Institut für Theoretische Physik
Start / Aktuell / Institut
August  2015
Di
18.08.2015
Seminarraum A3.101
Theoretische Physik
14:15
Theoretisch-physikalisches Seminar

Dr. Janos Asboth
Wigner Research Center Budapest

2-Dimensional Quantum Walks with static disorder: Localization or diffusion? Topological phases hold the answer

The hallmark property of Quantum Walks is that they spread ballistically, faster than the diffusive spreading of random walks. This gives them a "quantum speedup", which can be exploited in quantum algorithms. In the presence of time-independent disorder, however, 1- and 2-dimensional (1D and 2D) quantum walks are expected to suffer Anderson localization, whereby their spread stops completely, except for special cases.

Simulating the 2D split-step Hadamard walk, we have found [1] that - contrary to earlier simulation results [2] - it does not undergo Anderson localization, instead, over long timescales, it spreads diffusively. We explained this phenomenon by showing that this quantum walk is an iterative dynamical system tuned to a critical point at a topological phase transition. The role of the Chern number is here taken over[3] by the Rudner invariant[4]. In the talk, I will explain this explanation.

[1]: J. M. Edge and J. K. Asboth, Phys. Rev. B 91, 104202 (2015) [2]: J. Svozilik, R. D. J. Leon-Montiel, and J. P. Torres, PRA 86, 052327 (2012) [3]: J. K. Asboth and J. M. Edge, PRA 91, 022324 (2015) [4]: M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, PRX 3, 031005 (2013)

Kontakt: Mariya Medvedyeva und Salvatore Manmana

September  2015
Di
29.09.2015
Seminarraum A3.101
Theoretische Physik
14:15
Theoretisch-physikalisches Seminar

Jörg Rottler
UBC Vancouver, CA

Plasticity in amorphous solids

Yielding and the slow plastic flow of amorphous solids exhibit striking heterogeneities: swift localised particle rearrangements take place in the midst of a more or less homogeneously deforming medium. At low temperatures, failure events become increasingly correlated and develop self-similar properties that resemble critical phenomena. Moreover, plastically deforming regions organize into macrocroscopic shear bands that limit the lifetime to failure. This talk will discuss two questions that must form essential ingredients in a statistical theory of amorphous plasticity: where to localized plastic events occur, and how do correlations arise from their interactions? With molecular dynamics simulations of model athermal solids driven by shear at constant strain rate, we first show that the loci and directions of local shear transformations can be predicted from a superposition of soft modes in the low energy vibrational spectrum [1]. The so-defined "soft spots" are long-lived structural features and remain correlated with plastic activity even in the supercooled fluid regime. We then compute spatiotemporal correlations of the plastic events and compare them to a mesoscale elastoplastic model that coarse-grains the atomistic dynamics into a lattice model that preserves only the essential features of the localized plastic events. Upon local yielding, energy is redistributed throughout the lattice with an elastic Green’s function that displays quadrupolar symmetry and algebraic decay. We test several assumptions in the mesoscopic theory directly against the behaviour on the molecular level [2,3]. Recent successes as well as avenues for further improvement of these class of models will be discussed.

[1] S. S. Schoenholz, A. J. Liu, R. A. Riggleman, J. Rottler, Physical Review X 4, 031014 (2014). [2] F. Puosi, J. Rottler, J. L. Barrat, Phys. Rev. E 89, 042302 (2014). [3] A. Nicolas, J. Rottler, J-L. Barrat, The European Physical Journal E 37, 1 (2014).

Kontakt: M. Müller

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