Equation of state of the unitary Fermi gas

Size: px
Start display at page:

Download "Equation of state of the unitary Fermi gas"

Transcription

1 Equation of state of the unitary Fermi gas Igor Boettcher Institute for Theoretical Physics, University of Heidelberg with S. Diehl, J. M. Pawlowski, and C. Wetterich C o ld atom s Δ13, tio c n Fu G R l na

2 The many-body problem

3 The many-body problem possibility of a statistical description collective degrees of freedom

4 The many-body problem 1st step: Find the right Hamiltonian H 2nd step: Determine the partition function Z

5 The many-body problem H is known for cold st 1 step: Find the right Hamiltonian H atoms and QCD! 2nd step: Determine the partition function Z

6 The many-body problem H is known for cold st 1 step: Find the right Hamiltonian H atoms and QCD! 2nd step: Determine the partition function Z path integral Euclidean quantum field theory

7 Shopping list What are the generic features of quantum many-body systems? What are reliable theoretical methods to describe such systems? What observables reveal advancements and short-comings of theory?

8 s m o t a cold Shopping list neutron stars What are the generic features of quantum many-body systems? high-tc superconductors early universe What are reliable theoretical methods to describe such systems? What observables reveal advancements and short-comings of theory? heavy ion collisions nuclear matter quark gluon plasma

9 Shopping list Experiments with cold atoms Theory Phase diagram and Equation of state Density images Momentum distribution Collective mode frequencies and damping constants Expansion after release from trap Transport coefficients... Response functions

10 Shopping list Experiments with cold atoms Theory Phase diagram and Equation of state Density images Momentum distribution Collective mode frequencies and damping constants Expansion after release from trap Transport coefficients... Response functions

11 The equation of state Classical ideal gas: Virial expansion for interacting gas: Van-der-Waals equation of state:

12 Pressure P(μ,T) Bose gas

13 Density n=( P/ μ)t Bose gas

14 2 2 Isothermal compressibility ( P/ μ )T Bose gas

15 2 2 Isothermal compressibility ( P/ μ )T Bose gas Position of critical line: phase diagram Superfluid phase transition

16 The BCS-BEC Crossover Two cornerstones of quantum condensation: BCS Cooper pairing of weakly attractive fermions BEC Bose condensation of weakly repulsive bosons

17 The BCS-BEC Crossover Two cornerstones of quantum condensation: BCS BEC

18 The BCS-BEC Crossover Two cornerstones of quantum condensation: Unitary Fermi gas BCS BEC

19 The BCS-BEC Crossover 3D BCS-BEC crossover (results from Functional Renormalization Group)

20 The BCS-BEC Crossover BKT BCS 2D BCS-BEC crossover High Tc superconductors!? (results from Functional Renormalization Group)

21 The BCS-BEC Crossover Key observables Tan contact Equation of state Bertsch parameter Dimer-dimer scattering length Critical temperature

22 The BCS-BEC Crossover Key observables Tan contact Equation of state Bertsch parameter Dimer-dimer scattering length Critical temperature

23 The BCS-BEC Crossover One problem: Key observables Tan contact Equation of state Bertsch parameter Dimer-dimer scattering length Critical temperature

24 Thermodynamics from density profiles local density approximation Ho, Zhou S. Nascimbène et al.

25 Thermodynamics from density profiles M. J. H. Ku et al., Science 335, (2012) Unitary Fermi gas at MIT by Zwierlein group

26 Thermodynamics from density profiles Tc/TF=0.167(13) M. J. H. Ku et al., Science 335, (2012) Unitary Fermi gas at MIT by Zwierlein group

27 Thermodynamics from density profiles Bertsch parameter ξ: EoS at T=0 Unitary Fermi gas at MIT by Zwierlein group

28 Thermodynamics from density profiles Bertsch parameter ξ: EoS at T=0 Unitary Fermi gas at MIT by Zwierlein group

29 Thermodynamics from density profiles Bertsch parameter ξ: EoS at T=0 Unitary Fermi gas at MIT by Zwierlein group

30 Thermodynamics from density profiles Bertsch parameter ξ: EoS at T=0 ξ=0.376(5) Unitary Fermi gas at MIT by Zwierlein group

31 Thermodynamics from density profiles Bertsch parameter ξ: EoS at T=0 ξ=0.376(5) ξ=0.370(5)(8) Unitary Fermi gas at MIT by Zwierlein group

32 Equation of state from Functional RG Experiment: Latest FRG: (Floerchinger, Scherer, Wetterich)

33 Equation of state from Functional RG Experiment: sacrifice ξ and Tc/TF Latest FRG: (Floerchinger, Scherer, Wetterich)

34 Equation of state from Functional RG Experiment: sacrifice ξ and Tc/TF Most likely error source: Frequency-independent cutoffs Latest FRG: (Floerchinger, Scherer, Wetterich) First estimate: ξ=0.41 with 4D-fermion cutoff in the simplest truncation

35 Equation of state from Functional RG Experiment: sacrifice ξ and Tc/TF Most likely error source: Frequency-independent cutoffs Latest FRG: (Floerchinger, Scherer, Wetterich) First estimate: ξ=0.41 with 4D-fermion cutoff in the simplest truncation contact me during the workshop if you are interested in that

36 Tan contact Momentum distribution Tan relation Asymptotic fermion self-energy

37 Tan contact FRG: IB, S. Diehl, J. M. Pawlowski, C. Wetterich

38 Tan contact Thank you for your attention! FRG: IB, S. Diehl, J. M. Pawlowski, C. Wetterich

39 Additional slides

40 Microscopic Model Many-body Hamiltonian

41 Microscopic Model Many-body Hamiltonian Microscopic action

42 Macroscopic physics How to compute the partition function? Integration

43 Macroscopic physics How to compute the partition function? scale dependent partition function Solve flow equation

44 Wetterich equation effective action fluctuations Microphysics Macrophysics

45 Contact in the BCS-BEC Crossover

46 Momentum distribution Ideal Fermi gas: Fermi-Dirac distribution Interactions

47 Momentum distribution Tan contact C Several exact relations, e.g.:

48 Contact from the FRG full macroscopic propagator

49 Contact from the FRG Factorization of the RG flow for large p:

50 Contact from the FRG Factorization of the RG flow for large p: Flowing contact

51 Contact from the FRG Universal regime is enhanced for the Unitary Fermi gas

52 Contact from the FRG Universal regime is enhanced for the Unitary Fermi gas

53 Contact from the FRG Temperature dependent contact of the Unitary Fermi gas

54 Contact from the FRG Contact at T=0 in the BCS-BEC crossover

55 Contact from the FRG Momentum distribution of the Unitary Fermi Gas at the critical temperature without contact term with contact term

56 Increase of density Contribution from high energetic particles to the density at Tc Substantial effect on

57 Two-dimensional BCS-BEC Crossover

58 Two-dimensional BCS-BEC Crossover Why two dimensions? Enhanced effects of quantum fluctuations test and improve elaborate methods Understand pairing in two dimensions high temperature superconductors How? Highly anisotropic traps!

59 What is different? Scattering physics in two dimensions Scattering amplitude Crossover parameter No scale invariance, but strong correlations for

60 Equation of state at T=0 for

61 Equation of state at T=0 BCS BKT for

62 Superfluid phase transition for

63 Superfluid phase transition Damping of n-ththank mode:you for your attention and enjoy lunch! for

Dimensional BCS-BEC crossover

Dimensional BCS-BEC crossover Dimensional BCS-BEC crossover Igor Boettcher Institute for Theoretical Physics, Heidelberg University ERG 2014 Outline Ultracold atoms BCS-BEC Crossover 2D Experiments with... Theory Experiment C. Wetterich

More information

Towards a quantitative FRG approach for the BCS-BEC crossover

Towards a quantitative FRG approach for the BCS-BEC crossover Towards a quantitative FRG approach for the BCS-BEC crossover Michael M. Scherer Theoretisch Physikalisches Institut, Jena University in collaboration with Sebastian Diehl, Stefan Flörchinger, Holger Gies,

More information

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

Nuclear structure III: Nuclear and neutron matter. National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016 Nuclear structure III: Nuclear and neutron matter Stefano Gandolfi Los Alamos National Laboratory (LANL) National Nuclear Physics Summer School Massachusetts Institute of Technology (MIT) July 18-29, 2016

More information

Thermodynamics of the polarized unitary Fermi gas from complex Langevin. Joaquín E. Drut University of North Carolina at Chapel Hill

Thermodynamics of the polarized unitary Fermi gas from complex Langevin. Joaquín E. Drut University of North Carolina at Chapel Hill Thermodynamics of the polarized unitary Fermi gas from complex Langevin Joaquín E. Drut University of North Carolina at Chapel Hill INT, July 2018 Acknowledgements Organizers Group at UNC-CH (esp. Andrew

More information

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9

Contents. 1.1 Prerequisites and textbooks Physical phenomena and theoretical tools The path integrals... 9 Preface v Chapter 1 Introduction 1 1.1 Prerequisites and textbooks......................... 1 1.2 Physical phenomena and theoretical tools................. 5 1.3 The path integrals..............................

More information

Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA

Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA Lianyi He ( 何联毅 ) Department of Physics, Tsinghua University 2016 Hangzhou Workshop on Quantum Degenerate Fermi Gases,

More information

From BEC to BCS. Molecular BECs and Fermionic Condensates of Cooper Pairs. Preseminar Extreme Matter Institute EMMI. and

From BEC to BCS. Molecular BECs and Fermionic Condensates of Cooper Pairs. Preseminar Extreme Matter Institute EMMI. and From BEC to BCS Molecular BECs and Fermionic Condensates of Cooper Pairs Preseminar Extreme Matter Institute EMMI Andre Wenz Max-Planck-Institute for Nuclear Physics and Matthias Kronenwett Institute for

More information

Lecture 3 : ultracold Fermi Gases

Lecture 3 : ultracold Fermi Gases Lecture 3 : ultracold Fermi Gases The ideal Fermi gas: a reminder Interacting Fermions BCS theory in a nutshell The BCS-BEC crossover and quantum simulation Many-Body Physics with Cold Gases Diluteness:

More information

Small Trapped s-wave Interacting Fermi Gases: How to Quantify Correlations?

Small Trapped s-wave Interacting Fermi Gases: How to Quantify Correlations? Image: Peter Engels group at WSU Small Trapped s-wave Interacting Fermi Gases: How to Quantify Correlations? Doerte Blume and Kevin M. Daily Dept. of Physics and Astronomy, Washington State University,

More information

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke

BCS-BEC Crossover. Hauptseminar: Physik der kalten Gase Robin Wanke BCS-BEC Crossover Hauptseminar: Physik der kalten Gase Robin Wanke Outline Motivation Cold fermions BCS-Theory Gap equation Feshbach resonance Pairing BEC of molecules BCS-BEC-crossover Conclusion 2 Motivation

More information

Strongly correlated Cooper pair insulators and superfluids

Strongly correlated Cooper pair insulators and superfluids Strongly correlated Cooper pair insulators and superfluids Predrag Nikolić George Mason University Acknowledgments Collaborators Subir Sachdev Eun-Gook Moon Anton Burkov Arun Paramekanti Affiliations and

More information

Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC FERMI GASES

Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC FERMI GASES 1 INTERNATIONAL SCHOOL OF PHYSICS "ENRICO FERMI" Varenna, July 1st - July 11 th 2008 " QUANTUM COHERENCE IN SOLID STATE SYSTEMS " Introduction to Bose-Einstein condensation 4. STRONGLY INTERACTING ATOMIC

More information

The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other

The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other 1 The phases of matter familiar for us from everyday life are: solid, liquid, gas and plasma (e.f. flames of fire). There are, however, many other phases of matter that have been experimentally observed,

More information

Pairing properties, pseudogap phase and dynamics of vortices in a unitary Fermi gas

Pairing properties, pseudogap phase and dynamics of vortices in a unitary Fermi gas Pairing properties, pseudogap phase and dynamics of vortices in a unitary Fermi gas Piotr Magierski (Warsaw University of Technology/ University of Washington, Seattle) Collaborators: Aurel Bulgac (Seattle)

More information

Kolloquium Universität Innsbruck October 13, The renormalization group: from the foundations to modern applications

Kolloquium Universität Innsbruck October 13, The renormalization group: from the foundations to modern applications Kolloquium Universität Innsbruck October 13, 2009 The renormalization group: from the foundations to modern applications Peter Kopietz, Universität Frankfurt 1.) Historical introduction: what is the RG?

More information

Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases

Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases APCTP Focus Program on Quantum Condensation (QC12) Simulation of neutron-rich dilute nuclear matter using ultracold Fermi gases Munekazu Horikoshi Photon Science Center of University of Tokyo Grant-In-Aid

More information

Publications. Articles:

Publications. Articles: Publications Articles: 1. R. Combescot Coupling between Planes and Chains in Y Ba 2 Cu 3 O 7 : A Possible Solution for the Order Parameter Controversy, Phys. Rev. Lett. 75 (1995) 3732-3735 2. X. Leyronas

More information

Revolution in Physics. What is the second quantum revolution? Think different from Particle-Wave Duality

Revolution in Physics. What is the second quantum revolution? Think different from Particle-Wave Duality PHYS 34 Modern Physics Ultracold Atoms and Trappe Ions Today and Mar.3 Contents: a) Revolution in physics nd Quantum revolution b) Quantum simulation, measurement, and information c) Atomic ensemble and

More information

Lecture Overview... Modern Problems in Nuclear Physics I

Lecture Overview... Modern Problems in Nuclear Physics I Lecture Overview... Modern Problems in Nuclear Physics I D. Blaschke (U Wroclaw, JINR, MEPhI) G. Röpke (U Rostock) A. Sedrakian (FIAS Frankfurt, Yerevan SU) 1. Path Integral Approach to Partition Function

More information

Reference for most of this talk:

Reference for most of this talk: Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding ultracold Fermi gases. in Ultracold Fermi Gases, Proceedings of the International School

More information

Sarma phase in relativistic and non-relativistic systems

Sarma phase in relativistic and non-relativistic systems phase in relativistic and non-relativistic systems Tina Katharina Herbst In Collaboration with I. Boettcher, J. Braun, J. M. Pawlowski, D. Roscher, N. Strodthoff, L. von Smekal and C. Wetterich arxiv:149.5232

More information

Unification from Functional Renormalization

Unification from Functional Renormalization Unification from Functional Renormalization Wegner, Houghton / Effective potential includes all fluctuations Unification from Functional Renormalization fluctuations in d=0,1,2,3,... linear and non-linear

More information

A Mixture of Bose and Fermi Superfluids. C. Salomon

A Mixture of Bose and Fermi Superfluids. C. Salomon A Mixture of Bose and Fermi Superfluids C. Salomon INT workshop Frontiers in quantum simulation with cold atoms University of Washington, April 2, 2015 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner,

More information

F. Chevy Seattle May 2011

F. Chevy Seattle May 2011 THERMODYNAMICS OF ULTRACOLD GASES F. Chevy Seattle May 2011 ENS FERMION GROUPS Li S. Nascimbène Li/K N. Navon L. Tarruell K. Magalhaes FC C. Salomon S. Chaudhuri A. Ridinger T. Salez D. Wilkowski U. Eismann

More information

arxiv: v1 [cond-mat.quant-gas] 19 Apr 2012

arxiv: v1 [cond-mat.quant-gas] 19 Apr 2012 Nuclear Physics B Proceedings Supplement 00 (202) 73 Nuclear Physics B Proceedings Supplement Ultracold atoms and the Functional Renormalization Group ariv:204.4394v [cond-mat.quant-gas] 9 Apr 202 Igor

More information

Spectral Functions from the Functional RG

Spectral Functions from the Functional RG Spectral Functions from the Functional RG 7 th International Conference on the Exact Renormalization Group ERG 2014 22/09/14 Lefkada, Greece Nils Strodthoff, ITP Heidelberg 2-Point Functions and their

More information

Critical lines and points. in the. QCD phase diagram

Critical lines and points. in the. QCD phase diagram Critical lines and points in the QCD phase diagram Understanding the phase diagram Phase diagram for m s > m u,d quark-gluon plasma deconfinement quark matter : superfluid B spontaneously broken nuclear

More information

ICAP Summer School, Paris, Three lectures on quantum gases. Wolfgang Ketterle, MIT

ICAP Summer School, Paris, Three lectures on quantum gases. Wolfgang Ketterle, MIT ICAP Summer School, Paris, 2012 Three lectures on quantum gases Wolfgang Ketterle, MIT Cold fermions Reference for most of this talk: W. Ketterle and M. W. Zwierlein: Making, probing and understanding

More information

Fundamentals and New Frontiers of Bose Einstein Condensation

Fundamentals and New Frontiers of Bose Einstein Condensation Contents Preface v 1. Fundamentals of Bose Einstein Condensation 1 1.1 Indistinguishability of Identical Particles.......... 1 1.2 Ideal Bose Gas in a Uniform System............ 3 1.3 Off-Diagonal Long-Range

More information

Is a system of fermions in the crossover BCS-BEC. BEC regime a new type of superfluid?

Is a system of fermions in the crossover BCS-BEC. BEC regime a new type of superfluid? Is a system of fermions in the crossover BCS-BEC BEC regime a new type of superfluid? Finite temperature properties of a Fermi gas in the unitary regime Aurel Bulgac,, Joaquin E. Drut, Piotr Magierski

More information

Landau s Fermi Liquid Theory

Landau s Fermi Liquid Theory Thors Hans Hansson Stockholm University Outline 1 Fermi Liquids Why, What, and How? Why Fermi liquids? What is a Fermi liquids? Fermi Liquids How? 2 Landau s Phenomenological Approach The free Fermi gas

More information

Introduction to Cold Atoms and Bose-Einstein Condensation. Randy Hulet

Introduction to Cold Atoms and Bose-Einstein Condensation. Randy Hulet Introduction to Cold Atoms and Bose-Einstein Condensation Randy Hulet Outline Introduction to methods and concepts of cold atom physics Interactions Feshbach resonances Quantum Gases Quantum regime nλ

More information

Bose-condensed and BCS fermion superfluid states T ~ nano to microkelvin (coldest in the universe)

Bose-condensed and BCS fermion superfluid states T ~ nano to microkelvin (coldest in the universe) Deconfined quark-gluon plasmas made in ultrarelativistic heavy ion collisions T ~ 10 2 MeV ~ 10 12 K (temperature of early universe at ~1µ sec) Bose-condensed and BCS fermion superfluid states T ~ nano

More information

Transport coefficients from Kinetic Theory: Bulk viscosity, Diffusion, Thermal conductivity. Debarati Chatterjee

Transport coefficients from Kinetic Theory: Bulk viscosity, Diffusion, Thermal conductivity. Debarati Chatterjee Transport coefficients from Kinetic Theory: Bulk viscosity, Diffusion, Thermal conductivity Debarati Chatterjee Recap: Hydrodynamics of nearly perfect fluids Hydrodynamics: correlation functions at low

More information

Towards the shear viscosity of a cold unitary fermi gas

Towards the shear viscosity of a cold unitary fermi gas Towards the shear viscosity of a cold unitary fermi gas Jiunn-Wei Chen National Taiwan U. Shear viscosity y V x (y) x Frictional force T ij iv j ( x) V 2 j i ( x) 1 ij V ( x). 3 Shear viscosity measures

More information

The BCS-BEC Crossover and the Unitary Fermi Gas

The BCS-BEC Crossover and the Unitary Fermi Gas Lecture Notes in Physics 836 The BCS-BEC Crossover and the Unitary Fermi Gas Bearbeitet von Wilhelm Zwerger 1. Auflage 2011. Taschenbuch. xvi, 532 S. Paperback ISBN 978 3 642 21977 1 Format (B x L): 15,5

More information

Low- and High-Energy Excitations in the Unitary Fermi Gas

Low- and High-Energy Excitations in the Unitary Fermi Gas Low- and High-Energy Excitations in the Unitary Fermi Gas Introduction / Motivation Homogeneous Gas Momentum Distribution Quasi-Particle Spectrum Low Energy Excitations and Static Structure Function Inhomogeneous

More information

A Mixture of Bose and Fermi Superfluids. C. Salomon

A Mixture of Bose and Fermi Superfluids. C. Salomon A Mixture of Bose and Fermi Superfluids C. Salomon Enrico Fermi School Quantum Matter at Ultralow Temperatures Varenna, July 8, 2014 The ENS Fermi Gas Team F. Chevy, Y. Castin, F. Werner, C.S. Lithium

More information

Effective Field Theory and Ultracold Atoms

Effective Field Theory and Ultracold Atoms Effective Field Theory and Ultracold Atoms Eric Braaten Ohio State University support Department of Energy Air Force Office of Scientific Research Army Research Office 1 Effective Field Theory and Ultracold

More information

Functional RG for few-body physics

Functional RG for few-body physics Functional RG for few-body physics Michael C Birse The University of Manchester Review of results from: Schmidt and Moroz, arxiv:0910.4586 Krippa, Walet and Birse, arxiv:0911.4608 Krippa, Walet and Birse,

More information

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES

fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES Content-Thermodynamics & Statistical Mechanics 1. Kinetic theory of gases..(1-13) 1.1 Basic assumption of kinetic theory 1.1.1 Pressure exerted by a gas 1.2 Gas Law for Ideal gases: 1.2.1 Boyle s Law 1.2.2

More information

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in

PRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific

More information

BCS Pairing Dynamics. ShengQuan Zhou. Dec.10, 2006, Physics Department, University of Illinois

BCS Pairing Dynamics. ShengQuan Zhou. Dec.10, 2006, Physics Department, University of Illinois BCS Pairing Dynamics 1 ShengQuan Zhou Dec.10, 2006, Physics Department, University of Illinois Abstract. Experimental control over inter-atomic interactions by adjusting external parameters is discussed.

More information

Quantum gases in the unitary limit and...

Quantum gases in the unitary limit and... Quantum gases in the unitary limit and... Andre LeClair Cornell university Benasque July 2 2010 Outline The unitary limit of quantum gases S-matrix based approach to thermodynamics Application to the unitary

More information

SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES

SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES College de France, May 14, 2013 SUPERFLUIDTY IN ULTRACOLD ATOMIC GASES Sandro Stringari Università di Trento CNR-INFM PLAN OF THE LECTURES Lecture 1. Superfluidity in ultra cold atomic gases: examples

More information

Flow equations and phase transitions

Flow equations and phase transitions Flow equations and phase transitions phase transitions QCD phase transition Quark gluon plasma Gluons : 8 x 2 = 16 Quarks : 9 x 7/2 =12.5 Dof : 28.5 Chiral symmetry Hadron gas Light mesons : 8 (pions

More information

High-Temperature Superfluidity

High-Temperature Superfluidity High-Temperature Superfluidity Tomoki Ozawa December 10, 2007 Abstract With the recent advancement of the technique of cooling atomic gases, it is now possible to make fermionic atom gases into superfluid

More information

Part A - Comments on the papers of Burovski et al. Part B - On Superfluid Properties of Asymmetric Dilute Fermi Systems

Part A - Comments on the papers of Burovski et al. Part B - On Superfluid Properties of Asymmetric Dilute Fermi Systems Part A - Comments on the papers of Burovski et al. Part B - On Superfluid Properties of Asymmetric Dilute Fermi Systems Part A Comments on papers of E. Burovski,, N. Prokof ev ev,, B. Svistunov and M.

More information

Interaction between atoms

Interaction between atoms Interaction between atoms MICHA SCHILLING HAUPTSEMINAR: PHYSIK DER KALTEN GASE INSTITUT FÜR THEORETISCHE PHYSIK III UNIVERSITÄT STUTTGART 23.04.2013 Outline 2 Scattering theory slow particles / s-wave

More information

Spontaneous symmetry breaking in fermion systems with functional RG

Spontaneous symmetry breaking in fermion systems with functional RG Spontaneous symmetry breaking in fermion systems with functional RG Andreas Eberlein and Walter Metzner MPI for Solid State Research, Stuttgart Lefkada, September 24 A. Eberlein and W. Metzner Spontaneous

More information

Two-dimensional atomic Fermi gases. Michael Köhl Universität Bonn

Two-dimensional atomic Fermi gases. Michael Köhl Universität Bonn Two-dimensional atomic Fermi gases Michael Köhl Universität Bonn Ultracold Fermi gases as model systems BEC/BCS crossover Search for the perfect fluid: Cold fermions vs. Quark-gluon plasma Cao et al.,

More information

Inverse square potential, scale anomaly, and complex extension

Inverse square potential, scale anomaly, and complex extension Inverse square potential, scale anomaly, and complex extension Sergej Moroz Seattle, February 2010 Work in collaboration with Richard Schmidt ITP, Heidelberg Outline Introduction and motivation Functional

More information

Strongly Interacting Fermi Gases: Universal Thermodynamics, Spin Transport, and Dimensional Crossover

Strongly Interacting Fermi Gases: Universal Thermodynamics, Spin Transport, and Dimensional Crossover NewSpin, College Station, 1/16/011 Strongly Interacting ermi Gases: Universal hermodynamics, Spin ransport, and Dimensional Crossover Martin Zwierlein Massachusetts Institute of echnology Center for Ultracold

More information

Unitary Fermi gas in the ɛ expansion

Unitary Fermi gas in the ɛ expansion Unitary Fermi gas in the ɛ expansion Yusuke Nishida Department of Physics, University of Tokyo December 006 PhD Thesis Abstract We construct systematic expansions around four and two spatial dimensions

More information

Condensate fraction for a polarized three-dimensional Fermi gas

Condensate fraction for a polarized three-dimensional Fermi gas Condensate fraction for a polarized three-dimensional Fermi gas Luca Salasnich Dipartimento di Fisica e Astronomia Galileo Galilei, Università di Padova, Italy Camerino, June 26, 2014 Collaboration with:

More information

Non-equilibrium time evolution of bosons from the functional renormalization group

Non-equilibrium time evolution of bosons from the functional renormalization group March 14, 2013, Condensed Matter Journal Club University of Florida at Gainesville Non-equilibrium time evolution of bosons from the functional renormalization group Peter Kopietz, Universität Frankfurt

More information

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and :

We can then linearize the Heisenberg equation for in the small quantity obtaining a set of linear coupled equations for and : Wednesday, April 23, 2014 9:37 PM Excitations in a Bose condensate So far: basic understanding of the ground state wavefunction for a Bose-Einstein condensate; We need to know: elementary excitations in

More information

Pomiędzy nadprzewodnictwem a kondensacją Bosego-Einsteina. Piotr Magierski (Wydział Fizyki Politechniki Warszawskiej)

Pomiędzy nadprzewodnictwem a kondensacją Bosego-Einsteina. Piotr Magierski (Wydział Fizyki Politechniki Warszawskiej) Pomiędzy nadprzewodnictwem a kondensacją Bosego-Einsteina Piotr Magierski (Wydział Fizyki Politechniki Warszawskiej) 100 years of superconductivity and superfluidity in Fermi systems Discovery: H. Kamerlingh

More information

3D Hydrodynamics and Quasi-2D Thermodynamics in Strongly Correlated Fermi Gases. John E. Thomas NC State University

3D Hydrodynamics and Quasi-2D Thermodynamics in Strongly Correlated Fermi Gases. John E. Thomas NC State University 3D Hydrodynamics and Quasi-D Thermodynamics in Strongly Correlated Fermi Gases John E. Thomas NC State University JETLa Group J. E. Thomas Graduate Students: Ethan Elliot Willie Ong Chingyun Cheng Arun

More information

Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007

Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007 Superfluidity and superconductivity. IHP, Paris, May 7 and 9, 2007 L.P. Pitaevskii Dipartimento di Fisica, Universita di Trento, INFM BEC CNR,Trento, Italy; Kapitza Institute for Physical Problems, ul.

More information

Dynamic properties of interacting bosons and magnons

Dynamic properties of interacting bosons and magnons Ultracold Quantum Gases beyond Equilibrium Natal, Brasil, September 27 October 1, 2010 Dynamic properties of interacting bosons and magnons Peter Kopietz, Universität Frankfurt collaboration: A. Kreisel,

More information

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals

Quantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields

More information

Outline for Fundamentals of Statistical Physics Leo P. Kadanoff

Outline for Fundamentals of Statistical Physics Leo P. Kadanoff Outline for Fundamentals of Statistical Physics Leo P. Kadanoff text: Statistical Physics, Statics, Dynamics, Renormalization Leo Kadanoff I also referred often to Wikipedia and found it accurate and helpful.

More information

Cold atoms and AdS/CFT

Cold atoms and AdS/CFT Cold atoms and AdS/CFT D. T. Son Institute for Nuclear Theory, University of Washington Cold atoms and AdS/CFT p.1/20 What is common for strong coupled cold atoms and QGP? Cold atoms and AdS/CFT p.2/20

More information

Fermi Condensates ULTRACOLD QUANTUM GASES

Fermi Condensates ULTRACOLD QUANTUM GASES Fermi Condensates Markus Greiner, Cindy A. Regal, and Deborah S. Jin JILA, National Institute of Standards and Technology and University of Colorado, and Department of Physics, University of Colorado,

More information

The Phases of QCD. Thomas Schaefer. North Carolina State University

The Phases of QCD. Thomas Schaefer. North Carolina State University The Phases of QCD Thomas Schaefer North Carolina State University 1 Plan of the lectures 1. QCD and States of Matter 2. The High Temperature Phase: Theory 3. Exploring QCD at High Temperature: Experiment

More information

FRG approach to interacting fermions with partial bosonization: from weak to strong coupling

FRG approach to interacting fermions with partial bosonization: from weak to strong coupling FRG approach to interacting fermions with partial bosonization: from weak to strong coupling Talk at conference ERG08, Heidelberg, June 30, 2008 Peter Kopietz, Universität Frankfurt collaborators: Lorenz

More information

Present and future prospects of the (functional) renormalization group

Present and future prospects of the (functional) renormalization group Schladming Winter School 2011: Physics at all scales: the renormalization group Present and future prospects of the (functional) renormalization group Peter Kopietz, Universität Frankfurt panel discussion

More information

Bose-Einstein condensation of lithium molecules and studies of a strongly interacting Fermi gas

Bose-Einstein condensation of lithium molecules and studies of a strongly interacting Fermi gas Bose-Einstein condensation of lithium molecules and studies of a strongly interacting Fermi gas Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms 3/4/04 Workshop

More information

Nanoelectronics 14. [( ) k B T ] 1. Atsufumi Hirohata Department of Electronics. Quick Review over the Last Lecture.

Nanoelectronics 14. [( ) k B T ] 1. Atsufumi Hirohata Department of Electronics. Quick Review over the Last Lecture. Nanoelectronics 14 Atsufumi Hirohata Department of Electronics 09:00 Tuesday, 27/February/2018 (P/T 005) Quick Review over the Last Lecture Function Fermi-Dirac distribution f ( E) = 1 exp E µ [( ) k B

More information

liquid He

liquid He 8.333: Statistical Mechanics I Problem Set # 6 Due: 12/6/13 @ mid-night According to MIT regulations, no problem set can have a due date later than 12/6/13, and I have extended the due date to the last

More information

High order corrections to density and temperature of fermions and bosons from quantum fluctuations and the CoMD-α Model

High order corrections to density and temperature of fermions and bosons from quantum fluctuations and the CoMD-α Model High order corrections to density and temperature of fermions and bosons from quantum fluctuations and the CoMD-α Model Hua Zheng, 1,2 Gianluca Giuliani, 1 Matteo Barbarino, 1 and Aldo Bonasera 1,3 1 Cyclotron

More information

Path Integral (Auxiliary Field) Monte Carlo approach to ultracold atomic gases. Piotr Magierski Warsaw University of Technology

Path Integral (Auxiliary Field) Monte Carlo approach to ultracold atomic gases. Piotr Magierski Warsaw University of Technology Path Integral (Auxiliary Field) Monte Carlo approach to ultracold atomic gases Piotr Magierski Warsaw University of Technology Collaborators: A. Bulgac - University of Washington J.E. Drut - University

More information

Lecture 2: Weak Interactions and BEC

Lecture 2: Weak Interactions and BEC Lecture 2: Weak Interactions and BEC Previous lecture: Ideal gas model gives a fair intuition for occurrence of BEC but is unphysical (infinite compressibility, shape of condensate...) Order parameter

More information

1. Cold Collision Basics

1. Cold Collision Basics ICAP Summer School, Seoul, S. Korea, July 18, 2016 1. Cold Collision Basics Paul S. Julienne Joint Quantum Institute NIST and The University of Maryland Thanks to many colleagues in theory and experiment

More information

Evaluating the Phase Diagram at finite Isospin and Baryon Chemical Potentials in NJL model

Evaluating the Phase Diagram at finite Isospin and Baryon Chemical Potentials in NJL model Evaluating the Phase Diagram at finite Isospin and Baryon Chemical Potentials in NJL model Chengfu Mu, Peking University Collaborated with Lianyi He, J.W.Goethe University Prof. Yu-xin Liu, Peking University

More information

Many-Body Problems and Quantum Field Theory

Many-Body Problems and Quantum Field Theory Philippe A. Martin Francois Rothen Many-Body Problems and Quantum Field Theory An Introduction Translated by Steven Goldfarb, Andrew Jordan and Samuel Leach Second Edition With 102 Figures, 7 Tables and

More information

Specific heat of a fermionic atomic cloud in the bulk and in traps

Specific heat of a fermionic atomic cloud in the bulk and in traps Specific heat of a fermionic atomic cloud in the bulk and in traps Aurel Bulgac,, Joaquin E. Drut, Piotr Magierski University of Washington, Seattle, WA Also in Warsaw Outline Some general remarks Path

More information

A Superfluid Universe

A Superfluid Universe A Superfluid Universe Lecture 2 Quantum field theory & superfluidity Kerson Huang MIT & IAS, NTU Lecture 2. Quantum fields The dynamical vacuum Vacuumscalar field Superfluidity Ginsburg Landau theory BEC

More information

Shock waves in the unitary Fermi gas

Shock waves in the unitary Fermi gas Shock waves in the unitary Fermi gas Luca Salasnich Dipartimento di Fisica e Astronomia Galileo Galilei, Università di Padova Banff, May 205 Collaboration with: Francesco Ancilotto and Flavio Toigo Summary.

More information

BEC of 6 Li 2 molecules: Exploring the BEC-BCS crossover

BEC of 6 Li 2 molecules: Exploring the BEC-BCS crossover Institut für Experimentalphysik Universität Innsbruck Dresden, 12.10. 2004 BEC of 6 Li 2 molecules: Exploring the BEC-BCS crossover Johannes Hecker Denschlag The lithium team Selim Jochim Markus Bartenstein

More information

QGP Thermodynamics and Phase Transitions. Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad

QGP Thermodynamics and Phase Transitions. Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad QGP Thermodynamics and Phase Transitions Mahnaz Q. Haseeb Department of Physics CIIT, Islamabad Outline Thermodynamics in QGP What are the phase transitions? Order of the phase transition Where to study

More information

Quantum Field Theory 2 nd Edition

Quantum Field Theory 2 nd Edition Quantum Field Theory 2 nd Edition FRANZ MANDL and GRAHAM SHAW School of Physics & Astromony, The University of Manchester, Manchester, UK WILEY A John Wiley and Sons, Ltd., Publication Contents Preface

More information

Landau Theory of Fermi Liquids : Equilibrium Properties

Landau Theory of Fermi Liquids : Equilibrium Properties Quantum Liquids LECTURE I-II Landau Theory of Fermi Liquids : Phenomenology and Microscopic Foundations LECTURE III Superfluidity. Bogoliubov theory. Bose-Einstein condensation. LECTURE IV Luttinger Liquids.

More information

The nature of superfluidity in the cold atomic unitary Fermi gas

The nature of superfluidity in the cold atomic unitary Fermi gas The nature of superfluidity in the cold atomic unitary Fermi gas Introduction Yoram Alhassid (Yale University) Finite-temperature auxiliary-field Monte Carlo (AFMC) method The trapped unitary Fermi gas

More information

Functional renormalization for ultracold quantum gases

Functional renormalization for ultracold quantum gases Functional renormalization for ultracold quantum gases Stefan Floerchinger (Heidelberg) S. Floerchinger and C. Wetterich, Phys. Rev. A 77, 053603 (2008); S. Floerchinger and C. Wetterich, arxiv:0805.2571.

More information

The Phases of QCD. Thomas Schaefer. North Carolina State University

The Phases of QCD. Thomas Schaefer. North Carolina State University The Phases of QCD Thomas Schaefer North Carolina State University 1 Motivation Different phases of QCD occur in the universe Neutron Stars, Big Bang Exploring the phase diagram is important to understanding

More information

Fermions in the unitary regime at finite temperatures from path integral auxiliary field Monte Carlo simulations

Fermions in the unitary regime at finite temperatures from path integral auxiliary field Monte Carlo simulations Fermions in the unitary regime at finite temperatures from path integral auxiliary field Monte Carlo simulations Aurel Bulgac,, Joaquin E. Drut and Piotr Magierski University of Washington, Seattle, WA

More information

Superfluidity and Superconductivity Macroscopic Quantum Phenomena

Superfluidity and Superconductivity Macroscopic Quantum Phenomena Superfluid Bose and Fermi gases Wolfgang Ketterle Massachusetts Institute of Technology MIT-Harvard Center for Ultracold Atoms 3/11/2013 Universal Themes of Bose-Einstein Condensation Leiden Superfluidity

More information

Broad and Narrow Fano-Feshbach Resonances: Condensate Fraction in the BCS-BEC Crossover

Broad and Narrow Fano-Feshbach Resonances: Condensate Fraction in the BCS-BEC Crossover Broad and Narrow Fano-Feshbach Resonances: Condensate Fraction in the BCS-BEC Crossover Luca Salasnich Dipartimento di Fisica e Astronomia Galileo Galilei and CNISM, Università di Padova INO-CNR, Research

More information

Experiments with an Ultracold Three-Component Fermi Gas

Experiments with an Ultracold Three-Component Fermi Gas Experiments with an Ultracold Three-Component Fermi Gas The Pennsylvania State University Ken O Hara Jason Williams Eric Hazlett Ronald Stites John Huckans Overview New Physics with Three Component Fermi

More information

Hydrodynamics. Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010

Hydrodynamics. Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010 Hydrodynamics Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010 What is Hydrodynamics? Describes the evolution of physical systems (classical or quantum particles, fluids or fields) close to thermal

More information

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases

Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases Bahram M. Askerov Sophia R. Figarova Thermodynamics, Gibbs Method and Statistical Physics of Electron Gases With im Figures Springer Contents 1 Basic Concepts of Thermodynamics and Statistical Physics...

More information

arxiv: v1 [hep-ph] 22 Aug 2011

arxiv: v1 [hep-ph] 22 Aug 2011 (submitted to Annalen der Physik) Fermion Interactions and Universal Behavior in Strongly Interacting Theories Jens Braun Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Max-Wien-Platz

More information

Strongly paired fermions

Strongly paired fermions Strongly paired fermions Alexandros Gezerlis TALENT/INT Course on Nuclear forces and their impact on structure, reactions and astrophysics July 4, 2013 Strongly paired fermions Neutron matter & cold atoms

More information

Preface Introduction to the electron liquid

Preface Introduction to the electron liquid Table of Preface page xvii 1 Introduction to the electron liquid 1 1.1 A tale of many electrons 1 1.2 Where the electrons roam: physical realizations of the electron liquid 5 1.2.1 Three dimensions 5 1.2.2

More information

HIGHER ORDER THERMAL CORRECTIONS TO PHOTON SELF ENERGY

HIGHER ORDER THERMAL CORRECTIONS TO PHOTON SELF ENERGY HIGHER ORDER THERMAL CORRECTIONS TO PHOTON SELF ENERGY Mahnaz Q. Haseeb Physics Department COMSATS Institute of Information Technology Islamabad Outline Relevance Finite Temperature Effects One Loop Corrections

More information

Equilibrium and nonequilibrium properties of unitary Fermi gas from Quantum Monte Carlo

Equilibrium and nonequilibrium properties of unitary Fermi gas from Quantum Monte Carlo Equilibrium and nonequilibrium properties of unitary ermi gas from Quantum Monte Carlo Piotr Magierski Warsaw University of Technology Collaborators: A. Bulgac - University of Washington J.E. Drut - University

More information

Lecture 4. Feshbach resonances Ultracold molecules

Lecture 4. Feshbach resonances Ultracold molecules Lecture 4 Feshbach resonances Ultracold molecules 95 Reminder: scattering length V(r) a tan 0( k) lim k0 k r a: scattering length Single-channel scattering a 96 Multi-channel scattering alkali-metal atom:

More information

Statistical Mechanics

Statistical Mechanics Franz Schwabl Statistical Mechanics Translated by William Brewer Second Edition With 202 Figures, 26 Tables, and 195 Problems 4u Springer Table of Contents 1. Basic Principles 1 1.1 Introduction 1 1.2

More information