## 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

- 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.*

- "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. - "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

- 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*. - "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

- "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. - "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

- 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. - 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

- 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.") - 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.* - Read, N. "Large
*N*Calculation."*J. Phys*. C18 (1985): 2651;

also see a book by Hewson, A. C.*The Kondo Problem to Heavy Fermions.*

- Anderson, P. W. "The Anderson Model."
*Phys. Rev.*142 (1961): 41.

## One Dimensional Fermions (Luttinger Liquid); Bosonization

- 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*. - "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.