Project acronym 3D-QUEST
Project 3D-Quantum Integrated Optical Simulation
Researcher (PI) Fabio Sciarrino
Host Institution (HI) UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA
Country Italy
Call Details Starting Grant (StG), PE2, ERC-2012-StG_20111012
Summary "Quantum information was born from the merging of classical information and quantum physics. Its main objective consists of understanding the quantum nature of information and learning how to process it by using physical systems which operate by following quantum mechanics laws. Quantum simulation is a fundamental instrument to investigate phenomena of quantum systems dynamics, such as quantum transport, particle localizations and energy transfer, quantum-to-classical transition, and even quantum improved computation, all tasks that are hard to simulate with classical approaches. Within this framework integrated photonic circuits have a strong potential to realize quantum information processing by optical systems.
The aim of 3D-QUEST is to develop and implement quantum simulation by exploiting 3-dimensional integrated photonic circuits. 3D-QUEST is structured to demonstrate the potential of linear optics to implement a computational power beyond the one of a classical computer. Such ""hard-to-simulate"" scenario is disclosed when multiphoton-multimode platforms are realized. The 3D-QUEST research program will focus on three tasks of growing difficulty.
A-1. To simulate bosonic-fermionic dynamics with integrated optical systems acting on 2 photon entangled states.
A-2. To pave the way towards hard-to-simulate, scalable quantum linear optical circuits by investigating m-port interferometers acting on n-photon states with n>2.
A-3. To exploit 3-dimensional integrated structures for the observation of new quantum optical phenomena and for the quantum simulation of more complex scenarios.
3D-QUEST will exploit the potential of the femtosecond laser writing integrated waveguides. This technique will be adopted to realize 3-dimensional capabilities and high flexibility, bringing in this way the optical quantum simulation in to new regime."
Summary
"Quantum information was born from the merging of classical information and quantum physics. Its main objective consists of understanding the quantum nature of information and learning how to process it by using physical systems which operate by following quantum mechanics laws. Quantum simulation is a fundamental instrument to investigate phenomena of quantum systems dynamics, such as quantum transport, particle localizations and energy transfer, quantum-to-classical transition, and even quantum improved computation, all tasks that are hard to simulate with classical approaches. Within this framework integrated photonic circuits have a strong potential to realize quantum information processing by optical systems.
The aim of 3D-QUEST is to develop and implement quantum simulation by exploiting 3-dimensional integrated photonic circuits. 3D-QUEST is structured to demonstrate the potential of linear optics to implement a computational power beyond the one of a classical computer. Such ""hard-to-simulate"" scenario is disclosed when multiphoton-multimode platforms are realized. The 3D-QUEST research program will focus on three tasks of growing difficulty.
A-1. To simulate bosonic-fermionic dynamics with integrated optical systems acting on 2 photon entangled states.
A-2. To pave the way towards hard-to-simulate, scalable quantum linear optical circuits by investigating m-port interferometers acting on n-photon states with n>2.
A-3. To exploit 3-dimensional integrated structures for the observation of new quantum optical phenomena and for the quantum simulation of more complex scenarios.
3D-QUEST will exploit the potential of the femtosecond laser writing integrated waveguides. This technique will be adopted to realize 3-dimensional capabilities and high flexibility, bringing in this way the optical quantum simulation in to new regime."
Max ERC Funding
1 474 800 €
Duration
Start date: 2012-08-01, End date: 2017-07-31
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 AGEnTh
Project Atomic Gauge and Entanglement Theories
Researcher (PI) Marcello DALMONTE
Host Institution (HI) SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE
Country Italy
Call Details Starting Grant (StG), PE2, ERC-2017-STG
Summary AGEnTh is an interdisciplinary proposal which aims at theoretically investigating atomic many-body systems (cold atoms and trapped ions) in close connection to concepts from quantum information, condensed matter, and high energy physics. The main goals of this programme are to:
I) Find to scalable schemes for the measurements of entanglement properties, and in particular entanglement spectra, by proposing a shifting paradigm to access entanglement focused on entanglement Hamiltonians and field theories instead of probing density matrices;
II) Show how atomic gauge theories (including dynamical gauge fields) are ideal candidates for the realization of long-sought, highly-entangled states of matter, in particular topological superconductors supporting parafermion edge modes, and novel classes of quantum spin liquids emerging from clustering;
III) Develop new implementation strategies for the realization of gauge symmetries of paramount importance, such as discrete and SU(N)xSU(2)xU(1) groups, and establish a theoretical framework for the understanding of atomic physics experiments within the light-from-chaos scenario pioneered in particle physics.
These objectives are at the cutting-edge of fundamental science, and represent a coherent effort aimed at underpinning unprecedented regimes of strongly interacting quantum matter by addressing the basic aspects of probing, many-body physics, and implementations. The results are expected to (i) build up and establish qualitatively new synergies between the aforementioned communities, and (ii) stimulate an intense theoretical and experimental activity focused on both entanglement and atomic gauge theories.
In order to achieve those, AGEnTh builds: (1) on my background working at the interface between atomic physics and quantum optics from one side, and many-body theory on the other, and (2) on exploratory studies which I carried out to mitigate the conceptual risks associated with its high-risk/high-gain goals.
Summary
AGEnTh is an interdisciplinary proposal which aims at theoretically investigating atomic many-body systems (cold atoms and trapped ions) in close connection to concepts from quantum information, condensed matter, and high energy physics. The main goals of this programme are to:
I) Find to scalable schemes for the measurements of entanglement properties, and in particular entanglement spectra, by proposing a shifting paradigm to access entanglement focused on entanglement Hamiltonians and field theories instead of probing density matrices;
II) Show how atomic gauge theories (including dynamical gauge fields) are ideal candidates for the realization of long-sought, highly-entangled states of matter, in particular topological superconductors supporting parafermion edge modes, and novel classes of quantum spin liquids emerging from clustering;
III) Develop new implementation strategies for the realization of gauge symmetries of paramount importance, such as discrete and SU(N)xSU(2)xU(1) groups, and establish a theoretical framework for the understanding of atomic physics experiments within the light-from-chaos scenario pioneered in particle physics.
These objectives are at the cutting-edge of fundamental science, and represent a coherent effort aimed at underpinning unprecedented regimes of strongly interacting quantum matter by addressing the basic aspects of probing, many-body physics, and implementations. The results are expected to (i) build up and establish qualitatively new synergies between the aforementioned communities, and (ii) stimulate an intense theoretical and experimental activity focused on both entanglement and atomic gauge theories.
In order to achieve those, AGEnTh builds: (1) on my background working at the interface between atomic physics and quantum optics from one side, and many-body theory on the other, and (2) on exploratory studies which I carried out to mitigate the conceptual risks associated with its high-risk/high-gain goals.
Max ERC Funding
1 055 317 €
Duration
Start date: 2018-05-01, End date: 2023-04-30
Project acronym AISENS
Project New generation of high sensitive atom interferometers
Researcher (PI) Marco Fattori
Host Institution (HI) CONSIGLIO NAZIONALE DELLE RICERCHE
Country Italy
Call Details Starting Grant (StG), PE2, ERC-2010-StG_20091028
Summary Interferometers are fundamental tools for the study of nature laws and for the precise measurement and control of the physical world. In the last century, the scientific and technological progress has proceeded in parallel with a constant improvement of interferometric performances. For this reason, the challenge of conceiving and realizing new generations of interferometers with broader ranges of operation and with higher sensitivities is always open and actual.
Despite the introduction of laser devices has deeply improved the way of developing and performing interferometric measurements with light, the atomic matter wave analogous, i.e. the Bose-Einstein condensate (BEC), has not yet triggered any revolution in precision interferometry. However, thanks to recent improvements on the control of the quantum properties of ultra-cold atomic gases, and new original ideas on the creation and manipulation of quantum entangled particles, the field of atom interferometry is now mature to experience a big step forward.
The system I want to realize is a Mach-Zehnder spatial interferometer operating with trapped BECs. Undesired decoherence sources will be suppressed by implementing BECs with tunable interactions in ultra-stable optical potentials. Entangled states will be used to improve the sensitivity of the sensor beyond the standard quantum limit to ideally reach the ultimate, Heisenberg, limit set by quantum mechanics. The resulting apparatus will show unprecedented spatial resolution and will overcome state-of-the-art interferometers with cold (non condensed) atomic gases.
A successful completion of this project will lead to a new generation of interferometers for the immediate application to local inertial measurements with unprecedented resolution. In addition, we expect to develop experimental capabilities which might find application well beyond quantum interferometry and crucially contribute to the broader emerging field of quantum-enhanced technologies.
Summary
Interferometers are fundamental tools for the study of nature laws and for the precise measurement and control of the physical world. In the last century, the scientific and technological progress has proceeded in parallel with a constant improvement of interferometric performances. For this reason, the challenge of conceiving and realizing new generations of interferometers with broader ranges of operation and with higher sensitivities is always open and actual.
Despite the introduction of laser devices has deeply improved the way of developing and performing interferometric measurements with light, the atomic matter wave analogous, i.e. the Bose-Einstein condensate (BEC), has not yet triggered any revolution in precision interferometry. However, thanks to recent improvements on the control of the quantum properties of ultra-cold atomic gases, and new original ideas on the creation and manipulation of quantum entangled particles, the field of atom interferometry is now mature to experience a big step forward.
The system I want to realize is a Mach-Zehnder spatial interferometer operating with trapped BECs. Undesired decoherence sources will be suppressed by implementing BECs with tunable interactions in ultra-stable optical potentials. Entangled states will be used to improve the sensitivity of the sensor beyond the standard quantum limit to ideally reach the ultimate, Heisenberg, limit set by quantum mechanics. The resulting apparatus will show unprecedented spatial resolution and will overcome state-of-the-art interferometers with cold (non condensed) atomic gases.
A successful completion of this project will lead to a new generation of interferometers for the immediate application to local inertial measurements with unprecedented resolution. In addition, we expect to develop experimental capabilities which might find application well beyond quantum interferometry and crucially contribute to the broader emerging field of quantum-enhanced technologies.
Max ERC Funding
1 068 000 €
Duration
Start date: 2011-01-01, End date: 2015-12-31
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 ANTIGONE
Project Archaeology of shariNg pracTIces: the material evidence of mountain marGinalisatiON in Europe (18th- 21st c. AD)
Researcher (PI) Anna Maria STAGNO
Host Institution (HI) UNIVERSITA DEGLI STUDI DI GENOVA
Country Italy
Call Details Starting Grant (StG), SH6, ERC-2019-STG
Summary The main aim of the ANTIGONE project is to investigate how the disappearance of practices for managing shared environmental resources played a role in the abandonment and political marginalisation of European mountain areas from the 18th c onwards. The legacy of these processes can be seen in population levels in these areas, and in the worsening of their natural and cultural heritage. Current policies – aiming to promote their ‘heritagisation’ – do not seem likely to be more effective, in the long-term, as development interventions than the drive for rationalisation in the 19th c. and modernisation in the 20th c. A new historical perspective is needed which addresses the process of abandonment and marginalisation in its entire complexity. ANTIGONE will analyse the critical period from the 18th to the 21st c. and provide new insights into the links between individuals, communities, central States and landscape, grounded in a new understanding of the relationship between practices, resources and objects.
By means of archaeological, historical, environmental, ethnological analyses, and through the comparison of case studies from European mountain areas, ANTIGONE aims to verify if alleged ‘improvement’ practices involved not just changes in management technique, but also contributed to decline in the sharing of work, time and space, with knock-on effects on the social dimension of the whole historic system.
Through its multidisciplinary approach ANTIGONE aims at provide: new knowledge on the historical mechanisms underlying the abandonment of mountain and, more broadly, rural areas, as a key to understanding marginalisation; new knowledge on landscapes, practices and their features; a new methodological toolbox for interdisciplinary investigations driven by archaeology; a new role for archaeology, beyond the acknowledged one as a heritage science; new contributions to community based policies for local sustainable development and landscape management.
Summary
The main aim of the ANTIGONE project is to investigate how the disappearance of practices for managing shared environmental resources played a role in the abandonment and political marginalisation of European mountain areas from the 18th c onwards. The legacy of these processes can be seen in population levels in these areas, and in the worsening of their natural and cultural heritage. Current policies – aiming to promote their ‘heritagisation’ – do not seem likely to be more effective, in the long-term, as development interventions than the drive for rationalisation in the 19th c. and modernisation in the 20th c. A new historical perspective is needed which addresses the process of abandonment and marginalisation in its entire complexity. ANTIGONE will analyse the critical period from the 18th to the 21st c. and provide new insights into the links between individuals, communities, central States and landscape, grounded in a new understanding of the relationship between practices, resources and objects.
By means of archaeological, historical, environmental, ethnological analyses, and through the comparison of case studies from European mountain areas, ANTIGONE aims to verify if alleged ‘improvement’ practices involved not just changes in management technique, but also contributed to decline in the sharing of work, time and space, with knock-on effects on the social dimension of the whole historic system.
Through its multidisciplinary approach ANTIGONE aims at provide: new knowledge on the historical mechanisms underlying the abandonment of mountain and, more broadly, rural areas, as a key to understanding marginalisation; new knowledge on landscapes, practices and their features; a new methodological toolbox for interdisciplinary investigations driven by archaeology; a new role for archaeology, beyond the acknowledged one as a heritage science; new contributions to community based policies for local sustainable development and landscape management.
Max ERC Funding
1 498 000 €
Duration
Start date: 2020-11-01, End date: 2025-10-31
Project acronym AQSuS
Project Analog Quantum Simulation using Superconducting Qubits
Researcher (PI) Gerhard KIRCHMAIR
Host Institution (HI) UNIVERSITAET INNSBRUCK
Country Austria
Call Details Starting Grant (StG), PE3, ERC-2016-STG
Summary AQSuS aims at experimentally implementing analogue quantum simulation of interacting spin models in two-dimensional geometries. The proposed experimental approach paves the way to investigate a broad range of currently inaccessible quantum phenomena, for which existing analytical and numerical methods reach their limitations. Developing precisely controlled interacting quantum systems in 2D is an important current goal well beyond the field of quantum simulation and has applications in e.g. solid state physics, computing and metrology.
To access these models, I propose to develop a novel circuit quantum-electrodynamics (cQED) platform based on the 3D transmon qubit architecture. This platform utilizes the highly engineerable properties and long coherence times of these qubits. A central novel idea behind AQSuS is to exploit the spatial dependence of the naturally occurring dipolar interactions between the qubits to engineer the desired spin-spin interactions. This approach avoids the complicated wiring, typical for other cQED experiments and reduces the complexity of the experimental setup. The scheme is therefore directly scalable to larger systems. The experimental goals are:
1) Demonstrate analogue quantum simulation of an interacting spin system in 1D & 2D.
2) Establish methods to precisely initialize the state of the system, control the interactions and readout single qubit states and multi-qubit correlations.
3) Investigate unobserved quantum phenomena on 2D geometries e.g. kagome and triangular lattices.
4) Study open system dynamics with interacting spin systems.
AQSuS builds on my backgrounds in both superconducting qubits and quantum simulation with trapped-ions. With theory collaborators my young research group and I have recently published an article in PRB [9] describing and analysing the proposed platform. The ERC starting grant would allow me to open a big new research direction and capitalize on the foundations established over the last two years.
Summary
AQSuS aims at experimentally implementing analogue quantum simulation of interacting spin models in two-dimensional geometries. The proposed experimental approach paves the way to investigate a broad range of currently inaccessible quantum phenomena, for which existing analytical and numerical methods reach their limitations. Developing precisely controlled interacting quantum systems in 2D is an important current goal well beyond the field of quantum simulation and has applications in e.g. solid state physics, computing and metrology.
To access these models, I propose to develop a novel circuit quantum-electrodynamics (cQED) platform based on the 3D transmon qubit architecture. This platform utilizes the highly engineerable properties and long coherence times of these qubits. A central novel idea behind AQSuS is to exploit the spatial dependence of the naturally occurring dipolar interactions between the qubits to engineer the desired spin-spin interactions. This approach avoids the complicated wiring, typical for other cQED experiments and reduces the complexity of the experimental setup. The scheme is therefore directly scalable to larger systems. The experimental goals are:
1) Demonstrate analogue quantum simulation of an interacting spin system in 1D & 2D.
2) Establish methods to precisely initialize the state of the system, control the interactions and readout single qubit states and multi-qubit correlations.
3) Investigate unobserved quantum phenomena on 2D geometries e.g. kagome and triangular lattices.
4) Study open system dynamics with interacting spin systems.
AQSuS builds on my backgrounds in both superconducting qubits and quantum simulation with trapped-ions. With theory collaborators my young research group and I have recently published an article in PRB [9] describing and analysing the proposed platform. The ERC starting grant would allow me to open a big new research direction and capitalize on the foundations established over the last two years.
Max ERC Funding
1 498 515 €
Duration
Start date: 2017-04-01, End date: 2022-03-31