walk is given by the repeated application of the resulting evolution operator. The coin as well as the step operator can suffer from imperfections and this leads to deviations from the ideal situation. The way how the ideal situation is alternated leads to additional interesting effects. We present results on theoretical and experimental studies of ideal and perturbed quantum walks [3-8] based on the all optical implementation of quantum walks. We point out the main results and future trends.
References
[1] Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48, 1687 (1993).
[2] D. A. Meyer, J. Stat. Phys. 85, 551 (1996).
[3] A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gabris, P.J. Mosley, E. Andersson, I. Jex, Ch. Silberhorn, Phys. Rev. Lett. 104, 050502 (2010).
[4] A. Schreiber, K. N. Cassemiro, V. Potocek, A. Gábris, E, I. Jex, Ch. Silberhorn, Phys. Rev. Lett. 104, 050502 (2011).
[5] A. Schreiber, A. Gábris, P. P. Rohde, K. Laiho, M. Štefanák, V. Potocek, C. Hamilton, I. Jex, Ch. Silberhorn,. Science 336, 55 (2012).
[6] F. Elster, S. Barkhofen, T. Nitsche, J. Novotný, A. Gábris, I. Jex, Ch. Silberhorn, Sci. Rep. 5 (2015) 13495.
[7] T. Nitsche, F. Elster, J. Novotný, A. Gábris, I. Jex, S. Barkhofen, Ch. Silberhorn, New J. Phys. 18 (2016) 063017.
[8] T. Nitsche, S. Barkhofen, R. Kruse, L. Sansoni, M. Štefanák, A. Gábris, V. Potocek, T. Kiss, I. Jex, Ch. Silberhorn, Science Adv. 4, eaar6444 (2018). (TCPL 201) |
15:00 - 15:45 |
Tom Bannink: Power series in stochastic processes ↓ This talk is about a class of classical random processes on graphs that include the discrete Bak-Sneppen process, introduced in 1993, and the several versions of the contact process. These processes are parametrized by a probability 0≤p≤1 that controls a local update rule. Numerical simulations reveal a phase transition when p goes from 0 to 1, which I will discuss in the talk. Analytically little is known about the phase transition threshold, even for one-dimensional chains. In this talk we consider a power-series approach based on representing certain quantities, such as the survival probability or expected hitting times, as a power-series in p. We prove that the coefficients of those power series stabilize as the length n of the chain grows, and I will give a sketch of this proof in the talk. This stabilization of coefficients is a phenomenon that has been used in the physics community but was not yet proven. We show that for local events A, B of which the support is a distance d apart we have cor(A,B)=O(pd). The stabilization is useful because it allows for the (exact) computation of coefficients for arbitrary large systems which can then be analyzed using the wide range of existing methods of power series analysis. (TCPL 201) |