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Electrical and thermal transport near quantum phase transitions in condensed matter, and in dyonic blac

Electrical and thermal transport near quantum phase transitions in condensed matter, and in dyonic black holes. Sean Hartnoll (KITP) Pavel Kovtun (KITP) Marcus Müller (Harvard) Subir Sachdev (Harvard) . Outline. Transport near strongly interacting quantum critical points.

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Electrical and thermal transport near quantum phase transitions in condensed matter, and in dyonic blac

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  1. Electrical and thermal transport near quantum phase transitions in condensed matter, and in dyonic black holes Sean Hartnoll (KITP) Pavel Kovtun (KITP) Marcus Müller (Harvard) Subir Sachdev (Harvard)

  2. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  3. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  4. Trap for ultracold 87Rb atoms

  5. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  6. Boson Hubbard model M.PA. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher Phys. Rev. B40, 546 (1989).

  7. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  8. Velocity distribution of 87Rb atoms Superfliud M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  9. Velocity distribution of 87Rb atoms Insulator M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Nature415, 39 (2002).

  10. The insulator:

  11. Excitations of the insulator:

  12. Excitations of the insulator:

  13. Excitations of the insulator:

  14. Non-zero temperature phase diagram Insulator Superfluid Depth of periodic potential

  15. Non-zero temperature phase diagram Dynamics of the classical Gross-Pitaevski equation Insulator Superfluid Depth of periodic potential

  16. Non-zero temperature phase diagram Dilute Boltzmann gas of particle and holes Insulator Superfluid Depth of periodic potential

  17. Non-zero temperature phase diagram No wave or quasiparticle description Insulator Superfluid Depth of periodic potential

  18. Resistivity of Bi films D. B. Haviland, Y. Liu, and A. M. Goldman, Phys. Rev. Lett.62, 2180 (1989) M. P. A. Fisher, Phys. Rev. Lett.65, 923 (1990)

  19. Non-zero temperature phase diagram Insulator Superfluid Depth of periodic potential

  20. Non-zero temperature phase diagram Collisionless-to hydrodynamic crossover of a conformal field theory (CFT) Insulator Superfluid Depth of periodic potential K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

  21. Collisionless-to-hydrodynamic crossover of a CFT in 2+1 dimensions K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

  22. Collisionless-to-hydrodynamic crossover of a CFT in 2+1 dimensions K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

  23. Hydrodynamics of a conformal field theory (CFT) The scattering cross-section of the thermal excitations is universal and so transport co-efficients are universally determined by kBT Charge diffusion constant Conductivity K. Damle and S. Sachdev, Phys. Rev. B56, 8714 (1997).

  24. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  25. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  26. Exact solutions of CFTs in 1+1 dimensions

  27. Exact solutions of CFTs in 1+1 dimensions

  28. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  29. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  30. Hydrodynamics of a conformal field theory (CFT) The AdS/CFT correspondence (Maldacena, Polyakov) relates the hydrodynamics of CFTs to the quantum gravity theory of the horizon of a black hole in Anti-de Sitter space.

  31. Hydrodynamics of a conformal field theory (CFT) The AdS/CFT correspondence (Maldacena, Polyakov) relates the hydrodynamics of CFTs to the quantum gravity theory of the horizon of a black hole in Anti-de Sitter space. Holographic representation of black hole physics in a 2+1 dimensional CFT at a temperature equal to the Hawking temperature of the black hole. 3+1 dimensional AdS space Black hole

  32. Hydrodynamics of a conformal field theory (CFT) Hydrodynamics of a CFT Waves of gauge fields in a curved background

  33. Hydrodynamics of a conformal field theory (CFT) For the (unique) CFT with a SU(N) gauge field and 16 supercharges, we know the exact diffusion constant associated with a global SO(8) symmetry: Spin diffusion constant Spin conductivity P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)

  34. Collisionless-to-hydrodynamic crossover of solvable SYM3 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)

  35. CFT at T=0 ImC/k2 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)

  36. Collisionless-to-hydrodynamic crossover of solvable SYM3 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)

  37. diffusion peak ImC/k2 P. Kovtun, C. Herzog, S. Sachdev, and D.T. Son, Phys. Rev. D 75, 085020 (2007)

  38. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  39. Outline Transport near strongly interacting quantum critical points • The superfluid-insulator transition in the boson Hubbard model: Hydrodynamic-collisionless crossover of a CFT • Exact solutions of CFTs in 1+1 dimensions No hydrodynamics • Exact solution of a CFT in 2+1 dimensions - Yang-Mills theory with N=8 supersymmetry: Black holes in AdS4 • General hydrodynamic theory in the presence of a magnetic field, chemical potential and impurities: Nernst effect in the cuprate superconductors; Dyonic black holes in AdS4

  40. For experimental applications, we must move away from the ideal CFT e.g.

  41. For experimental applications, we must move away from the ideal CFT • A chemical potential  e.g.

  42. For experimental applications, we must move away from the ideal CFT • A chemical potential  CFT e.g.

  43. For experimental applications, we must move away from the ideal CFT • A chemical potential  e.g.

  44. For experimental applications, we must move away from the ideal CFT • A chemical potential  CFT e.g.

  45. For experimental applications, we must move away from the ideal CFT • A chemical potential  • A magnetic field B CFT e.g.

  46. S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, arXiv:0706.3215

  47. Conservation laws/equations of motion S.A. Hartnoll, P.K. Kovtun, M. Müller, and S. Sachdev, arXiv:0706.3215

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