Speaker
Tobias Ambjörnsson
(Lund University)
Description
There exists compelling experimental evidence in numerous
systems for logarithmically slow time evolution, yet its
full theoretical understanding remains elusive. In this talk
two examples of systems displaying logarithmic time
evolutions will be discussed.
First, we consider, pictorially, a hitchhiker traveling
through a series of towns [1]. In each town, traffic starts
in the morning, and friendly drivers (persons willing to
pick up our hitchhiker) appear at random intervals governed
by a waiting time density, psi(tau). The hitchhiker
typically arrives to a new town in between two friendly
drivers showing up, and the delay time, i.e., the time the
hitchhiker actually has to wait until the next ride, is
non-trivially related to the interarrival times of friendly
drivers. For heavy-tailed psi(tau) we show that the expected
number of towns visited increase logarithmically with time,
t. Also for medium-tailed psi(tau) we find interesting
behaviour.
Second, we study a labelled particle in a generic system of
identical particles with hard-core interactions in a
strongly disordered environment [2]. The disorder is
manifested through intermittent motion with scale-free
sticking times at the single particle level, i.e. a
continuous time random walk with a power-law exponent
between 0 and 1. We demonstrate that the combination of the
disordered environment with the many-body interactions leads
to an ultraslow, logarithmic dynamics -- the tracer
particle's mean square displacement increase as the square
root of the logarithm of time.
[1] Michael A. Lomholt, Ludvig Lizana, Ralf Metzler, and
Tobias Ambjörnsson, Phys. Rev. Lett. 110, 208301 (2013).
[2] Lloyd P Sanders, Michael A Lomholt, Ludvig Lizana, Karl
Fogelmark, Ralf Metzler and Tobias Ambjörnsson, New J. Phys.
16, 113050 (2014).
