Project acronym ABINITIODGA
Project Ab initio Dynamical Vertex Approximation
Researcher (PI) Karsten Held
Host Institution (HI) TECHNISCHE UNIVERSITAET WIEN
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2012-StG_20111012
Summary Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Summary
Some of the most fascinating physical phenomena are experimentally observed in strongly correlated electron systems and, on the theoretical side, only poorly understood hitherto. The aim of the ERC project AbinitioDGA is the development, implementation and application of a new, 21th century method for the ab initio calculation of materials with such strong electronic correlations. AbinitioDGA includes strong electronic correlations on all time and length scales and hence is a big step beyond the state-of-the-art methods, such as the local density approximation, dynamical mean field theory, and the GW approach (Green function G times screened interaction W). It has the potential for an extraordinary high impact not only in the field of computational materials science but also for a better understanding of quantum critical heavy fermion systems, high-temperature superconductors, and transport through nano- and heterostructures. These four physical problems and related materials will be studied within the ERC project, besides the methodological development.
On the technical side, AbinitioDGA realizes Hedin's idea to include vertex corrections beyond the GW approximation. All vertex corrections which can be traced back to a fully irreducible local vertex and the bare non-local Coulomb interaction are included. This way, AbinitioDGA does not only contain the GW physics of screened exchange and the strong local correlations of dynamical mean field theory but also non-local correlations beyond on all length scales. Through the latter, AbinitioDGA can prospectively describe phenomena such as quantum criticality, spin-fluctuation mediated superconductivity, and weak localization corrections to the conductivity. Nonetheless, the computational effort is still manageable even for realistic materials calculations, making the considerable effort to implement AbinitioDGA worthwhile.
Max ERC Funding
1 491 090 €
Duration
Start date: 2013-01-01, End date: 2018-07-31
Project acronym ACTIVENP
Project Active and low loss nano photonics (ActiveNP)
Researcher (PI) Thomas Arno Klar
Host Institution (HI) UNIVERSITAT LINZ
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2010-StG_20091028
Summary This project aims at designing novel hybrid nanophotonic devices comprising metallic nanostructures and active elements such as dye molecules or colloidal quantum dots. Three core objectives, each going far beyond the state of the art, shall be tackled: (i) Metamaterials containing gain materials: Metamaterials introduce magnetism to the optical frequency range and hold promise to create entirely novel devices for light manipulation. Since present day metamaterials are extremely absorptive, it is of utmost importance to fight losses. The ground-breaking approach of this proposal is to incorporate fluorescing species into the nanoscale metallic metastructures in order to compensate losses by stimulated emission. (ii) The second objective exceeds the ansatz of compensating losses and will reach out for lasing action. Individual metallic nanostructures such as pairs of nanoparticles will form novel and unusual nanometre sized resonators for laser action. State of the art microresonators still have a volume of at least half of the wavelength cubed. Noble metal nanoparticle resonators scale down this volume by a factor of thousand allowing for truly nanoscale coherent light sources. (iii) A third objective concerns a substantial improvement of nonlinear effects. This will be accomplished by drastically sharpened resonances of nanoplasmonic devices surrounded by active gain materials. An interdisciplinary team of PhD students and a PostDoc will be assembled, each scientist being uniquely qualified to cover one of the expertise fields: Design, spectroscopy, and simulation. The project s outcome is twofold: A substantial expansion of fundamental understanding of nanophotonics and practical devices such as nanoscopic lasers and low loss metamaterials.
Summary
This project aims at designing novel hybrid nanophotonic devices comprising metallic nanostructures and active elements such as dye molecules or colloidal quantum dots. Three core objectives, each going far beyond the state of the art, shall be tackled: (i) Metamaterials containing gain materials: Metamaterials introduce magnetism to the optical frequency range and hold promise to create entirely novel devices for light manipulation. Since present day metamaterials are extremely absorptive, it is of utmost importance to fight losses. The ground-breaking approach of this proposal is to incorporate fluorescing species into the nanoscale metallic metastructures in order to compensate losses by stimulated emission. (ii) The second objective exceeds the ansatz of compensating losses and will reach out for lasing action. Individual metallic nanostructures such as pairs of nanoparticles will form novel and unusual nanometre sized resonators for laser action. State of the art microresonators still have a volume of at least half of the wavelength cubed. Noble metal nanoparticle resonators scale down this volume by a factor of thousand allowing for truly nanoscale coherent light sources. (iii) A third objective concerns a substantial improvement of nonlinear effects. This will be accomplished by drastically sharpened resonances of nanoplasmonic devices surrounded by active gain materials. An interdisciplinary team of PhD students and a PostDoc will be assembled, each scientist being uniquely qualified to cover one of the expertise fields: Design, spectroscopy, and simulation. The project s outcome is twofold: A substantial expansion of fundamental understanding of nanophotonics and practical devices such as nanoscopic lasers and low loss metamaterials.
Max ERC Funding
1 494 756 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym AFDMATS
Project Anton Francesco Doni – Multimedia Archive Texts and Sources
Researcher (PI) Giovanna Rizzarelli
Host Institution (HI) SCUOLA NORMALE SUPERIORE
Country Italy
Call Details Starting Grant (StG), SH4, ERC-2007-StG
Summary This project aims at creating a multimedia archive of the printed works of Anton Francesco Doni, who was not only an author but also a typographer, a publisher and a member of the Giolito and Marcolini’s editorial staff. The analysis of Doni’s work may be a good way to investigate appropriation, text rewriting and image reusing practices which are typical of several authors of the 16th Century, as clearly shown by the critics in the last decades. This project intends to bring to light the wide range of impulses from which Doni’s texts are generated, with a great emphasis on the figurative aspect. The encoding of these texts will be carried out using the TEI (Text Encoding Initiative) guidelines, which will enable any single text to interact with a range of intertextual references both at a local level (inside the same text) and at a macrostructural level (references to other texts by Doni or to other authors). The elements that will emerge from the textual encoding concern: A) The use of images Real images: the complex relation between Doni’s writing and the xylographies available in Marcolini’s printing-house or belonging to other collections. Mental images: the remarkable presence of verbal images, as descriptions, ekphràseis, figurative visions, dreams and iconographic allusions not accompanied by illustrations, but related to a recognizable visual repertoire or to real images that will be reproduced. B) The use of sources A parallel archive of the texts most used by Doni will be created. Digital anastatic reproductions of the 16th-Century editions known by Doni will be provided whenever available. The various forms of intertextuality will be divided into the following typologies: allusions; citations; rewritings; plagiarisms; self-quotations. Finally, the different forms of narrative (tales, short stories, anecdotes, lyrics) and the different idiomatic expressions (proverbial forms and wellerisms) will also be encoded.
Summary
This project aims at creating a multimedia archive of the printed works of Anton Francesco Doni, who was not only an author but also a typographer, a publisher and a member of the Giolito and Marcolini’s editorial staff. The analysis of Doni’s work may be a good way to investigate appropriation, text rewriting and image reusing practices which are typical of several authors of the 16th Century, as clearly shown by the critics in the last decades. This project intends to bring to light the wide range of impulses from which Doni’s texts are generated, with a great emphasis on the figurative aspect. The encoding of these texts will be carried out using the TEI (Text Encoding Initiative) guidelines, which will enable any single text to interact with a range of intertextual references both at a local level (inside the same text) and at a macrostructural level (references to other texts by Doni or to other authors). The elements that will emerge from the textual encoding concern: A) The use of images Real images: the complex relation between Doni’s writing and the xylographies available in Marcolini’s printing-house or belonging to other collections. Mental images: the remarkable presence of verbal images, as descriptions, ekphràseis, figurative visions, dreams and iconographic allusions not accompanied by illustrations, but related to a recognizable visual repertoire or to real images that will be reproduced. B) The use of sources A parallel archive of the texts most used by Doni will be created. Digital anastatic reproductions of the 16th-Century editions known by Doni will be provided whenever available. The various forms of intertextuality will be divided into the following typologies: allusions; citations; rewritings; plagiarisms; self-quotations. Finally, the different forms of narrative (tales, short stories, anecdotes, lyrics) and the different idiomatic expressions (proverbial forms and wellerisms) will also be encoded.
Max ERC Funding
559 200 €
Duration
Start date: 2008-08-01, End date: 2012-07-31
Project acronym AGNES
Project ACTIVE AGEING – RESILIENCE AND EXTERNAL SUPPORT AS MODIFIERS OF THE DISABLEMENT OUTCOME
Researcher (PI) Taina Tuulikki RANTANEN
Host Institution (HI) JYVASKYLAN YLIOPISTO
Country Finland
Call Details Advanced Grant (AdG), SH3, ERC-2015-AdG
Summary The goals are 1. To develop a scale assessing the diversity of active ageing with four dimensions that are ability (what people can do), activity (what people do do), ambition (what are the valued activities that people want to do), and autonomy (how satisfied people are with the opportunity to do valued activities); 2. To examine health and physical and psychological functioning as the determinants and social and build environment, resilience and personal skills as modifiers of active ageing; 3. To develop a multicomponent sustainable intervention aiming to promote active ageing (methods: counselling, information technology, help from volunteers); 4. To test the feasibility and effectiveness on the intervention; and 5. To study cohort effects on the phenotypes on the pathway to active ageing.
“If You Can Measure It, You Can Change It.” Active ageing assessment needs conceptual progress, which I propose to do. A quantifiable scale will be developed that captures the diversity of active ageing stemming from the WHO definition of active ageing as the process of optimizing opportunities for health and participation in the society for all people in line with their needs, goals and capacities as they age. I will collect cross-sectional data (N=1000, ages 75, 80 and 85 years) and model the pathway to active ageing with state-of-the art statistical methods. By doing this I will create novel knowledge on preconditions for active ageing. The collected cohort data will be compared to a pre-existing cohort data that was collected 25 years ago to obtain knowledge about changes over time in functioning of older people. A randomized controlled trial (N=200) will be conducted to assess the effectiveness of the envisioned intervention promoting active ageing through participation. The project will regenerate ageing research by launching a novel scale, by training young scientists, by creating new concepts and theory development and by producing evidence for active ageing promotion
Summary
The goals are 1. To develop a scale assessing the diversity of active ageing with four dimensions that are ability (what people can do), activity (what people do do), ambition (what are the valued activities that people want to do), and autonomy (how satisfied people are with the opportunity to do valued activities); 2. To examine health and physical and psychological functioning as the determinants and social and build environment, resilience and personal skills as modifiers of active ageing; 3. To develop a multicomponent sustainable intervention aiming to promote active ageing (methods: counselling, information technology, help from volunteers); 4. To test the feasibility and effectiveness on the intervention; and 5. To study cohort effects on the phenotypes on the pathway to active ageing.
“If You Can Measure It, You Can Change It.” Active ageing assessment needs conceptual progress, which I propose to do. A quantifiable scale will be developed that captures the diversity of active ageing stemming from the WHO definition of active ageing as the process of optimizing opportunities for health and participation in the society for all people in line with their needs, goals and capacities as they age. I will collect cross-sectional data (N=1000, ages 75, 80 and 85 years) and model the pathway to active ageing with state-of-the art statistical methods. By doing this I will create novel knowledge on preconditions for active ageing. The collected cohort data will be compared to a pre-existing cohort data that was collected 25 years ago to obtain knowledge about changes over time in functioning of older people. A randomized controlled trial (N=200) will be conducted to assess the effectiveness of the envisioned intervention promoting active ageing through participation. The project will regenerate ageing research by launching a novel scale, by training young scientists, by creating new concepts and theory development and by producing evidence for active ageing promotion
Max ERC Funding
2 044 364 €
Duration
Start date: 2016-09-01, End date: 2021-08-31
Project acronym ALEM
Project ADDITIONAL LOSSES IN ELECTRICAL MACHINES
Researcher (PI) Matti Antero Arkkio
Host Institution (HI) AALTO KORKEAKOULUSAATIO SR
Country Finland
Call Details Advanced Grant (AdG), PE8, ERC-2013-ADG
Summary "Electrical motors consume about 40 % of the electrical energy produced in the European Union. About 90 % of this energy is converted to mechanical work. However, 0.5-2.5 % of it goes to so called additional load losses whose exact origins are unknown. Our ambitious aim is to reveal the origins of these losses, build up numerical tools for modeling them and optimize electrical motors to minimize the losses.
As the hypothesis of the research, we assume that the additional losses mainly result from the deterioration of the core materials during the manufacturing process of the machine. By calorimetric measurements, we have found that the core losses of electrical machines may be twice as large as comprehensive loss models predict. The electrical steel sheets are punched, welded together and shrink fit to the frame. This causes residual strains in the core sheets deteriorating their magnetic characteristics. The cutting burrs make galvanic contacts between the sheets and form paths for inter-lamination currents. Another potential source of additional losses are the circulating currents between the parallel strands of random-wound armature windings. The stochastic nature of these potential sources of additional losses puts more challenge on the research.
We shall develop a physical loss model that couples the mechanical strains and electromagnetic losses in electrical steel sheets and apply the new model for comprehensive loss analysis of electrical machines. The stochastic variables related to the core losses and circulating-current losses will be discretized together with the temporal and spatial discretization of the electromechanical field variables. The numerical stochastic loss model will be used to search for such machine constructions that are insensitive to the manufacturing defects. We shall validate the new numerical loss models by electromechanical and calorimetric measurements."
Summary
"Electrical motors consume about 40 % of the electrical energy produced in the European Union. About 90 % of this energy is converted to mechanical work. However, 0.5-2.5 % of it goes to so called additional load losses whose exact origins are unknown. Our ambitious aim is to reveal the origins of these losses, build up numerical tools for modeling them and optimize electrical motors to minimize the losses.
As the hypothesis of the research, we assume that the additional losses mainly result from the deterioration of the core materials during the manufacturing process of the machine. By calorimetric measurements, we have found that the core losses of electrical machines may be twice as large as comprehensive loss models predict. The electrical steel sheets are punched, welded together and shrink fit to the frame. This causes residual strains in the core sheets deteriorating their magnetic characteristics. The cutting burrs make galvanic contacts between the sheets and form paths for inter-lamination currents. Another potential source of additional losses are the circulating currents between the parallel strands of random-wound armature windings. The stochastic nature of these potential sources of additional losses puts more challenge on the research.
We shall develop a physical loss model that couples the mechanical strains and electromagnetic losses in electrical steel sheets and apply the new model for comprehensive loss analysis of electrical machines. The stochastic variables related to the core losses and circulating-current losses will be discretized together with the temporal and spatial discretization of the electromechanical field variables. The numerical stochastic loss model will be used to search for such machine constructions that are insensitive to the manufacturing defects. We shall validate the new numerical loss models by electromechanical and calorimetric measurements."
Max ERC Funding
2 489 949 €
Duration
Start date: 2014-03-01, End date: 2019-02-28
Project acronym AMETIST
Project Advanced III-V Materials and Processes Enabling Ultrahigh-efficiency ( 50%) Photovoltaics
Researcher (PI) Mircea Dorel GUINA
Host Institution (HI) TAMPEREEN KORKEAKOULUSAATIO SR
Country Finland
Call Details Advanced Grant (AdG), PE8, ERC-2015-AdG
Summary Compound semiconductor solar cells are providing the highest photovoltaic conversion efficiency, yet their performance lacks far behind the theoretical potential. This is a position we will challenge by engineering advanced III-V optoelectronics materials and heterostructures for better utilization of the solar spectrum, enabling efficiencies approaching practical limits. The work is strongly motivated by the global need for renewable energy sources. To this end, AMETIST framework is based on three vectors of excellence in: i) material science and epitaxial processes, ii) advanced solar cells exploiting nanophotonics concepts, and iii) new device fabrication technologies.
Novel heterostructures (e.g. GaInNAsSb, GaNAsBi), providing absorption in a broad spectral range from 0.7 eV to 1.4 eV, will be synthesized and monolithically integrated in tandem cells with up to 8-junctions. Nanophotonic methods for light-trapping, spectral and spatial control of solar radiation will be developed to further enhance the absorption. To ensure a high long-term impact, the project will validate the use of state-of-the-art molecular-beam-epitaxy processes for fabrication of economically viable ultra-high efficiency solar cells. The ultimate efficiency target is to reach a level of 55%. This would enable to generate renewable/ecological/sustainable energy at a levelized production cost below ~7 ¢/kWh, comparable or cheaper than fossil fuels. The work will also bring a new breath of developments for more efficient space photovoltaic systems.
AMETIST will leverage the leading position of the applicant in topical technology areas relevant for the project (i.e. epitaxy of III-N/Bi-V alloys and key achievements concerning GaInNAsSb-based tandem solar cells). Thus it renders a unique opportunity to capitalize on the group expertize and position Europe at the forefront in the global competition for demonstrating more efficient and economically viable photovoltaic technologies.
Summary
Compound semiconductor solar cells are providing the highest photovoltaic conversion efficiency, yet their performance lacks far behind the theoretical potential. This is a position we will challenge by engineering advanced III-V optoelectronics materials and heterostructures for better utilization of the solar spectrum, enabling efficiencies approaching practical limits. The work is strongly motivated by the global need for renewable energy sources. To this end, AMETIST framework is based on three vectors of excellence in: i) material science and epitaxial processes, ii) advanced solar cells exploiting nanophotonics concepts, and iii) new device fabrication technologies.
Novel heterostructures (e.g. GaInNAsSb, GaNAsBi), providing absorption in a broad spectral range from 0.7 eV to 1.4 eV, will be synthesized and monolithically integrated in tandem cells with up to 8-junctions. Nanophotonic methods for light-trapping, spectral and spatial control of solar radiation will be developed to further enhance the absorption. To ensure a high long-term impact, the project will validate the use of state-of-the-art molecular-beam-epitaxy processes for fabrication of economically viable ultra-high efficiency solar cells. The ultimate efficiency target is to reach a level of 55%. This would enable to generate renewable/ecological/sustainable energy at a levelized production cost below ~7 ¢/kWh, comparable or cheaper than fossil fuels. The work will also bring a new breath of developments for more efficient space photovoltaic systems.
AMETIST will leverage the leading position of the applicant in topical technology areas relevant for the project (i.e. epitaxy of III-N/Bi-V alloys and key achievements concerning GaInNAsSb-based tandem solar cells). Thus it renders a unique opportunity to capitalize on the group expertize and position Europe at the forefront in the global competition for demonstrating more efficient and economically viable photovoltaic technologies.
Max ERC Funding
2 492 719 €
Duration
Start date: 2017-01-01, End date: 2021-12-31
Project acronym ANALYTIC
Project ANALYTIC PROPERTIES OF INFINITE GROUPS:
limits, curvature, and randomness
Researcher (PI) Gulnara Arzhantseva
Host Institution (HI) UNIVERSITAT WIEN
Country Austria
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.
My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?
My motivation is two-fold:
- Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious.
- In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.
The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior.
Summary
The overall goal of this project is to develop new concepts and techniques in geometric and asymptotic group theory for a systematic study of the analytic properties of discrete groups. These are properties depending on the unitary representation theory of the group. The fundamental examples are amenability, discovered by von Neumann in 1929, and property (T), introduced by Kazhdan in 1967.
My main objective is to establish the precise relations between groups recently appeared in K-theory and topology such as C*-exact groups and groups coarsely embeddable into a Hilbert space, versus those discovered in ergodic theory and operator algebra, for example, sofic and hyperlinear groups. This is a first ever attempt to confront the analytic behavior of so different nature. I plan to work on crucial open questions: Is every coarsely embeddable group C*-exact? Is every group sofic? Is every hyperlinear group sofic?
My motivation is two-fold:
- Many outstanding conjectures were recently solved for these groups, e.g. the Novikov conjecture (1965) for coarsely embeddable groups by Yu in 2000 and the Gottschalk surjunctivity conjecture (1973) for sofic groups by Gromov in 1999. However, their group-theoretical structure remains mysterious.
- In recent years, geometric group theory has undergone significant changes, mainly due to the growing impact of this theory on other branches of mathematics. However, the interplay between geometric, asymptotic, and analytic group properties has not yet been fully understood.
The main innovative contribution of this proposal lies in the interaction between 3 axes: (i) limits of groups, in the space of marked groups or metric ultralimits; (ii) analytic properties of groups with curvature, of lacunary or relatively hyperbolic groups; (iii) random groups, in a topological or statistical meaning. As a result, I will describe the above apparently unrelated classes of groups in a unified way and will detail their algebraic behavior.
Max ERC Funding
1 065 500 €
Duration
Start date: 2011-04-01, End date: 2016-03-31
Project acronym ANGULON
Project Angulon: physics and applications of a new quasiparticle
Researcher (PI) Mikhail Lemeshko
Host Institution (HI) INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2018-STG
Summary This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Summary
This project aims to develop a universal approach to angular momentum in quantum many-body systems based on the angulon quasiparticle recently discovered by the PI. We will establish a general theory of angulons in and out of equilibrium, and apply it to a variety of experimentally studied problems, ranging from chemical dynamics in solvents to solid-state systems (e.g. angular momentum transfer in the Einstein-de Haas effect and ultrafast magnetism).
The concept of angular momentum is ubiquitous across physics, whether one deals with nuclear collisions, chemical reactions, or formation of galaxies. In the microscopic world, quantum rotations are described by non-commuting operators. This makes the angular momentum theory extremely involved, even for systems consisting of only a few interacting particles, such as gas-phase atoms or molecules.
Furthermore, in most experiments the behavior of quantum particles is inevitably altered by a many-body environment of some kind. For example, molecular rotation – and therefore reactivity – depends on the presence of a solvent, electronic angular momentum in solids is coupled to lattice phonons, highly excited atomic levels can be perturbed by a surrounding ultracold gas. If approached in a brute-force fashion, understanding angular momentum in such systems is an impossible task, since a macroscopic number of particles is involved.
Recently, the PI and his team have shown that this challenge can be met by introducing a new quasiparticle – the angulon. In 2017, the PI has demonstrated the existence of angulons by comparing his theory with 20 years of measurements on molecules rotating in superfluids. Most importantly, the angulon concept allows one to gain analytical insights inaccessible to the state-of-the-art techniques of condensed matter and chemical physics. The angulon approach holds the promise of opening up a new interdisciplinary research area with applications reaching far beyond what is proposed here.
Max ERC Funding
1 499 588 €
Duration
Start date: 2019-02-01, End date: 2024-01-31
Project acronym ANPROB
Project Analytic-probabilistic methods for borderline singular integrals
Researcher (PI) Tuomas Pentinpoika Hytoenen
Host Institution (HI) HELSINGIN YLIOPISTO
Country Finland
Call Details Starting Grant (StG), PE1, ERC-2011-StG_20101014
Summary The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg.
The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals.
Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area.
Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.
Summary
The proposal consists of an extensive research program to advance the understanding of singular integral operators of Harmonic Analysis in various situations on the borderline of the existing theory. This is to be achieved by a creative combination of techniques from Analysis and Probability. On top of the standard arsenal of modern Harmonic Analysis, the main probabilistic tools are the martingale transform inequalities of Burkholder, and random geometric constructions in the spirit of the random dyadic cubes introduced to Nonhomogeneous Analysis by Nazarov, Treil and Volberg.
The problems to be addressed fall under the following subtitles, with many interconnections and overlap: (i) sharp weighted inequalities; (ii) nonhomogeneous singular integrals on metric spaces; (iii) local Tb theorems with borderline assumptions; (iv) functional calculus of rough differential operators; and (v) vector-valued singular integrals.
Topic (i) is a part of Classical Analysis, where new methods have led to substantial recent progress, culminating in my solution in July 2010 of a celebrated problem on the linear dependence of the weighted operator norm on the Muckenhoupt norm of the weight. The proof should be extendible to several related questions, and the aim is to also address some outstanding open problems in the area.
Topics (ii) and (v) deal with extensions of the theory of singular integrals to functions with more general domain and range spaces, allowing them to be abstract metric and Banach spaces, respectively. In case (ii), I have recently been able to relax the requirements on the space compared to the established theories, opening a new research direction here. Topics (iii) and (iv) are concerned with weakening the assumptions on singular integrals in the usual Euclidean space, to allow certain applications in the theory of Partial Differential Equations. The goal is to maintain a close contact and exchange of ideas between such abstract and concrete questions.
Max ERC Funding
1 100 000 €
Duration
Start date: 2011-11-01, End date: 2016-10-31
Project acronym ANTEGEFI
Project Analytic Techniques for Geometric and Functional Inequalities
Researcher (PI) Nicola Fusco
Host Institution (HI) UNIVERSITA DEGLI STUDI DI NAPOLI FEDERICO II
Country Italy
Call Details Advanced Grant (AdG), PE1, ERC-2008-AdG
Summary Isoperimetric and Sobolev inequalities are the best known examples of geometric-functional inequalities. In recent years the PI and collaborators have obtained new and sharp quantitative versions of these and other important related inequalities. These results have been obtained by the combined use of classical symmetrization methods, new tools coming from mass transportation theory, deep geometric measure tools and ad hoc symmetrizations. The objective of this project is to further develop thes techniques in order to get: sharp quantitative versions of Faber-Krahn inequality, Gaussian isoperimetric inequality, Brunn-Minkowski inequality, Poincaré and Sobolev logarithm inequalities; sharp decay rates for the quantitative Sobolev inequalities and Polya-Szegö inequality.
Summary
Isoperimetric and Sobolev inequalities are the best known examples of geometric-functional inequalities. In recent years the PI and collaborators have obtained new and sharp quantitative versions of these and other important related inequalities. These results have been obtained by the combined use of classical symmetrization methods, new tools coming from mass transportation theory, deep geometric measure tools and ad hoc symmetrizations. The objective of this project is to further develop thes techniques in order to get: sharp quantitative versions of Faber-Krahn inequality, Gaussian isoperimetric inequality, Brunn-Minkowski inequality, Poincaré and Sobolev logarithm inequalities; sharp decay rates for the quantitative Sobolev inequalities and Polya-Szegö inequality.
Max ERC Funding
600 000 €
Duration
Start date: 2009-01-01, End date: 2013-12-31