Alexander Abanov's Home Page

Alexander G. Abanov Department of Physics and Astronomy Stony Brook University Stony Brook, NY 11794-3800, USA tel:     (631)632-8174 fax:    (631)632-4977 email: alexandre.abanovatstonybrook.edu I am a Professor in the Department of Physics and Astronomy of Stony Brook University. I am working in theoretical condensed matter physics. My main interests lie in the field of strongly correlated electron systems. In studying such systems, strong electron-electron interactions prevent the full use of perturbation theory, with famous examples being high temperature superconductors and quantum Hall systems. Therefore, "non-perturbative" method become essential for theoretical analysis. In particular, the "topological" properties of strongly correlated systems play an important role because they are insensitive to interaction strength and provide us with some universal properties both at weak and strong coupling. This field involves an interplay among condensed matter theory, modern quantum field theory, and mathematics.

Benjamin-Ono equation: Solitons and Shock Waves

Teaching at Stony Brook University

Undergraduate classes


• Classical Physics A (PHY 125): Spring 2006


• Electromagnetic Theory I (PHY 301/571): Fall 2004


• Electromagnetic Theory II (PHY 302): Spring 2005

Graduate classes


• Classical Mechanics (PHY 501): Fall 2011 , Fall 2005


• Methods of Mathematical Physics (PHY 503): Fall 2008 , Fall 2007, Fall 2006, Fall 2003, Fall 2002, Fall 2001.


• Quantum Mechanics I, II (PHY 511/512): Spring 2011 , Fall 2010, Spring 2010, Fall 2009.


• Statistical Mechanics I (PHY 540): Spring 2002


• Solid State Physics II (PHY 556): Spring 2012 , Spring 2008


• Graduate seminar (Atomic, Molecular, Optical and Solid State) (PHY 598): Fall 2004


• Quantum Magnetism (PHY 682, 680): Spring 2004, Spring 2001.


• Topological terms in condensed matter physics (PHY 680): Spring 2009.

Other teaching

• SchoolNova @ Stony Brook. I teach math to children of different grades (5 to 9) in Sunday enrichment program. SchoolNova @ Stony Brook is a math and language school for children 3-15 year old. Classes are held at Stony Brook University and are taught in English. Classes in math, science (Earth science and physics), art, languages (French, Russian, Italian, Spanish, and advanced English) and an enrichment program for 3-5 years old.
  


• Krasnoyarsk Summer School for gifted high school students. КЛШ (in Russian)
  
  • Classical Mechanics with elements of dimensional analysis (in Russian) Summer 2006
  • Noneuclidian geometry. Lobahevsky, Riemann and others (in Russian) Summer 2007
  • Fibonacci Rabbits, Golden Mean and Complex Numbers (in Russian) Summer 2010
  • Cosmography (in Russian) Summer 2010
  • Knots and Braids (in Russian) Summer 2012
  • Geometries (intro to noneuclidian geometry) (in Russian) Summer 2012
  
  
• ITP, EPFL, Lausanne, Switzerland. ITP
  
  • Topological terms in condensed matter physics. Spring 2007
  
  
• The Princeton Summer School for Condensed Matter Physics School
  
  • Shock waves in cold atoms. Dispersion vs. Dissipation. Lectures
  
  
• Summer Camp (Cherry Plain State Park, New York State).
  
  • Topology for 8-year olds, August 2009.
  • Solving problems in kinematics for children age 12-15, August 2011.
  
  

Family

• Family Pictures

Selected Publications

• A. G. Abanov, E. Bettelheim, P. Wiegmann, preprint, 2008. [arXiv:0810.5327]
  Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation.


• E. Bettelheim, A. G. Abanov, and P. Wiegmann, J. Phys. A: Math. Theor. 41 (2008) 392003. [arXiv:0804.2272]
  Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas.


• A. G. Abanov and D. A. Ivanov, Phys. Rev. Lett. 100, 086602 (2008). [arXiv:0709.2898]
  Allowed charge transfers between coherent conductors driven by a time-dependent scatterer.


• E. Bettelheim, A. G. Abanov, P. Wiegmann, Phys. Rev. Lett. 97, 246402 (2006). [arXiv:cond-mat/0607453]
  Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas.


• E. Bettelheim, A. G. Abanov, P. Wiegmann, Phys. Rev. Lett. 97, 246401 (2006). [arXiv:cond-mat/0606778]
  Nonlinear Quantum Shock Waves in Fractional Quantum Hall Edge States.


• A. G. Abanov and P. B. Wiegmann, Phys. Rev. Lett. 95, 076402 (2005). [arXiv:cond-mat/0504041]
  Quantum Hydrodynamics, the Quantum Benjamin-Ono Equation, and the Calogero Model


• A. G. Abanov, in "Application of random matrices in physics", Brezin, E.; Kazakov, V.; Serban, D.; Wiegmann, P.; Zabrodin, A. (Eds.) NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 221 Springer, Les Houches, June 2004. [arXiv:cond-mat/0504307]
  Hydrodynamics of correlated systems. Emptiness Formation Probability and Random Matrices


• A. G. Abanov and V. I. Korepin, Nucl. Phys. B647, 565-580 (2002). [arXiv:cond-mat/0206353]
  On the probability of ferromagnetic strings in antiferromagnetic spin chains


• A. G. Abanov and Ar. Abanov, Phys. Rev. B, 65, 184407 (2002). [arXiv:cond-mat/0111284]
  Berry phase for ferromagnet with fractional spin


• A. G. Abanov and P. B. Wiegmann, Phys. Rev. Lett. 86, 1319 (2001). [arXiv:hep-th/0006157]
  Chiral Nonlinear σ-Models as Models for Topological Superconductivity


• A. G. Abanov, Phys. Lett. B492, 321 (2000). [arXiv:hep-th/0005150]
  Hopf term induced by fermions


• A. G. Abanov and P. B. Wiegmann, Nucl. Phys. B570, 685 (2000). [arXiv:hep-th/9911025]
  Theta-terms in non-linear sigma-models


• A. G. Abanov, J. C. Talstra, and P. B. Wiegmann, Nucl. Phys. B525, 571 (1998) . [arXiv:cond-mat/9711274]
  Hierarchical structure of Azbel-Hofstadter problem: Strings and loose ends of the Bethe Ansatz


• A. G. Abanov, J. C. Talstra, and P. B. Wiegmann, Phys. Rev. Lett. 81, 2112 (1998). [arXiv:cond-mat/9803179]
  Asymptotically exact solutions of Harper equation


• A. G. Abanov and P. B. Wiegmann, Phys. Rev. Lett. 78, 4103 (1997). [arXiv:cond-mat/9701163]
  Tunneling and orthogonality catastrophe in the topological mechanisms of superconductivity


• A. G. Abanov and O. A. Petrenko, Phys. Rev. B 50, 6271 (1994). [arXiv:cond-mat/9402024]
  Enhancement of Anisotropy Due to Fluctuations in Quasi-One-Dimensional Antiferromagnets


• A. G. Abanov, Sov. Phys. JETP 74, 1036 (1992).
  Phase Transitions in Dimer Systems