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GREEN FUNCTIONS FOR NONEQUILIBRIUM SYSTEMS

GREEN FUNCTIONS FOR NONEQUILIBRIUM SYSTEMS. Ceyda Sanli Supervisor(s): Vikram Tripathi & Kader Damle. OUTLINE. MOTIVATION THEORY GREEN FUNCTIONS DYSON EQUATION-DIAGRAM TECHNIQUE QUANTUM BOLTZMANN EQUATION QUANTUM BOLTZMANN-LANGEVIN EQUATION FUTURE WORK

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GREEN FUNCTIONS FOR NONEQUILIBRIUM SYSTEMS

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  1. GREEN FUNCTIONSFOR NONEQUILIBRIUM SYSTEMS Ceyda Sanli Supervisor(s):Vikram Tripathi & Kader Damle VSRP-07-DTP-TIFR-MUMBAI

  2. OUTLINE • MOTIVATION • THEORY • GREEN FUNCTIONS • DYSON EQUATION-DIAGRAM TECHNIQUE • QUANTUM BOLTZMANN EQUATION • QUANTUM BOLTZMANN-LANGEVIN EQUATION • FUTURE WORK • DISCUSSION VSRP-07-DTP-TIFR-MUMBAI

  3. MOTIVATION AIM:UNDERSTANDING QUANTUM PHASE TRANSITION POINTS BY CALCULATING FLUCTUATION. GREEN FUNCTION + NOISE MODEL (IDEA):SUPERFLUID-MOTT INSULATOR (SI) TRANSITION. SIMPLFY !! VSRP-07-DTP-TIFR-MUMBAI

  4. SI TRANSITION Rb 10 nanoKelvin 87 Grainer, et. al., Nature, 415, 39 (2002). VSRP-07-DTP-TIFR-MUMBAI

  5. SI TRANSITION Bose-Hubbard Model*: tunnelling strength repulsion strength *Fisher et. al., PRB, 40, 546 (1989). *Jaksch et. al., PRL, 81, 3108 (1998). VSRP-07-DTP-TIFR-MUMBAI

  6. SI TRANSITION REAL SYSTEM: WHERE WE ARE : NO PAIR EFFECTS!! • BOSONS • @ T=10 nanoKelvin • STRONGLY CORRELATED • STRONG EXTERNAL FIELD • LONG RANGE INTERACTION FINITE TEMPERATURE WEAKLY CORRELATED NO EXTERNAL FIELD SHORT RANGE VSRP-07-DTP-TIFR-MUMBAI

  7. Low frequency transport (QBE) FINITE TEMPERATURE WEAKLY CORRELATED Low density, slowly varying field, sufficiently close to equilibrium limit. VSRP-07-DTP-TIFR-MUMBAI

  8. THEORY- GREEN FUNCTION SCHWINGER-KELDYSH GREEN FUNCTION Real-time Contour , VSRP-07-DTP-TIFR-MUMBAI

  9. VSRP-07-DTP-TIFR-MUMBAI

  10. SELF ENERGY Proper Self Energy VSRP-07-DTP-TIFR-MUMBAI

  11. PROPER SELF ENERGY C ~ Born collision term Hartree term vertex points = + … VSRP-07-DTP-TIFR-MUMBAI

  12. DYSON EQUATION VSRP-07-DTP-TIFR-MUMBAI

  13. Q-BOLTZMANN EQUATION (QBE) VSRP-07-DTP-TIFR-MUMBAI

  14. QBE • Long time limit: Center of mass coordinates may be same. After taking FT: • Weakly interacting regime: = VSRP-07-DTP-TIFR-MUMBAI

  15. QBE VSRP-07-DTP-TIFR-MUMBAI

  16. LANGEVIN EQUATION - NOISE QBLE VSRP-07-DTP-TIFR-MUMBAI

  17. FLUCTUATIONS ~ long time limit: fluctuations statistically independent VSRP-07-DTP-TIFR-MUMBAI

  18. FUTURE WORK \ DISCUSSION • COMPLETE TERMINOLOGY TO CALCULATE FLUCTUATIONS IN QUANTUM CRITICAL POINTS. (COMBINE TWO TECHNICS: GREEN FUNCT. + NOISE) • AFTER FORMULATION, IMPROVE THE TOY MODEL (IDENTICAL BOSONS, SHORT RANGE INT., NO EXTERNAL FIELD, SLOWLY VARYING BACKGROUND POTENTIAL, NO PAIR EFFECTS, FINITE TEMPERATURE, CLOSE TO EQUILIUBRIUM) • DISCUSS MORE ABOUT THE PHYSICS BEHIND!! VSRP-07-DTP-TIFR-MUMBAI

  19. VSRP-07-DTP-TIFR-MUMBAI

  20. ACKNOWLEDGEMENT • I want to thank Dr. Vikram Tripathi and Dr. Kader Damle for this nice study. • Special thanks for Dr. Achanta Venu Gopal, and my friends Arindam Mazumdar, Sandipan Kundu, Dipikaben B. Patel. VSRP-07-DTP-TIFR-MUMBAI

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