ERC FUNDED PROJECTS

The main focus of this project is the mathematical analysis of many-body quantum systems, in particular, interacting quantum gases at low temperature. The recent experimental advances in studying ultra-cold atomic gases have led to renewed interest in these systems. They display a rich variety of quantum phenomena, including, e.g., Bose–Einstein condensation and superfluidity, which makes them interesting both from a physical and a mathematical point of view. The goal of this project is the development of new mathematical tools for dealing with complex problems in many-body quantum systems. New mathematical methods lead to different points of view and thus increase our understanding of physical systems. From the point of view of mathematical physics, there has been significant progress in the last few years in understanding the interesting phenomena occurring in quantum gases, and the goal of this project is to investigate some of the key issues that remain unsolved. Due to the complex nature of the problems, new mathematical ideas and methods will have to be developed for this purpose. One of the main question addressed in this proposal is the validity of the Bogoliubov approximation for the excitation spectrum of many-body quantum systems. While its accuracy has been successfully shown for the ground state energy of various models, its predictions concerning the excitation spectrum have so far only been verified in the Hartree limit, an extreme form of a mean-field limit where the interaction among the particles is very weak and ranges over the whole system. The central part of this project is concerned with the extension of these results to the case of short-range interactions. Apart from being mathematically much more challenging, the short-range case is the one most relevant for the description of actual physical systems. Hence progress along these lines can be expected to yield valuable insight into the complex behavior of these many-body quantum systems.

1 497 755 €

Start date: 2016-10-01, End date: 2021-09-30

We envisage a new generation of dynamic holographic laser tweezers and stretching tools with unprecedented spatial control of gradient and scattering light forces, to unravel functional mysteries of cell biology and genetics: Based on our recently developed, highly successful and widely recognized amplitude and phase shaping techniques with cascaded spatial light modulators (SLM), we will create new holographic optical manipulators consisting of a line-shaped trap with balanced net scattering forces and controllable local phase-gradients. Combining these line stretchers with spiral phase contrast imaging or nonlinear optical microscopy will allow quantitative study of functional shape changes. The novel tool is hugely more versatile than standard optical tweezers, since direction and magnitude of the scattering force can be designed to precisely follow the structure. In combination with conventional multi-spot traps the line stretcher acts as a sensitive and adaptable local force sensor. In collaboration with local experts we want to tackle hot topics in Genetics, e.g. search for force profile signatures in regions with Copy Number Variations. Possibly the approach may shed light on basic physical characteristics such as, for example, chromosomal fragility in Fra(X) syndrome, the most common monogenic cause of mental retardation. The new design intrinsically offers enhanced microscopic resolution, as SLM-synthesized apertures and waveforms can enlarge the number of spatial frequencies forming the image. Ultimately, nonlinear holography can be implemented, sending phase shaped wavefronts to target samples. This can, e.g., be used to push the sensitivity of nonlinear chemical imaging, or for controlled photo-activation of targeted regions in neurons.

1 987 428 €

Start date: 2010-05-01, End date: 2015-04-30

What makes music so important, what can make a performance so special and stirring? It is the things the music expresses, the emotions it induces, the associations it evokes, the drama and characters it portrays. The sources of this expressivity are manifold: the music itself, its structure, orchestration, personal associations, social settings, but also – and very importantly – the act of performance, the interpretation and expressive intentions made explicit by the musicians through nuances in timing, dynamics etc. Thanks to research in fields like Music Information Research (MIR), computers can do many useful things with music, from beat and rhythm detection to song identification and tracking. However, they are still far from grasping the essence of music: they cannot tell whether a performance expresses playfulness or ennui, solemnity or gaiety, determination or uncertainty; they cannot produce music with a desired expressive quality; they cannot interact with human musicians in a truly musical way, recognising and responding to the expressive intentions implied in their playing. The project is about developing machines that are aware of certain dimensions of expressivity, specifically in the domain of (classical) music, where expressivity is both essential and – at least as far as it relates to the act of performance – can be traced back to well-defined and measurable parametric dimensions (such as timing, dynamics, articulation). We will develop systems that can recognise, characterise, search music by expressive aspects, generate, modify, and react to expressive qualities in music. To do so, we will (1) bring together the fields of AI, Machine Learning, MIR and Music Performance Research; (2) integrate theories from Musicology to build more well-founded models of music understanding; (3) support model learning and validation with massive musical corpora of a size and quality unprecedented in computational music research.

2 318 750 €

Start date: 2016-01-01, End date: 2021-12-31

The ELE project will study the foundational principles of programming language evolution and develop practical tools and technologies for supporting the evolution of complete ecosystems. If successful, ELE will drastically decrease the cost of evolution and avoid the need to invent completely new languages every time there is a shift in hardware trends or in programming methodology. Instead, ELE will allow evolution of languages and will support migration of code and knowledge bases. The project proceeds along two major axes. The first axis is language dynamics where new features and new capabilities are added to a preexisting language. This requires changing, at the same time, the language's specification, it's semantics, and the language's implementation, the compiler and interpreter that runs code written in the language as well the runtime libraries that provide basic capabilities. The second axis for evolution is language statics where new rules are added to enforce novel programming disciplines and where existing code artifacts are adapted to new semantics. These axes are not entirely disjoint, as static restrictions, such as a new type system, can feedback into the implementation by providing behavioral information that can be exploited by a compiler.

3 234 000 €

Start date: 2016-10-01, End date: 2021-09-30

Mirror symmetry arose originally in physics, as a duality between $N = 2$ superconformal field theories. Witten formulated a more mathematically accessible version, in terms of topological field theories. Both conformal and topological field theories can be defined axiomatically, but more interestingly, there are several geometric ways of constructing them. A priori, the mirror correspondence is not unique, and it does not necessarily remain within a single class of geometric models. The classical case relates $\sigma$-models, but in a more modern formulation, one has mirror dualities between different Landau-Ginzburg models, as well as between such models and $\sigma$-models; orbifolds should also be included in this. The simplest example would be the function $W: \C \rightarrow \C$, $W(x) = x^{n+1}$, which is self-mirror (up to dividing by the $\bZ/n+1$ symmetry group, in an orbifold sense). While the mathematics of the $\sigma$-model mirror correspondence is familiar by now, generalizations to Landau-Ginzburg theories are only beginning to be understood. Today it is clear that Homologcal Mirror Symmetry (HMS) as a categorical correspondence works and it is time for developing direct geometric applications to classical problems - rationality of algebraic varieties and Hodge conjecture. This the main goal of the proposal. But in order to attack the above problems we need to generalize HMS and explore its connection to new developments in modern Hodge theory. In order to carry the above program we plan to further already working team Vienna, Paris, Moscow, MIT.

1 060 800 €

Start date: 2009-01-01, End date: 2013-12-31

Antihydrogen is the simplest atom consisting entirely of antimatter. Since its counterpart hydrogen is one of the best studied atoms in physics, a comparison of antihydrogen and hydrogen offers one of the most sensitive tests of CPT symmetry. CPT, the successive application of charge conjugation, parity and time reversal transformation is a fundamental symmetry conserved in the standard model (SM) of particle physics as a consequence of a mathematical theorem. These conditions for this theorem to be fulfilled are not valid any more in extensions of the SM like string theory or quantum gravity. Furthermore, even a tiny violation of CPT symmetry at the time of the big bang could be a cause of the observed antimatter absence in the universe. Thus the observation of CPT violation might offer a first indication for the validity of string theory, and would have important cosmological consequences. This project proposes to measure the ground state hyperfine (HFS) splitting of antihydrogen (HBAR), which is known in hydrogen with relative precision of 10^–12. The experimental method pursued within the ASACUSA collaboration at CERN-AD consists in the formation of an antihydrogen beam and a measurement using a spin-flip cavity and a sextupole magnet as spin analyser like it was done initially for hydrogen. A major milestone was achieved in 2010 when antihydrogen was first synthesized by ASACUSA. In the first phase of this proposal, an antihydrogen beam will be produced and the HBAR-HFS will be measured to a precision of around 10^–7 using a single microwave cavity. In a second phase, the Ramsey method of separated oscillatory fields will be used to increase the precision further. In parallel methods will be developed towards trapping and laser cooling the antihydrogen atoms. Letting the cooled antihydrogen escape in a field free region and perform microwave spectroscopy offers the ultimate precision achievable to measure the HBAR-HFS and one of the most sensitive tests of CPT.

2 599 900 €

Start date: 2012-03-01, End date: 2017-02-28

The aim of the project is to build and promote a team of excellence in the mathematical theory of water flows, with emphasis on nonlinear aspects. Our aim is to advance the state-of-the-art of water flows with vorticity. Flows within a fixed fluid domain as well as free surface flows will be considered and we strive to provide an accurate description of the entire flow; for example, the flow beneath a water wave and not just a description of the water wave profile. Problems of this type are currently of great interest, for example in the context of wave-current interactions and for a better understanding of tsunami waves. In addition to methods from the theory of partial differential equations to investigate the governing equations for water waves, the use of simplified models with a rich structure (e.g. integrable systems arising in the shallow water regime) will identify and highlight qualitative features. Numerical simulation in conjunction with experimental feedback and the gathering of field data will be of great support. Provision is made for consultation and collaboration with research groups in engineering and physics. Due to the interest of the general public in tsunamis, one of the objectives is to have a positive impact on the perception of science by society and on the raising of scientific interest of the younger generation through public lectures and contacts with high-schools.

1 324 797 €

Start date: 2011-04-01, End date: 2016-03-31

Recent studies in Vienna have shown that surprising quantum phenomena, such as matter-wave interferometry with molecules composed of hundreds of covalently bound atoms, are actually feasible. PROBIOTIQUS will now be the first project world-wide to develop experimental tools for matter-wave physics with large biomolecules from amino acid clusters up to proteins and self-replicating molecules. First, we shall exploit the full potential of coherent molecule metrology for biomolecules, and molecules in a biomimetic environment. This research connects quantum physics with chemistry and biophysics, since already a restricted number of precisely determined geometrical, electrical, magnetic or optical properties may provide tell-tale analytical information. Embedding the biomolecules in a hydrate layer will allow us to study their properties in a context that approaches the ‘natural’ environment. Second, we will develop molecular beam methods, optical manipulation tools and detection schemes to prepare proteins and other large biomolecules for advanced quantum experiments. This includes new laser-assisted acoustic and thermal volatilization methods, slowing and focusing in optical forces, diffraction at ionization and neutralization gratings as well as tagging of proteins with ionizable small biomolecules. Third, we will prepare a cryogenic biomolecular sample in a buffer-gas loaded ion trap, where optical ionization and neutralization will be optimized in order to enable optical diffraction gratings. The target temperature of 10 K will be the starting point for interference experiments with proteins and self-replicating RNA, on the way towards full viruses. Quantum interference with large biomolecules at the edge to life has remained an outstanding challenge throughout the last two decades. The ERC advanced grant will now focus on this goal with novel and interdisciplinary strategies, in world-wide unique experiments.

2 266 904 €

Start date: 2013-04-01, End date: 2018-03-31

Relaxation processes in many-body quantum systems arise in many diverse areas of physics ranging from inflation in the early universe to the emergence of classical properties in complex quantum systems. Ultracold atoms provide a unique opportunity for studying non-equilibrium quantum systems in the laboratory. The coherent quantum evolution can be observed on experimentally accessible timescales and the tunability in interaction, temperature and dimensionality allows the realization of a multitude of different relevant physical situations. Through building specific model systems we propose to study a wide variety of non-equilibrium quantum dynamics under conditions ranging from weakly interacting to strongly correlated, from weakly disturbed to quantum turbulent and search for universal properties in non-equilibrium quantum evolution. We address questions of de-coherence in a split many-body system and the concomitant emergence of classical properties. We will study the fate of the highly entangled quantum states that are created when a system in its excited state decays. Systems with instabilities and controlled quenches will give us insight into the creation of defects and excitations. We will experiment with bosons, fermions and mixtures, and take advantage of the rich internal structure of the atoms. Our systems will also be observed when interacting with ‘baths’, which can be internal or external with controlled coupling and can be engineered from simple thermal to squeezed, from large to mesoscopic with non-Markovian properties. Our ultimate goal is insight into the answers to fundamental questions: What does it take for an isolated many-body quantum system with a set of conserved quantities to relax to an equilibrium state? Which universal properties and scaling laws govern its evolution? Can classical physics and thermodynamics emerge from quantum physics through the dynamics of complex many-body systems?

2 025 400 €

Start date: 2013-06-01, End date: 2018-05-31