Abstracts of posters

The energy levels of a quantum graph with time reversal symmetry and unidirectional classical
dynamics are doubly degenerate and obey the GUE statistics. These degeneracies, however, are lifted when the
unidirectionality is broken in one of the graph's vertices by a singular perturbation. We present, based on a
RMT model, an analytic expression for the nearest neighbour distribution which does not belong to one of the
three standard ensembles. If the distribution of eigenfunctions on the graph is uniform, this result agrees
with the observed statistics. Yet, the presence of scars is marked by quite substantial deviations. (arXiv:1503.01342 [math-ph])

A mapping of potentially chaotic time-dependent quantum systems to an equivalent effective time-independent scenario,
whereby the system is rendered integrable, will be presented. The time-evolution is factorized into an initial kick, followed by an
evolution dictated by a time-independent Hamiltonian and a final kick. This method is much superior than the existing Cambell-Baker-Hausdorff
based method. We discuss this superiority by applying the new method to the kicked top model, a very well-studied model of quantum and classical chaos.
The density of states for the effective system exhibits sharp peak-like features, pointing towards quantum criticality. Our results indicate that
the derived effective Hamiltonian serves as a replacement for the actual system in the non-chaotic regime at both the quantum and classical level.

A series of quantum search algorithms has been proposed recently providing an algebraic speed-up compared to classical search algorithms from &N; to &sqrt{N}; where &N; is the number of items in the search space.
In particular, devising searches on regular lattices have become popular extending Grover's original algorithm to spatial searching.
Working in a tight-binding setup, it could be demonstrated theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possess Dirac points.
We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement.
The idea is based on bringing localized search states in resonance with an extended lattice state in an energy region of low spectral density - namely at or near the Dirac point.
The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e.artificial graphene.
We furthermore investigate the scaling behavior experimentally using linear chains.

We study in momentum-conserving systems, how nonintegrable dynamics
may affect thermal transport properties. As illustrating examples, two
one-dimensional (1D) diatomic chains, representing 1D fluids and lattices,
respectively, are numerically investigated. In both models, the two species
of atoms are assigned two different masses and are arranged alternatively.
The systems are nonintegrable unless the mass ratio is one. We find that
when the mass ratio is slightly different from one, the heat conductivity
may keep significantly unchanged over a certain range of the system size
and as the mass ratio tends to one, this range may expand rapidly. These
results establish a new connection between the macroscopic thermal transport
properties and the underlying dynamics.

In open quantum systems a fundamental question concerns the phasespace
localization of resonance states. For a fully chaotic phase space
the resonance states are supported on a fractal set of classically trapped
orbits. We investigate the possibility of quantum ergodicity, i.e. semiclassical
equidistribution with respect to suitable classical densities on
this fractal set. We explain why these classical densities have to be
chosen according to the quantum decay rate.

Quantized torus Hamiltonians are hermitian matrices living on an finite dimensional Hilbert space but with dimension
going to infinity if the semiclassical parameter is $hbar$ is going to zero. We will show how to approximate the time evolution
operator in the limit $hbarrightarrow 0$. The representation of the time evolution operator by means of a suitable discrete
Fourier integral expression allows to derive a trace formula for the quantized Hamiltonian.  

In generic Hamiltonian systems regions of regular motion coexist with regions
of chaotic motion in phase space.  While classically both types of motion are
separated, quantum-mechanically dynamical tunneling from the regular towards
the chaotic phase-space region occurs. In particular in the semiclassical
regime, where the effective reduced Planck constant $hbar$ is small, this
regular-to-chaotic tunneling process is strongly enhanced due to the presence of
nonlinear resonance chains within the regular region.  We present a
first semiclassical prediction of resonance-assisted regular-to-chaotic
tunneling that is based on integrable approximations of the regular
phase-space region which include the nonlinear resonance chain.  The
application of this theoretical prediction to the standard map leads to
excellent agreement with numerical data.

In recent years, growing experimental and theoretical evidence suggests the existence of quantum spin liquid phase in
kagome antiferromagnets, however its nature is still controversial. In this talk, I will introduce our study on kagome
antiferromagnets with XXZ anisotropy. Numerically (by DMRG), we find that the emergence of the spin-liquid phase is independent
of the anisotropy of the XXZ interaction. In particular, the two extreme limitsÑthe easy-axis and the easy-planeÑhost the same
spin-liquid phases as the isotropic Heisenberg model. Both a time-reversal-invariant spin liquid and a chiral spin liquid with
spontaneous time-reversal symmetry breaking are obtained. We show that they evolve continuously into each other by tuning the
second- and the third-neighbor interactions. Theoretically, we focus on the strong easy axis limit, by performing a duality
transformation we obtain an effective model, which is basically a compact U(1)-Higgs lattice gauge model. I will also discuss
the possible spin liquid phase of this effective model, which naively is not captured by AndersonÕs RVB picture for spin liquid.

Triangular microcavities are an interesting class of optical billiards. On the one hand side,
triangles are the simplest case of polygons. On the other hand side, the properties of lasing
modes and even ray orbits in generic triangular billiards are not fully understood. Whereas
highly  symmetrical and rational triangles are well studied in literature, triangular billiards
with a low degree of symmetry are not extensively investigated.
In a recent experiment (C. Lafargue et al., Phys. Rev. E 90, 052922 (2014)), triangular
microlasers with different degrees of symmetry are analyzed. The far-field emission pattern of
highly symmetrical triangles appears to originate from modes localized on short periodic orbits,
whereas the emission of less symmetrical triangles cannot be explained in this picture.
Here, we perform ray-tracing simulations for all classes of triangles studied in the experiment.
We augment the geometrical optics description with semiclassical effects Ð Goos-Hänchen shift and
Fresnel filtering Ð as well as amplification in order to better predict  the far-field emission of the microlasers and can, thereby, improve the understanding of the modes and their lasing properties. 

It is generally accepted that the equilibrium properties of quantum gases give the same results for the canonical and
grand canonical ensemble. For finite systems well below the thermodynamic limit, however, this equivalence breaks down. The total
number of particles can not be fixed within the grand canonical formalism where by definition this quantity is always subject to
thermal and quantum fluctuations except in the strict thermodynamic limit. This poses a serious problem, as most of the powerful
techniques to deal with quantum and interaction effects in quantum gases depend in an essential way on the use of the grand canonical
formalism. In particular in order to calculate the many body density of states of quantum systems one strictly requires a canonical
approach, as the grand canonical formalism will mix energies belonging to subspectra with different numbers of particles. To the
best of our knowledge, a purely canonical approach to address quantum and interaction effects on both the density of states and
equilibrium thermodynamics of quantum gases with a fixed number of particles is not available.

In this contribution we present such an approach, with the specific intention to obtain analytic information about the spectral and equilibrium
properties of the finite Lieb-Liniger model, i.e. bosons on a circle with contact-interaction. In our formalism the canonical partition function
and the many-body density of states are both given by a textit{finite} expansion in the volume, thus providing closed explicit expressions.

We investigate the structure of eigenstates of quantized 4D maps whose classical dynamics has a mixed phase space in which regions of regular and
chaotic motion coexist. One of the challenges is the strong increase in computing time of the matrix
diagonalization in the semiclassical limit, which can be minimized by a symmetry reduction.
Furthermore, a direct visualization of eigenstates in 4D phase-space is not possible.
By applying the method of textsc{3D} phase-space slices [1] we visualize Husimi functions of eigenstates and
compare them with the classical phase-space structures. This allows for identifying regular states, chaotic
states and also scarred states concentrating around hyperbolic periodic orbits.


[1] M.Richter, S.Lange, A.Bäcker, and R.Ketzmerick, Visualization and comparison of classical structures and quantum states of four-dimensional maps, Phys.~Rev.~E  89, 022902 (2014)

Quantum vortices in weakly coupled superfluids are characterized by a large healing length, such that a large number
of particles reside within the vortex core. Their dynamics are governed by the Gross-Pitaevskii equations deep within the core,
which dictate that the superfluid velocity diverges to a singular point at the vortex center. This singularity is topologically
protected by the superfluids vorticity quantization. We analyze the motion of a vortex in a 2D spinless superfluid, and find that
the vortex core is in fact unstable to pertubations that obey the topological constraint. In practice, the point singularity deforms
into a line singularity, proportional to the applied Magnus force. This core deformation is described by weak solutions of the
Gross-Pitaevskii equations. The core deformation produces an anomalously large dipole moment associated with an anomalously large mass.
As a result, the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum. The deformation also impacts the
dynamics of few-vortex systems, leading to chaotic behaviour of vortex-antivortex dipoles.

Microcavity lasers made of dielectric disk-shaped resonators with sizes in the micrometer range have gained a lot
of interest in recent years. A drawback of pure disk resonators for microlaser applications is their isotropic light output.
To overcome this problem, deformed cavities were proposed such as limacon-shaped resonators which display directional light
emission attractive for microcavity lasers.

In this work we study the coupling of a disk resonator to a limacon-shaped cavity using three dimensional FDTD wave-calculations.
For this purpose a limacon resonator is placed on top of a disk resonator, a whispering gallery mode with high Q-factor is excited
inside the disk resonator and its coupling into the limacon cavity is analyzed for different geometric configurations. Furthermore
we investigate the directional light emission and its tuning in such microcavity arrangements. In detail we calculate a full three
dimensional emission profile with respect to the limacon cavity size and its position on the disk resonator. Thus we obtain the
direction of light output in 3D and its benefit for microcavity laser applications.

We investigate the propagation of electrons starting from a quantum point contact-like source in a two dimensional
random potential. We present the density of classical trajectories which shows the well-known branching pattern near the source
and its gradual disappearance into a homogeneously fluctuating pattern at larger distances. This is accompanied by a continuous
change in the trajectory-density probability distribution from lognormal to Gaussian as the distance from the source increases.
We also calculate the semiclassical Green's function for each trajectory, and discuss how its amplitude is related to both the
branching features and the conjugate points (caustics) along the trajectory. We show that large semiclassical amplitudes are
attached to prominent branches where they remain constant, whereas generally the semiclassical amplitude decreases exponentially
as the trajectory evolves. We complement our discussions by including full quantum mechanical results and confirm a quantum-classical
correspondence. 

The chaotic dynamics of generic Hamiltonian systems is governed by partial barriers. They also strongly
influence the systemÕs quantum-mechanical properties and can lead to a localization of eigenstates on either side of
a partial barrier. We demonstrate that even if the classical flux across a partial barrier is larger than Planck's cell,
such that eigenstates delocalize in closed systems, opening the system leads to a reappearance of localization.
We derive an analytical prediction for the localization of resonance states around partial barriers in the semiclassical
limit and describe quantum corrections quantitatively. Based on these localized resonance states we can generalize the fractal
Weyl law to open systems with a mixed phase space.

The Ising model with a pulsed transverse and a continuous longitudinal field is studied. Starting from a
large transverse field and a state that is nearly an eigenstate, the pulsed transverse field is quenched with a simultaneous
enhancement of the longitudinal field. The generation of multipartite entanglement is observed along with a phenomenon akin to
quantum resonance when the entanglement does not evolve for certain values of the pulse period. Away from the resonance,
the longitudinal field can drive the entanglement to near maximum values that is shown to agree well with those of random states.
An exactly solvable case is also discussed wherein the entanglement of any block of spins increases at the rate of one
ebit till it is maximally entangled. 

While power-law trapping in 2D maps can be explained by a hierarchy of
partial transport barriers, its origin in higher dimensional maps is
still an open question.
We study 4D symplectic maps with a regular region embedded in a large chaotic sea,
i.e., far away from the near-integrable regime. Chaotic orbits are
trapped in the vicinity of the regular region and show a power-law
decay of survival times. We search for the trapping mechanism by
visualizing the trapped orbits in 3D phase-space slices and analyzing
their time-dependent frequencies. While this has not yet revealed the
mechanism, we can make the following statements about the power-law
trapping: It is clearly different from trapping in 2D maps, as the
trapped orbits do not explore the hierarchy of the 4D phase space.
Moreover, it is not related to the Arnol'd web.

We show that conserved charges can be constructed analytically in terms of the microscopic parameters of non-interacting lattice 
models in one dimension with localized phases. These charges are obtained as power series in the hopping 
parameters of these models. We show that they exist only in localized phases by postulating an  appropriate condition
for the convergence of the power series. For an interesting class of models with long-range hopping (type I matrices),
the power series truncates at linear order. We also explicitly demonstrate the connection between localization and the
existence of conserved charges by studying a model with a localization-delocalization transition (the Aubry-Andre model).
In this model, the constructed charges exist only when localization occurs and cease to exist when delocalization sets in.
Finally, we also obtain the conserved charges for a model with interactions to lowest order in the interaction strength.  

The dynamics of Hamiltonian systems (e.g., planetary motion, electron dynamics in nano-structures, molecular dynamics) can be investigated by symplectic maps. While a lot of work has been done for 2 D maps,
much less is known for higher dimensions.
For a generic 4 D map regular 2D-tori are organized around a skeleton of families of elliptic 1D-tori~[1], which can be visualized by 3D phase-space slices~[2]. We present an analysis of the different
bifurcations of the families of textsc{1d}-tori in phase space and in frequency space by computing the involved hyperbolic and elliptic textsc{1d}-tori. Applying known results of normal form analysis, both the local and
the global structure can be understood: Close to a bifurcation of a 1D-torus, the phase-space structures are surprisingly similar to bifurcations of periodic orbits in 2D maps. Far away the phase-space
structures can be explained by remnants of broken resonant 2D-tori.

[1] S.Lange, M.Richter, F.Onken, A.Bäcker und R.Ketzmerick:   Global
  structure of regular tori in a generic 4D symplectic map, Chaos  24,
  024409 (2014)

[2] M.Richter, S.Lange, A.Bäcker, and R.Ketzmerick,  Visualization
  and comparison of classical structures and quantum states of four-dimensional
  maps, Phys.~Rev.~E  89, 022902 (2014)

A major experimental challenge with cold atoms is to study Anderson localization
of three-dimensional samples exposed to laser speckles. These random potentials are characterized by an exponential on-site distribution P(V ) and finite spatial correlations.
In this talk I will present numerically exact results [1] for the position of the mobility edge obtained by discretizing the system on a finite grid and applying the transfer
matrix technique to the effective Anderson model. These results deviate significantly from previous implementations of the self-consistent theory of localization and I will explain the
reasons of the discrepancy. In particular the asymmetry of P(V) under V->-V lead to completely different predictions for the mobility edge of atoms in blue and in red speckles.

[1] D. Delande and G. Orso, PRL 113, 060601 (2014).

Over the past years, a remarkable variety of novel correlated states was discovered in graphene
and its bilayer in a magnetic field. These states exhibit previously unseen richness due to an interplay of
electron spin, valley and orbital degrees of freedom. They are furthermore distinguished by their high degree
of tunability, e.g. via the in-plane magnetic or the perpendicular electric field, which allows one to probe
their properties in a more flexible and direct way than in GaAs semiconductor systems. In this talk I will present
a theoretical overview of the phase diagram of the partially-filled zeroth Landau level of bilayer graphene.
Using realistic large-scale numerical calculations that incorporate strong mixing between orbitally degenerate
sublevels, as well as the screening of the Coulomb interaction, we identify several robust quantum Hall states
with odd denominators such as nu=?4/3,?5/3,?8/5. Furthermore, we find evidence for the existence of an incompressible,
even-denominator nu=?1/2 state, and argue that this state is in the universality class of the non-Abelian Moore-Read
state or its particle-hole conjugate, while other candidates such as the 331 state are unlikely to describe it.
Finally, we show that symmetry breaking, induced by an electric field applied perpendicular to the basal plane,
is a useful experimental knob to tune the quantum phase transitions between integer or fractional states in
bilayer graphene at a fixed filling factor. These results illustrate the potential of bilayer graphene as a model
platform to study the emergent topologically ordered phases and transitions between them via symmetry breaking.

We study Anderson localization of cold atoms in anisotropic disordered speckle potentials with a focus towards the interpretation of recent experimental results.
In particular, we present results for the mobility edge obtained from quasi-exact numerical calculations in realistic conditions.

Martin Puschmann (1), Philipp Cain (1), Michael Schreiber (1), and Thomas Vojta (2)

1) Institute of Physics, Technische Universität Chemnitz, Chemnitz, Germany
2) Department of Physics, Missouri University of Science and Technology, Rolla, Missouri, USA

The random Voronoi-Delaunay lattice (VDL) is a simple model for amorphous solids and foams. It is defined as a set of
bonds between randomly positioned sites. The bonds connect neighboring Voronoi cells and are obtained by the Delaunay
triangulation. The resulting topologically disordered lattice features strong anticorrelations between the coordination
numbers of neighboring sites. The disorder fluctuations therefore decay qualitatively faster with increasing length scale
than those of generic random systems. A recent study showed that this modifies the Harris and Imry-Ma criteria and leads
to qualitatively changes of the scaling behavior at magnetic phase transitions [1]. 
We consider the transport of non-interacting electrons on two- and three dimensional random VDLs and study the electronic
wave functions by multifractal analysis. We observe localized states for all energies in the two-dimensional system.
In three dimensions, we find two phase transitions towards extended states very close to the band edges. The scaling
analysis shows that the scaling exponent of the localization length is 1.6, in accordance with the usual orthogonal
universality class. An additional generic energetic randomness by on-site potentials does not lead to qualitative changes.
We obtain a phase diagram by varying the disorder strength of these potentials. 

In conclusion, the unusual coordination number anticorrelations of random VDLs do not lead to qualitatively different
behavior compared to the well-known Anderson model of localization on regular lattices.

[1] H. Barghathi and T. Vojta, Phys. Rev. Lett. 113, 120602 (2014)

We consider quantum wave propagation in one-dimensional quasiperiodic lattices. We
propose an iterative construction of quasiperiodic potentials from sequences of potentials with
increasing spatial period. At each finite iteration step, the eigenstates reflect the properties
of the limiting quasiperiodic potential properties up to a controlled maximum system size.
We then observe approximate MetalÐInsulator Transitions (MIT) at the finite iteration steps.
We also report evidence on mobility edges, which are at variance to the celebrated AubryÐAndre
 model. The dynamics near the MIT shows a critical slowing down of the ballistic group velocity
 in the metallic phase, similar to the divergence ofthe localization length in the insulating phase.

We predict the spontaneous modulated emission from a pair of exciton-polariton condensates
due to coherent (Josephson) and dissipative coupling. We show that strong polariton-polariton inter- action
generates complex dynamics in the weak-lasing domain way beyond Hopf bifurcations. As a result, the exciton
polariton condensates exhibit self-induced oscillations and emit an equidistant
frequency comb light spectrum. A plethora of possible emission spectra with asymmetric peak distributions
appears due to spontaneously broken time-reversal symmetry. The lasing dynamics is affected by the shot noise
arising from the influx of polaritons. That results in a complex inhomogeneous line broadening.

Many-body localized (MBL) phase (BAA) is the exotic state of matter that is characterized
by the ergodicity breaking. The variety of systems known to possess such a state is very limited -- mostly to spin
chains and their equivalents (see e.g. (ZPP, OPH)). \

It is known that the periodically kicked systems can show dynamical localization. The canonical example
of the classically ergodic system that shows dynamical Anderson localization is the kicked rotor (FGP).
We generalize this concept to the many-body physics and consider periodically kicked non-interacting many-body systems.
We confirm the ergodicity of the classical models and look for the signatures of the MBL phase within
the quantum Floquet framework.


BAA D.M. Basko, I.L. Aleiner, and B.L. Altshuler, Annals of Physics textbf{321}, 1126 (2006).
ZPP M. &zscaron;nidari&cscaron;, T. Prosen, and P. Prelov&sscaron;ek, Phys. Rev. B 77, 064426 (2008).
OPH Arijeet Pal and David A. Huse, Phys. Rev. B 2, 174411 (2010).
FGP S. Fishman, D. B. Grempel, and B. E. Prange, Phys. Rev. Lett. 49, 509 (1982).


list of authors:
Aydin Cem Keser, Efim Rozenbaum, and Victor Galitski.
Affiliation of all the authors: University of Maryland, College Park (USA).

We predict a generic signature of quantum interference in many-body bosonic systems resulting in a
coherent enhancement of the average return probability in Fock space [1]. This enhancement is robust with respect
to variations of external parameters even though it represents a dynamical manifestation of the delicate superposition
principle in Fock space. It is a genuine quantum many-body effect which lies beyond the reach of any mean-field approach.
Using a semiclassical approach based on interfering paths in Fock space, we calculate the magnitude of the
backscattering peak and its dependence on gauge fields that break time-reversal invariance. We confirm our
predictions by comparing them to exact quantum evolution probabilities in Bose-Hubbard models, and discuss
their relevance in the context of many-body thermalization. We furthermore propose a specific experimental
setup in order to detect this many-body coherent backscattering phenomenon with ultracold bosonic atoms.

[1] T. Engl, J. Dujardin, A. Argüelles, P. Schlagheck, K. Richter, and J. D. Urbina, Phys. Rev. Lett. 112, 140403 (2014).

The level-spacing distribution and intensity distribution for the quantized four-dimensional
coupled standard map are investigated. With increasing coupling one observes a transition from Poissonian
to random matrix statistics of the circular unitary ensemble. The same is also observed at fixed non-zero
coupling when approaching the semiclassical limit. Identifying a universal scaling
parameter, the full transition can be described by a random matrix model. The transition is also well
described by a 2 ? 2 matrix model. For the intensity distribution of eigenvectors we obtain a transition
from a strongly peaked distribution at small spacings to a Poissonian distribution for
strong coupling.

Triangular microcavities are an interesting class of optical billiards. On the one hand, triangles
are the simplest case of polygons. On the other hand, the properties of orbits in generic triangular billiards
are not fully understood. Whereas highly symmetrical and rational triangles are well studied in literature,
triangular billiards with a low degree of symmetry are not extensively investigated.
In a recent experiment (C. Lafargue et al., Phys. Rev. E 90, 052922 (2014)), triangular microlasers with different
degrees of symmetry are analyzed. The far-field emission pattern of highly symmetrical triangles appears to
originate from modes localized on short periodic orbits, whereas, the emission of less symmetrical triangles
cannot be explained in this picture.
Here, we perform ray-tracing simulations for the classes of triangles studied in the experiment.
We augment the geometrical optics description with semiclassical effects Ð Goos-Hänchen shift and
Fresnel filtering Ð and amplification to make better predictions for the far-field emission of the microlasers.
Further, we perform full electromagnetic wave calculations using the FDTD method on triangular shaped dielectric
resonators. We compare the experimental results and the ray and wave simulations to gain insight in the mode
structure of generic triangular microcavities.

Echoes are a hallmark manifestation of quantum coherence, as they are a directly consequence of
the superposition principle. However, for single-particle systems, the superposition principle is actually
equivalent to the real wave character of the quantum dynamics: quantum and wave interefernce are then indistinguishable.
In the framework of interacting quantum systems made of identical particles, a quantum field, wave and quantum
interefence actually represent different phenomena, where the later is always present while the former is a
classical property that gets suppressed due to interaction effects.
We presentt here a novel approach to quantum interference in Fock space that is fully independent on the
presence of wave interference at the classical (mean field) level, and we use our formalism to study echo
phenomena for both bosonic and fermionic systems.   

Recent years have witnessed a growth of interest in topological states of matter. One of the
exotic excitations that is predicted to exists in some of these setups are the Majorana fermions, which unique
physical properties  make them an ideal candidate for Quantum Computation. These elusive excitations are difficult
to detect, and a myriad of methods have been suggested for their identification.

One of the signatures of a Majorana bound state is a zero-bias peak at the conductance in tunneling experiments.
While the conductance into a Majorana state in principle is quantized to 2e^2/h, observation of this quantization
has been elusive, presumably due to temperature broadening in the normal-lead tip. Here, we propose to use a
superconducting lead, whose gap strongly suppresses thermal excitations. We find that a Majorana state is signaled
by symmetric conductance peaks at eV=±?, which are quantized to G=(4-¹)2e^2/h. This value persists over a wide range
of tunneling strengths, which results in spatial conductance plateaus. In contrast, the conductance peak varies
strongly with the local wavefunction for trivial Andreev bound states.

Due to its richness, the emission properties of random lasers is still a subject of interest both
theoretically and experimentally. From a theoretical perspective we still lack a satisfactory quantum theory of
laser which is able to incorporate entirely the varied phenomenology exhibit by random lasers. In this contribution
I present a quantum theory for lasers with overlapping modes which allows for a statistical description of random lasers.
The grounding point of this theory is the quantum description of light in optical cavities with low quality factors,
i.e. cavities with large loses. The emphasis of our work is on the description of the spectrum of emission in the
nonlinear regime above the laser threshold for lasers working in a single mode, which due to the presence of below
threshold resonances, besides the expected linewidth enhancement, shows significant deviations from the Lorentzian
shape emission spectrum of standard lasers. By means of a Random Matrix model to simulate the dynamics of light in
a chaotic optical cavity we use our theory to study the threshold distribution in an ensemble of chaotic lasers.

The description of scattering at time-dependent potentials is usually restricted to time periodic or
adiabatic motion. We extend this to other time dependencies.
We start by considering quantum graphs and analyze perturbatively in the strength of the potential the effect of
Brownian motion on the topological transmission resonances of the graph. This work was published in [1]
We then characterize [2] in a nonperturbative manner the wavefunction and the current through a quantum dot in a
time dependent field. For the time dependence again Brownian motion as well as Levy walks are considered.
As an application we compute the root mean square of the pumped charge and current in this setup.

[1] Daniel Waltner and Uzy Smilansky, Transmission through a noisy network, J. Phys. A 47 (2014) 355101, selected for the 2014 Highlight collection.
[2] Stanislav Derevyanko and Daniel Waltner, Non-adiabatic quantum pumping by a randomly moving quantum dot,  arXiv:1502.02822. 

The energy spectra of systems that are chaotic in the classical limit generally exhibit universal
fluctuation statistics coincident with those of random matrix theory. In the presence of a discrete group &G;
of unitary symmetries, the spectrum decomposes into a superposition of mutually uncorrelated subspectra, each
associated with an irreducible representation of &G;. In order to predict which RMT ensemble describes a given
subspectrum, one needs to understand the structure of the full symmetry group of unitary and antiunitary operators.
Such groups are most conveniently understood within the context of Wigner's theory of group corepresentations.
We use this approach to construct a spinless Aharonov-Bohm billiard possessing a GSE subspectrum.

We point out that in the first-order time-dependent perturbation theory, the transition probability
may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be
sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas.
Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function sinc x ? sin x/x.
These physical effects appear in many systems with approximately equally spaced spectra, and are also robust for
larger amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven
tight-binding model to illustrate these effects, both within and outside the perturbative regime.

[1] J. M. Zhang and M. Haque, ScienceOpen Research (2014).