Description |
The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy will organize a School on Non-linear Dynamics, Dynamical Transitions and Instabilities in Classical and Quantum Systems, to be held at ICTP, Trieste, Italy, from 14 July to 1 August 2014. The School aims at covering a selection of modern topics at the interface between Condensed Matter Physicsand Statistical Mechanics, classical and quantum, with an emphasis on aspects of non-equilibrium physics: • Steady States, Patterns and Scaling in Driven Systems • Growth Processes • Classical and Quantum Turbulence • Nonlinear Quantum Dynamics • Quantum Gases out of Equilibrium • Numerical Methods out of Equilibrium • Entropy Generation and Transport far from Equilibrium |
School on Non-linear Dynamics, Dynamical Transitions and Instabilities in Classical and Quantum Systems | (smr 2594)
Go to day
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08:45 - 20:00
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08:45
OPENING REMARKS
15' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: Profs. Calabrese, Lamacraft, Le Doussal, Müller and Silva -
09:00
Quantum Quenches and Integrability - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: F. ESSLER (Oxford, Rudolf Peierls Centre for Theoretical Physics, U.K.) Material: Video - 10:30 Coffee/tea break and REGISTRATION formalities (Leonardo Building entrance, outside Main lecture Hall) 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Anomalous Hydrodynamics of Classical and Quantum Liquids - PART I: Anomalous Hydrodynamics of Electronic Systems in One Spatial Dimensions
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: P. WIEGMANN (CIS Center for Integrative Science, Univ. Chicago, USA) Material: Video - 12:30 Lunch Break and REGISTRATION formalities (Leonardo Building entrance, outside Main lecture Hall) 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Conservation Laws after a Global Quench
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: M. FAGOTTI (Oxford, Rudolf Peierls Centre for Theoretical Physics, U.K.) Material: Video -
14:45
Non-thermal Fixed Points in Bose Systems: Universality, Topology and Turbulence
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: T. GASENZER (Univ. Heidelberg, Inst. Theoretische Physik, Germany) Material: Video slides - 15:30 Coffee/tea break and REGISTRATION formalities (Leonardo Building entrance, outside Main lecture Hall) 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Informal Discussion
45' (
Leonardo da Vinci Building Main Lecture Hall
)
- 18:00 Welcome Reception 2h0' ( Leonardo da Vinci Building Cafeteria )
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08:45
OPENING REMARKS
15' (
Leonardo da Vinci Building Main Lecture Hall
)
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08:45 - 20:00
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09:00 - 16:45
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09:00
Anomalous Hydrodynamics of Classical and Quantum Liquids - PART II: Anomalous Hydrodynamics of Vortex Flow in Two Spatial Dimensions
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: P. WIEGMANN (CIS Center for Integrative Science, Univ. Chicago, USA) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Classical Transport, Steady States and Phase Transitions in Non Equilibrium 1 D Systems - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: B. DERRIDA (ENS-LPS, Paris, France) - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Fluctuations for 1D KPZ equation and Related Models
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: T. SASAMOTO (Tokyo Institute of Technology, Physics, Japan) Material: Video -
14:45
Electronic Strongly-localized Systems and Directed Polymers
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. SOMOZA (Univ. de Murcia, Physics, Spain) - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Exclusion Processes and Quantum Phase Transitions in XXZ Spin Chains
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: V. LECOMTE (LPMA, Universite' Paris VI-VII, France) Material: Video
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09:00
Anomalous Hydrodynamics of Classical and Quantum Liquids - PART II: Anomalous Hydrodynamics of Vortex Flow in Two Spatial Dimensions
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 16:45
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09:00 - 16:45
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09:00
Interference Experiments and Their Use in Non-equilibrium Dynamics - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. SCHMIEDMAYER (Atominstitut, Vienna Univ. of Technology, Austria) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Quantum Quenches and Integrability - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: F. ESSLER (Oxford, Rudolf Peierls Centre for Theoretical Physics, U.K.) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Classical Transport, Steady States and Phase Transitions in Non Equilibrium 1 D Systems - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: B. DERRIDA (ENS-LPS, Paris, France) - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Dynamics of Quantum Impurities
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: E. DEMLER (Univ. Harvard, Physics, Cambridge, U.S.A.)
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09:00
Interference Experiments and Their Use in Non-equilibrium Dynamics - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 16:45
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09:00 - 16:45
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09:00
Quantum Quenches and Integrability - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: F. ESSLER (Oxford, Rudolf Peierls Centre for Theoretical Physics, U.K.) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Interference Experiments and Their Use in Non-equilibrium Dynamics - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. SCHMIEDMAYER (Atominstitut, Vienna Univ. of Technology, Austria) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
POSTER SESSION and GET TOGETHER DRINK
2h0' (
Leonardo da Vinci Building Main Lecture Hall
)
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16:00
Discussion
45' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00
Quantum Quenches and Integrability - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 16:45
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09:00 - 21:30
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09:00
Anomalous Hydrodynamics of Classical and Quantum Liquids - PART III: Anomalous Hydrodynamics of Fractional Quantum Hall Liquid
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: P. WIEGMANN (CIS Center for Integrative Science, Univ. Chicago, USA) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Classical Transport, Steady States and Phase Transitions in Non Equilibrium 1 D Systems - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: B. DERRIDA (ENS-LPS, Paris, France) - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
-
14:00
Interference Experiments and Their Use in Non-equilibrium Dynamics - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. SCHMIEDMAYER (Atominstitut, Vienna Univ. of Technology, Austria) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
- 19:00 The African Night at ICTP 3rd Edition - with live music and dance performances at the Leonardo Building Terrace 2h30' ( Leonardo da Vinci Building Main Lecture Hall )
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09:00
Anomalous Hydrodynamics of Classical and Quantum Liquids - PART III: Anomalous Hydrodynamics of Fractional Quantum Hall Liquid
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 21:30
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09:00 - 16:00
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09:00
Superradiant Phase Transitions: The Dicke Model and Cold Atoms - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. KEELING (Univ. St Andrews, School of Physics & Astronomy, U.K.) Material: Video slides - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Nonlinear Fluctuating Hydrodynamics and Anharmonic Chains - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: H. SPOHN (TUM, Mathematik M5, Garching, Germany) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Controlling Quantum Flux Through Measurement
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: D. BERNARD (CNRS & ENS-LPT Paris, France) Material: Video -
14:45
Non-equilibrium Steady States in Higher-Dimensional Critical Systems
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: B. DOYON (King's College London, Mathematics, London, U.K.) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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09:00
Superradiant Phase Transitions: The Dicke Model and Cold Atoms - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 16:00
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09:00 - 17:30
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09:00
Nonlinear Fluctuating Hydrodynamics and Anharmonic Chains - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: H. SPOHN (TUM, Mathematik M5, Garching, Germany) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Superradiant Phase Transitions: The Dicke Model and Cold Atoms - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. KEELING (Univ. St Andrews, School of Physics & Astronomy, U.K.) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Introduction to DMRG/MPS Methods in 1D and Applications to Non-equilibrium Situations - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: C. KOLLATH (Helmholtz Inst. fuer Strahlen und Kernphysik, Bonn, Germany) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Feedback and Information Processing in Stochastic Thermodynamics
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: U. SEIFERT (Univ. Stuttgart, Inst. Theoretische Physik II, Germany) Material: Video -
16:45
Phase Transitions and Edge Scaling of Number Variance in Gaussian Random Matrices
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: S. MAJUMDAR (LPTMS, Univ. XI Paris Sud, Orsay, France) Material: Video
-
09:00
Nonlinear Fluctuating Hydrodynamics and Anharmonic Chains - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 17:30
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-
09:00 - 17:30
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09:00
Nonlinear Fluctuating Hydrodynamics and Anharmonic Chains - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: H. SPOHN (TUM, Mathematik M5, Garching, Germany) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Introduction to DMRG/MPS Methods in 1D and Applications to Non-equilibrium Situations - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: C. KOLLATH (Helmholtz Inst. fuer Strahlen und Kernphysik, Bonn, Germany) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Non-equilibrium Many-body Physics in Photonic Systems
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: I. CARUSOTTO (INO CNR BEC Center & Univ. Trento, Italy) Material: Video -
14:45
Nonlinear Quantum Transport, Quantum Impurities, Circuit Quantum Elecrodynamics
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: K. LE HUR (Ecole Polytechnique, Centre de Physique Theorique, Palaiseau, France) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Quantum Integrability and the Kardar-Parisi-Zhang Universality Class - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: I. CORWIN (MIT, Dept. of Mathematics, Cambridge, MA, U.S.A.) Material: CORWIN abstract.pdf Video
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09:00
Nonlinear Fluctuating Hydrodynamics and Anharmonic Chains - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 17:30
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-
09:00 - 16:00
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09:00
Introduction to DMRG/MPS Methods in 1D and Applications to Non-equilibrium Situations - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: C. KOLLATH (Helmholtz Inst. fuer Strahlen und Kernphysik, Bonn, Germany) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
-
11:00
Quantum Integrability and the Kardar-Parisi-Zhang Universality Class - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: I. CORWIN (MIT, Dept. of Mathematics, Cambridge, MA, U.S.A.) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Superradiant Phase Transitions: The Dicke Model and Cold Atoms - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. KEELING (Univ. St Andrews, School of Physics & Astronomy, U.K.) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
-
09:00
Introduction to DMRG/MPS Methods in 1D and Applications to Non-equilibrium Situations - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 16:00
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09:00 - 16:00
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09:00
Quantum Integrability and the Kardar-Parisi-Zhang Universality Class - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: I. CORWIN (MIT, Dept. of Mathematics, Cambridge, MA, U.S.A.) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Non-equilbrium Phenomena in Luttinger Liquids
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. MIRLIN (Karlsruhe Institute of Technology, Germany) Material: Video -
11:45
Emergent Newtonian Dynamics and Dynamical Localization Near Quantum Critical Points
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. POLKOVNIKOV (Boston University, Physics, U.S.A.) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Discussion
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
- 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
-
09:00
Quantum Integrability and the Kardar-Parisi-Zhang Universality Class - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 16:00
-
-
09:00 - 16:00
-
09:00
Instabilities and Nonthermal Fixed Points: From Cosmology to Cold Atoms - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. BERGES (Univ. Heidelberg, Inst. Theoretische Physik, Germany) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Turbulence - PART I: Symmetries and Operator Product Expansion
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: G. FALKOVICH (The Weizmann Institute of Science, Rehovot, Israel) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Integrability of Non-equilibrium Steady State Density-operators and Quantum Transport in One-dimension
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: T. PROSEN (Univ. Ljubljana, Physics, Slovenia) Material: Video -
14:45
Instabilities and Active Turbulence in Bacterial Suspensions
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: I. ARONSON (Argonne Nat. Laboratory, Materials Science, U.S.A.) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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09:00
Instabilities and Nonthermal Fixed Points: From Cosmology to Cold Atoms - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
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09:00 - 16:00
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-
09:00 - 16:45
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09:00
Dynamical and Out of Equilibrium Phase Transitions - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: G. BIROLI (CEA Saclay, Physique Theorique, Gif sur Yvette, France) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Turbulence - PART II: Flight-crash Events and Irreversibility
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: G. FALKOVICH (The Weizmann Institute of Science, Rehovot, Israel) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Keldysh Technique (out of equilibrium): BEC, Superconductivity - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. KAMENEV (School of Physics & Astronomy, Univ. Minnesota, Minneapolis, U.S.A.) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
-
16:00
Discussion
45' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00
Dynamical and Out of Equilibrium Phase Transitions - PART I
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 16:45
-
-
09:00 - 16:30
-
09:00
Keldysh Technique (out of equilibrium): BEC, Superconductivity - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. KAMENEV (School of Physics & Astronomy, Univ. Minnesota, Minneapolis, U.S.A.) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
-
11:00
Dynamical and Out of Equilibrium Phase Transitions - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: G. BIROLI (CEA Saclay, Physique Theorique, Gif sur Yvette, France) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Instabilities and Nonthermal Fixed Points: From Cosmology to Cold Atoms - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. BERGES (Univ. Heidelberg, Inst. Theoretische Physik, Germany) Material: Video -
15:30
POSTER SESSION and GET TOGETHER DRINK
1h0' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00
Keldysh Technique (out of equilibrium): BEC, Superconductivity - PART II
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 16:30
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09:00 - 17:30
-
09:00
Instabilities and Nonthermal Fixed Points: From Cosmology to Cold Atoms - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: J. BERGES (Univ. Heidelberg, Inst. Theoretische Physik, Germany) Material: Video - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Superconductivity - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. KAMENEV (School of Physics & Astronomy, Univ. Minnesota, Minneapolis, U.S.A.) Material: Video - 12:30 Lunch Break 1h30' ( Leonardo da Vinci Building Main Lecture Hall )
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14:00
Dynamical and Out of Equilibrium Phase Transitions - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: G. BIROLI (CEA Saclay, Physique Theorique, Gif sur Yvette, France) Material: Video - 15:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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16:00
Prethermalization in a Nonintegrable Quantum Spin Chain
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. GAMBASSI (SISSA, Trieste, Italy) Material: Video -
16:45
Hydrodynamics of Light-Matter Quantum Fluids
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: A. BRAMATI (ENS-CNRS Physique, Paris, France) Material: Video
-
09:00
Instabilities and Nonthermal Fixed Points: From Cosmology to Cold Atoms - PART III
1h30' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 17:30
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-
09:00 - 12:00
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09:00
Experimental Evidence of KPZ Growing Interfaces and Beyond
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: K.A. TAKEUCHI (Univ. Tokyo, Physics, Japan) Material: Video -
09:45
KPZ- and Related Behavior of Hydrodynamics in One Dimension
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: H. VAN BEIJEREN (Institute Theoretical Physics, Univ. Utrecht, Netherlands) Material: VAN BEIJEREN abstract.pdf Video slides - 10:30 Coffee/tea break 30' ( Leonardo da Vinci Building Main Lecture Hall )
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11:00
Universality in Driven-Dissipative Bose-Einstein Condensation
45' (
Leonardo da Vinci Building Main Lecture Hall
)
Speaker: L. SIEBERER (Institut fuer Theoretische Physik, Innsbruck, Austria) Material: SIEBERER abstract.pdf Video -
11:45
Closing Remarks
15' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00
Experimental Evidence of KPZ Growing Interfaces and Beyond
45' (
Leonardo da Vinci Building Main Lecture Hall
)
-
09:00 - 12:00