# Projects

## Term Paper

The term paper counts as 40% of the course grade. It should contain a short introduction presenting an overview of the topic, a main part developing and discussing the key ideas, and a conclusion. It is due during the last lecture, in class.

## Topics Suggestions for Term Paper References

Suggested topics numbered by 1), 2) etc. are grouped into categories corresponding to different parts of the course. The papers are selected according to a combination of the novelty and readability criteria applied quite freely. I tried to keep in the list only the papers which one can enjoy reading.

## Superconductivity

1. Abrikosov, A. A. "Vortices and Magnetic Flux Quantization." (2003, Nobel prize) Sov. Phys. JETP 5 (1957): 1174.
   Useful background material on Ginzburg-Landau equation can be found in the book by M. Tinkham, Introduction to Superconductivity.
2. "BCS Theory Generalized to Pairing with Nonzero Orbital Momentum and Spin."
   Pitaevskii, L. P. Sov. Phys. JETP 10 (1960): 1267;
   Thouless, D. J. Ann Phys 10 (1960): 553. New York;
   Brueckner, K. A., T. Soda, P. W. Anderson, and P. Morel. Phys. Rev. 118 (1960): 1442.
3. "The Interpretation of the Experimental Observations of a MicroKelvin Transition in Liquid 3He in Terms of Anisotropic Pairing." (2003, Nobel prize)
   Leggett, A. J. Phys. Rev. Lett. 29 (1972): 1227;
   Leggett, A. J. Phys. Rev. Lett. 31 (1973): 352;
   Leggett, A. J. J. Phys. C6 (1973): 3187.

## Tunneling in Macroscopic Systems

1. Affleck, I. "A Unified Description of Tunneling and Thermally Activated Escape." Phys. Rev. Lett. 46 (1981): 388.
   Keldysh, L. V., V. Melnikov, and B. Ivlev. "Tunneling Stimulated by an External Periodic Field Considered in Terms of Trajectories in Complex Time." Sov. Phys. JETP.
2. "Tunneling and Escape in Field Theory."
   Coleman, S. Phys. Rev. D15 (1977): 2829;
   Callan, C., and S. Coleman. Phys. Rev. D16 (1977): 1762.

## Quantum Mechanics with Dissipation

1. "Quantum Dissipative Brownian Walks and Driven Dynamics."
   Schmid, A. Phys. Rev. Lett. 15 (1983): 1506;
   Fisher and Zwerger. Phys Rev B32 (1985): 6190.
   Schmid, A. "A very Pedagogical Discussion of the Relation Between Dissipative Quantum Dynamics and Classical Langevin Dynamics." Ann. Phys. (New York) 170 (1986): 333.
2. "Fermi-liquid as a Dissipative Bath. Heavy Particle Moving in Fermi-liquid."
   This problem was first considered by Josephson and Lekner in early 70's and then argued about for a long time until the views converged. The current situation is summarized in a recent review by A. Rosch, Phys. Rep.
   Anderson, P. W. "Orthogonality Catastrophe." Phys. Rev. Lett. 18 (1967): 1049.

## The Fermi liquid Problem

1. Landau, L. D. "Kinetic Equation Approach." Sov. Phys. JETP 3 (1956): 920; 5 (1957): 101.
   Pomeranchuk, I. Ya. "Instabilities of Landau Fermi-liquid via Spontaneous Fermi Surface Deformations." Sov. Phys. JETP 8 (1959): 535.
2. Particle-hole Excitations as Tomonaga Bosons; Oscillator Representation of Fermi-liquid.
   Sawada, K. Phys. Rev. 106 (1957): 372;
   Sawada, K., et. al. Phys Rev 108 (1957): 507;
   Wentzel, G. Phys. Rev. 108 (1957): 1593.

## The Kondo Problem

1. Anderson, P. W., G. Yuval, and D. R. Hamann. "Renormalization Group from Logarithmic Kink Interaction." Phys. Rev. B1 (1970): 4464.
   (see also Anderson, P. W. "Basic Notions of Condensed Matter Physics.")
2. Abrikosov, A. A. "Renormalization Group from Diagrammatic Calculations with Kondo Spin Represented by a Pseudofermion." Physics 2 (1965): 5;
   also Suhl, H. Phys. Rev. 138 (1965): A515;
   see also a discussion in Abrikosov's book Fundamentals of the Theory of Metals.
3. Read, N. "Large N Calculation." J. Phys. C18 (1985): 2651;
   also see a book by Hewson, A. C. The Kondo Problem to Heavy Fermions.
4. Anderson, P. W. "The Anderson Model." Phys. Rev. 142 (1961): 41.

## One Dimensional Fermions (Luttinger Liquid); Bosonization

1. The Transformation of the Interacting 1D Fermiona to Noninteracting 1D Bosons first appeared in: Tomonaga, S. Progr Theor Phys (Kyoto) 5 (1950): 544.
   The inverse transformation allowing to express fermi operators through bose fields (bosonization) was first introduced by K. Schotte, and U. Schotte. Phys. Rev. 182 (1969): 479.
   A good summary can be found in: Haldane, F. D. M. J. Phys. C14 (1981): 2585, and in the book by Mahan, Many-Body Physics.
2. "Tunneling in a 1D Fermi System."
   Kane, C., and M. P. A. Fisher. Phys. Rev. Lett. 68 (1992): 1220;
   Phys. Rev. B46 (1992): 15223;
   Wen, X. G. Phys. Rev. B43 (1991): 11025;
   Phys. Rev. Lett. 64 (1990): 2206.