Seminars 2016
Seminar
Wednesday, September 28
Spontaneous symmetry breaking in nonlinear dualcore
optical and bosonic waveguides
Tel Aviv University
Abstract
Models of various physical media based on
configurations with two parallel nonlinear waveguides
(cores) amount to systems of linearly coupled nonlinear
Schrödinger equations (NLSEs), or by a single NLSE with
an effective doublewell trapping potential [1].
Wellknown examples are models of dualcore optical
fibers or planar waveguides, with the Kerr
selffocusing nonlinearity in each core. In such
systems, the competition of the linear intercore
coupling and intracore nonlinearity gives rise to
symmetrybreaking bifurcations (SBBs), which
destabilize obvious states that are symmetric with
respect to the two cores, and replace them by
asymmetric ones, when the total power of the optical
wave exceeds a critical value. The same happens with
symmetric temporal or spatial solitons (in the
dualcore fibers and planar waveguides, respectively),
which are destabilized by the respective SBB, when the
soliton's energy exceeds a respective critical value.
Similar SBBs are known in dualcore traps for matter
waves in atomic BoseEinstein condensates (BECs). The
SBB may be of subcritical and supercritical types, the
former type giving rise to a narrow region of
bistability between the symmetric and asymmetric
states, while in the latter case there is no
bistability. The SBBs were studied in detail
theoretically, and observed experimentally in some
optical and BEC settings. The talk aims to present an
overview of basic models, results, and physical
realizations of the symmetrybreaking phenomena in
nonlinear photonic and matterwave media.
[1] B. A. Malomed, Symmetry breaking in laser cavities, Nature Photonics 9, 287 (2015).
The seminar will take place at 13:00 in classroom
2.1.C17 (Edificio Sabatini) Universidad Carlos III
Seminar
Thursday, June 23
Noiseinduced transitions in bistable systems
Duke University
Abstract
Bistable systems occur throughout the natural sciences
and when such systems are subjected to random noise,
one observes probabilistic transitions between
coexisting metastable states. Such behavior is found
in chemical reaction kinetics, driven nonlinear
mechanical systems, nonlinear electronic transport
systems, climate variability models, and pulse
propagation dynamics in neurons, to name but a few. In
this talk, I will discuss recent work carried out in my
group on noiseinduced transitions in bistable systems
that are far from thermal equilibrium. Experimental
studies focus on switching transitions between distinct
states of electrical current flow in quantum tunneling
structures such as semiconductor superlattices and
tunnel diodes.
The seminar will take place at 12:00 in classroom
2.1.C03 (Edificio Sabatini) Universidad Carlos III
Seminar
Monday, May 30
Effective boundary conditions (EBC) for semiopen
dispersive systems: Leaky rigid lid on the atmosphere.
MIT
Abstract
Much of our understanding of the tropospheric dynamics
relies on the concept of discrete internal modes.
However, discrete modes are the signature of a finite
system, while the atmosphere should be modeled as
infinite and "is characterized by a single isolated
eigenmode and a continuous spectrum" (Lindzen, JAS
2003). Is it then unphysical to use discrete modes? To
resolve this issue we obtain an approximate radiation
condition at the tropopausethis yields an EBC. We
then use this EBC to compute a new set of vertical
modes: the leaky rigid lid modes. These modes decay,
with decay timescales for the first few modes ranging
from an hour to a week. This suggests that the rate of
energy loss through upwards propagating waves may be an
important factor in setting the time scale for some
atmospheric phenomena. The modes are not orthogonal,
but they are complete, with a simple way to project
initial conditions onto them.
The EBC formulation requires an extension of the dispersive wave theory. There it is shown that sinusoidal waves carry energy with the group speed $c_g = d\omega/dk$, where both the frequency $\omega$ and wavenumber $k$ are real. However, when there are losses, complex $k$'s and $\omega$'s arise, and a more general theory is required. I will briefly comment on this theory, and on how the Laplace Transform can be used to implement generic EBC.
The seminar will take place at 16:00 in classroom
2.1.C17 (Edificio Sabatini) Universidad Carlos III
Seminar
Tuesday, May 17
New topological aspects in 2D
ICMMCSIC Madrid
Abstract
I will address three topics related to new
geometrical/topological aspects in 2D materials.
Firstly, I will discuss the magnetic response of
general 2D materials and point out that the standard
approach pioneered by Peierls and Landau was missing
important geometrical contributions related to the
Berry curvature. Secondly, I will discuss plasmonic
excitations in a thin slab of topological insulators
and point out that plasmons consist either of
collective charge or spin excitations (spincharge
separation). Last, I will focus on a new, theoretically
proposed twodimensional carbon allotrope that entirely
consists of carbon atoms forming pentagrams:
pentagraphene.
[1] G. GómezSantos and T. Stauber, Phys. Rev.
Lett. 106, 045504 (2011); A. GutiérrezRubio, T.
Stauber, G. GómezSantos, R. Asgari, and F. Guinea,
Phys. Rev. B 93, 085133 (2016).
The seminar will take place at 13:00 in classroom
2.1.C17 (Edificio Sabatini) Universidad Carlos III
Seminar
Thursday, April 21
Geometry at noise driven dynamical systems
U. of California at Berkeley and Duke University
Abstract
Feynman, in a little example in his path integral book,
formulated a stochastic action, so that the most
probable path from point q to point h in configuration
space minimizes it. Hence, the physics at most probable
path resembles geometric optics or geodesic motion. But
with a twist: The path from q to h is not the path from
h to q. This is the "geometric" interpretation of
breaking detailed balance. It is actually equivalent to
the conventional notion, in which detailed balance
means that there are equilibrium solutions of the
FokkerPlank equation so the probability current
vanishes identically. For linear stochastic dynamics,
you can detect the breaking of detailed balance by
direct measurements of trajectories: Project the
trajectory into the plane of any two independent
variables. If detailed balance is broken, the expected
area swept out by the trajectory is nonzero. You can do
this diagnosis without knowing details of the flow or
the noise.
The seminar will take place at 12:00 in classroom
2.1.D04 (Edificio Sabatini) Universidad Carlos III
Seminar
Thursday, April 6
LandauZener interference in double quantum dots
ICMMCSIC Madrid
Abstract
Quantum dots are constrictions in a twodimensional
electron gas by which the electronic states become
discrete. Thus, quantum dots represent a solidstate
realization of an atom which, in addition, can be
contacted with an electron source and drain. When two
quantum dots form a "molecule", the resulting current
is affected by quantum phenomena such as delocalization
and coherence which can be controlled by external
fields. For instance, if an energy level of one dot is
swept such that it crosses a level of the other dot,
one observes LandauZener transitions. Repeated sweeps
lead to the socalled LandauZenerStückelbergMajorana
interference visible in a characteristic pattern as a
function of the detuning and the amplitude of the
sweeps. Comparison of experimental results with
theoretical predictions provides the corresponding
decoherence rate [1], which is a crucial parameter for
applications in the context of quantum information
processing. When driving the system with two frequencies, the symmetry of the interference pattern depends on their commensurability. In particular, for commensurable frequencies, the symmetry depends on the relative phase between the two components, while in the incommensurable case, one finds the higher symmetry which otherwise is only found for certain phases. These predictions are confirmed by measurements [2]. [1] F.Forster et al., PRL 112,
116803 (2014).
The seminar will take place at 12:00 in classroom
2.1.C17 (Edificio Sabatini) Universidad Carlos III
Seminar
Thursday, February 25
Control of heat flow: From thermal rectifiers to
thermoelectric devices
UPM
Abstract
A better understanding of the underlying dynamical
mechanisms which determine the macroscopic laws of heat
conduction may lead to potentially interesting
applications based on the ability to control the heat
flow. In this talk I will discuss thermal rectification
and thermoelectric energy conversion from the
perspective of nonequilibrium statistical mechanics and
dynamical systems theory. This yields possible
microscopic mechanisms for the design of thermal diodes
and for the increase of thermoelectric efficiency.
The seminar will take place at 12:00 in classroom
2.1.C19 (Edificio Sabatini) Universidad Carlos III
Seminar
Friday, January 22
High Order Accurate Numerical Methods for Myxobacteria
Pattern
UC3M
Abstract
Rippling patterns of myxobacteria appear in starving
colonies before they aggregate to form fruiting bodies.
These periodic traveling cell density waves arise from
the coordination of individual cell reversals,
resulting from an internal clock regulating them, and
from contact signaling during bacterial collisions. One
of the field of interest in this research work focuses
on the numerical approximation with high order accuracy
in space of the solutions of mathematical model
proposed for myxobacteria rippling. We reconsider the
papers of Igoshin and coauthors [Proc. Natl. Acad. Sci,
USA 98, 14913 (2001) and Phys. Rev. E 70, 041911
(2004)] which describes the rippling phenomena of
myxobacteria as a system of hyperbolic conservation law
(when the diffusion is zero). Since the properties of
the solution of systems of conservation laws develop
jump discontinuities and spurious oscillations in time
and space, it is important to use accurate numerical
simulators in order to explain and predict the natural
biological process. Previously, patterns for this model
were obtained only by numerical methods of low order of
accuracy and it was not possible to find their
wavenumber analytically.
The outline of this seminar is the following. First, we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al. Next, we make a description of the high accuracy numerical methods employed in this work and a detailed explanation of the algorithms that we have developed and used for the numerical simulations. We present various numerical tests for the mathematical model of myxobacteria rippling formation. We show that in the absence of white noise sources introduced in the original model, the hyperbolic system of two coupled partial differential equations can reproduce the reversal process on a regular basis. We have used highprecision numerical tools in order to maintain the amplitude of the travelling waves. We derive an evolution equation for the reversal point density that selects the pattern wavenumber in the weak signaling limit. We show the validity of the selection rule by solving numerically the model equations and describe other stable patterns in the strong signaling limit. The nonlocal meanfield coupling tends to decohere and confine patterns. Under appropriate circumstances, it can anihilate the patterns leaving a constant density state via a nonequilibrium phase transition reminiscent of destruction of synchronization in the Kuramoto model. [1] O. A. Igoshin, A. Mogilner, R.D. Welch, D. Kaiser and G. Oster, Pattern formation and traveling waves in myxobacteria: Theory and modeling. Proc. Natl. Acad. Sci. USA 98, 1491314918 (2001).
The seminar will take place at 12:00 in classroom
2.1.C19 (Edificio Sabatini) Universidad Carlos III


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