Physics 682: Far From Equilibrium and Mesoscopic Physics, Spring 2024

Tentative course outline

Lecture notes: Part I     Part II     Part III      Part IV

Literature:

1. Mehta, Random Matrices, Elsevier, 3rd edition, 2004
2. Alhassid, The statistical theory of quantum dots, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
3. Tarucha et. al., Shell filling and spin effects in a few electron quantum dot, Phys. Rev. Lett, 77, 3613 (1996)
4. Rabson, Narozhny, and Millis, Crossover from Poisson to Wigner-Dyson level statistics in spin chains with integrability breaking, Phys. Rev. B 69 0644403 (2004)
5. Yuzbashyan, Altshuler, and Shastry, The origin of degeneracies and crossings in the 1d Hubbard model, J. Phys. A 35, 7525 (2002)
6. Heilmann and Lieb, Violation of the noncrossing rule: the Hubbard Hamiltonian for benzene, Annals of the NY Academy of Science 172, 584 (1971)
7. Akemann et. al., TERRITORIAL BEHAVIOUR OF BUZZARDS VERSUS RANDOM MATRIX SPACING DISTRIBUTIONS, J. Theor. Biol. 509 (2021), 110475:1-7
8. On the distribution of spacings between zeros of the zeta function, A. M. Odlyzko, Math. Comp., 48 (1987), pp. 273-308
9. Kurland, Aleiner, and Altshuler, Mesoscopic magnetization fluctuations for metallic grains close to the Stoner instability, Phys. Rev. B 62, 14886 (2000).
   
10. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity, Phys. Rev. 108, 1175 (1957).
11. Anderson,  Theory of dirty superconductors, J. Phys. Chem. Solids 11, 56 (1959).
    
12. K. A. Matveev and A. I. Larkin, Parity Effect in Ground State Energies of Ultrasmall Superconducting Grains, Phys. Rev. Lett. 78, 3749 (1997).
    
13. Arnold, Mathematical Methods of Classical Mechanics, Springer; 2nd edition (May 16, 1989).
14. Korteweg–De Vries equation - Wikipedia article
15. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras Volume I,  ‎ Birkhauser; Softcover reprint of the original 1st ed. 1990 edition (December 1, 1989).
16. Yuzbashyan, Altshuler, Kuznetsov, and Enolskii, Solution for the dynamics of the BCS and central spin problems, J. Phys. A 38, 7831, (2005).
17. E. A. Yuzbashyan, M. Dzero, V. Gurarie, and M. S. Foster, Quantum quench phase diagrams of an s-wave BCS-BEC condensate, Phys. Rev. A 91, 033628 (2015).
    

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