Physics 540:
Models solvable by Bethe Ansatz

Instructor: Vladimir Korepin, Professor
Office: Physics 6-116B
Web page: http://max2.physics.sunysb.edu/~korepin/
Office Hours: Tuesday 10:45-11:45
Help room: A132, Wednesday 5:15-7:15

Course description
Spin chains, Bose gas with delta interaction, Hubbard model, Sine Gordon and Massive Thirring model will be considered in the course.
The following are the subjects:

1. Structure of Bethe wave function

2. Ground state and excitations [dispersion curves and scattering matrix]

3. Thermodynamics

4. Correlation functions

Tentative Syllabus

Course requirements
Only enrolled students can attend lectures. Attendance is expected. Homework assignments should be turned on time, late homework will not be accepted. There will be two midterms and a final exam. Absence at a midterm can be justified by a medical problem of a student [or a legal dependent] supported by medical papers in English (the doctor will be contacted to verify the note). Taking the final exam is a requirement.

Grading and exams
Midterm I on April 1: Bethe wave function
Midterm II on April 29 Scattering matrix
Final exam on May 11, at 3:50 in YITP common rom
The final grade is calculated from

Homework --- 10%

Midterms --- 30%

Final exam --- 60%

Main textbooks

Quantum Inverse Scatttering Method and Correlation Function -by V.E. Korepin, N.M. Bogoliubov and A.G. Izergin , Cambridge University Press 1993

The One-Dimensional Hubbard model , A. Kluemper, F. Goehnamm, H. Frahm, F. Essler, V. Korepin

# Date Read Topic

1. Mon, Aug 29 G 1.1-1.3; FW 1.1-1.3 0. Introduction. Quantum nonlinear Schroedinger equation. Bethe wave function, two body reducibility and completeness.

2. Wed, Aug 31 G 1.2-1.3; FW 1.2-1.3; LL 1 Ground state and excitations

3. Fri, Sep 2 LL 2 HW 1 given. Yang-Yang thermodynamics 1. Fredholm integral operators of a special form Completely integrable integral operators.

Mon, Sep 5 NO CLASSES. Labor Day.

4. Wed, Sep 7 LL 2 Riemann-Hilbert prblem.

5. Fri, Sep 9 LL 3-5 Space time and temperature dependent correlation functions.

6. Mon, Sep 12 LL 5-7 HW 2 given. Massive Thiring model 2. Excitations renormalization.

7. Wed, Sep 14 LL 5-9 Scattering matrix

8. Fri, Sep 16 JS 3.2.2, LL 10 XXZ spin chain

9. Mon, Sep 19 LL 10-11 HW 3 given. Hubbard model 3. 1D Charge and spin separation.

10. Wed, Sep 21 LL 13-15 4. 2D motion. Central force motion. Reduced mass. Motion in central field. Kepler's problem. Kepler's laws.

11. Fri, Sep 23 LL 15-16 Conic sections. Time dependence in Kepler problem. Orbit precession in almost Newtonian potentials. Particle decay.

Mon, Sep 26 NO CLASSES. Prepare for the exam.

12. Wed, Sep 28 LL 1-15 Midterm 1. (open book).

13. Fri, Sep 30 LL 16-20 HW 4 given. Collision between particles. Total and differential scattering cross sections. Rutherford cross section.

Mon, Oct 3 NO CLASSES. Rosh Hashanah.

Wed, Oct 5 NO CLASSES. Rosh Hashanah.

14. Fri, Oct 7 LL 17, 20, 21 Scattering in laboratory reference frame. Scattering by small angle. 5. Small oscillations. Harmonic oscillator.

15. Mon, Oct 10 LL 21-22 Harmonic oscillator. Forced oscillations. Complex notations. Resonance. Beatings.

16. Wed, Oct 12 LL 23-24 HW 5 given. Oscillations with many degrees of freedom. Eigenfrequences and normal modes.

17. Fri, Oct 14 LL 24-25 Example on normal modes. Degeneracies. Vibrations of molecules. Damped oscillations (1 degree of freedom).

18. Mon, Oct 17 LL 25-26, 31 Damped oscillations (many degrees of freedom). Dissipative function. Forced oscillations under friction. 6. Rigid body motion. Angular velocity.

19. Wed, Oct 19 LL 32-33 HW 6 given. Kinetic energy of the rigid body. The inertia tensor and its properties.

20. Fri, Oct 21 LL 33-34 Angular momentum of the rigid body. Symmetric top I. Equations of motion.

21. Mon, Oct 24 LL 35-36 Euler angles. Equations of motion in the moving frame.

22. Wed, Oct 26 LL 36-37 HW 7 given. Euler equations. Symmetric top II. Asymmetric top.

23. Fri, Oct 28 LL 39, 40 Motion in an non-inertial frame of reference. Centrifugal and Coriolis forces. 7. Hamiltonian and Hamilton-Jacobi formalism. Hamilton's equations.

24. Mon, Oct 31 LL 40, JS 5.1, G 8.5 Hamilton's equations. The Legendre transform. Variational formulation.

25. Wed, Nov 2 LL 42, 45 HW 8 given. Poisson brackets. Examples. Canonical transformations.

26. Fri, Nov 4 LL 45 Canonical transformations.

27. Mon, Nov 7 LL 46 Invariants of canonical transformations: Poisson bracket, phase volume. Liouville therem.

28. Wed, Nov 9 LL 47-48 The Hamilton-Jacobi equation. Example. Separation of variables.

29. Fri, Nov 11 LL 48-49 Separation of variables. Adiabatic invariants (example of harmonic oscillator).

30. Mon, Nov 14 LL 50, 52 Adiabatic invariants. Action-angle variables. Conditionally periodic motion.

31. Wed, Nov 16 G Action-angle variables (examples). 8. Nonlinear dynamics and chaos. Introduction.

32. Fri, Nov 18 LL 16-49 Midterm 2. (open book).

33. Mon, Nov 21 G 11.1-11.3; JS 6.3 HW 9 given. Periodic motion. Perturbations.

34. Wed, Nov 23 G 11-4,5,7; LL 27-30 KAM. Attractors. Chaotic trajectories.

Fri, Nov 25 NO CLASSES. Thanksgiving.

35. Mon, Nov 28 G 11.8 Poincare maps. The logistic equation.

36. Wed, Nov 30 LL 27,30 HW 10 given. Parametric resonance.

37. Fri, Dec 2 LL7 1-2 9. Elasticity theory. Displacement field. the strain tensor. The stress tensor.

38. Mon, Dec 5 LL7 2-4 The stress tensor. Elastic energy. Elastic moduli (Hooke's law).

39. Wed, Dec 7 LL7 4-5, 7 Elastic moduli (Hooke's law). Homogenious deformations. Equilibrium for isotropic bodies.

40. Fri, Dec 9 LL7 7, 11-12 Equilibrium for isotropic bodies. Equilibrium for a plate.

41. Mon, Dec 12 LL7 22 10. Dynamics of continuous systems. Elastic waves. 11. Final remarks: towards field theory and quantum mechanics.

42. Mon, Dec 19 Room P-112 Solving problems in classical mechanics.

Final Wed, Dec 21 8:00-10:30 AM FINAL, P-112. Open book. Notes and textbooks are allowed. 4 problems.

For your information.
If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services (631) 632-6748. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Students requiring emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information, go to the following web site http://studentaffairs.stonybrook.edu/dss/

Disability Support Services, Academic Integrity and Critical Incident Management, see http://www.stonybrook.edu/provost/facultyinfo/index.shtml

Last updated

#	Date	Read	Topic
1.	Mon, Aug 29	G 1.1-1.3; FW 1.1-1.3	0. Introduction. Quantum nonlinear Schroedinger equation. Bethe wave function, two body reducibility and completeness.
2.	Wed, Aug 31	G 1.2-1.3; FW 1.2-1.3; LL 1	Ground state and excitations
3.	Fri, Sep 2	LL 2	HW 1 given. Yang-Yang thermodynamics 1. Fredholm integral operators of a special form Completely integrable integral operators.
	Mon, Sep 5		NO CLASSES. Labor Day.
4.	Wed, Sep 7	LL 2	Riemann-Hilbert prblem.
5.	Fri, Sep 9	LL 3-5	Space time and temperature dependent correlation functions.
6.	Mon, Sep 12	LL 5-7	HW 2 given. Massive Thiring model 2. Excitations renormalization.
7.	Wed, Sep 14	LL 5-9	Scattering matrix
8.	Fri, Sep 16	JS 3.2.2, LL 10	XXZ spin chain
9.	Mon, Sep 19	LL 10-11	HW 3 given. Hubbard model 3. 1D Charge and spin separation.
10.	Wed, Sep 21	LL 13-15	4. 2D motion. Central force motion. Reduced mass. Motion in central field. Kepler's problem. Kepler's laws.
11.	Fri, Sep 23	LL 15-16	Conic sections. Time dependence in Kepler problem. Orbit precession in almost Newtonian potentials. Particle decay.
	Mon, Sep 26		NO CLASSES. Prepare for the exam.
12.	Wed, Sep 28	LL 1-15	Midterm 1. (open book).
13.	Fri, Sep 30	LL 16-20	HW 4 given. Collision between particles. Total and differential scattering cross sections. Rutherford cross section.
	Mon, Oct 3		NO CLASSES. Rosh Hashanah.
	Wed, Oct 5		NO CLASSES. Rosh Hashanah.
14.	Fri, Oct 7	LL 17, 20, 21	Scattering in laboratory reference frame. Scattering by small angle. 5. Small oscillations. Harmonic oscillator.
15.	Mon, Oct 10	LL 21-22	Harmonic oscillator. Forced oscillations. Complex notations. Resonance. Beatings.
16.	Wed, Oct 12	LL 23-24	HW 5 given. Oscillations with many degrees of freedom. Eigenfrequences and normal modes.
17.	Fri, Oct 14	LL 24-25	Example on normal modes. Degeneracies. Vibrations of molecules. Damped oscillations (1 degree of freedom).
18.	Mon, Oct 17	LL 25-26, 31	Damped oscillations (many degrees of freedom). Dissipative function. Forced oscillations under friction. 6. Rigid body motion. Angular velocity.
19.	Wed, Oct 19	LL 32-33	HW 6 given. Kinetic energy of the rigid body. The inertia tensor and its properties.
20.	Fri, Oct 21	LL 33-34	Angular momentum of the rigid body. Symmetric top I. Equations of motion.
21.	Mon, Oct 24	LL 35-36	Euler angles. Equations of motion in the moving frame.
22.	Wed, Oct 26	LL 36-37	HW 7 given. Euler equations. Symmetric top II. Asymmetric top.
23.	Fri, Oct 28	LL 39, 40	Motion in an non-inertial frame of reference. Centrifugal and Coriolis forces. 7. Hamiltonian and Hamilton-Jacobi formalism. Hamilton's equations.
24.	Mon, Oct 31	LL 40, JS 5.1, G 8.5	Hamilton's equations. The Legendre transform. Variational formulation.
25.	Wed, Nov 2	LL 42, 45	HW 8 given. Poisson brackets. Examples. Canonical transformations.
26.	Fri, Nov 4	LL 45	Canonical transformations.
27.	Mon, Nov 7	LL 46	Invariants of canonical transformations: Poisson bracket, phase volume. Liouville therem.
28.	Wed, Nov 9	LL 47-48	The Hamilton-Jacobi equation. Example. Separation of variables.
29.	Fri, Nov 11	LL 48-49	Separation of variables. Adiabatic invariants (example of harmonic oscillator).
30.	Mon, Nov 14	LL 50, 52	Adiabatic invariants. Action-angle variables. Conditionally periodic motion.
31.	Wed, Nov 16	G	Action-angle variables (examples). 8. Nonlinear dynamics and chaos. Introduction.
32.	Fri, Nov 18	LL 16-49	Midterm 2. (open book).
33.	Mon, Nov 21	G 11.1-11.3; JS 6.3	HW 9 given. Periodic motion. Perturbations.
34.	Wed, Nov 23	G 11-4,5,7; LL 27-30	KAM. Attractors. Chaotic trajectories.
	Fri, Nov 25		NO CLASSES. Thanksgiving.
35.	Mon, Nov 28	G 11.8	Poincare maps. The logistic equation.
36.	Wed, Nov 30	LL 27,30	HW 10 given. Parametric resonance.
37.	Fri, Dec 2	LL7 1-2	9. Elasticity theory. Displacement field. the strain tensor. The stress tensor.
38.	Mon, Dec 5	LL7 2-4	The stress tensor. Elastic energy. Elastic moduli (Hooke's law).
39.	Wed, Dec 7	LL7 4-5, 7	Elastic moduli (Hooke's law). Homogenious deformations. Equilibrium for isotropic bodies.
40.	Fri, Dec 9	LL7 7, 11-12	Equilibrium for isotropic bodies. Equilibrium for a plate.
41.	Mon, Dec 12	LL7 22	10. Dynamics of continuous systems. Elastic waves. 11. Final remarks: towards field theory and quantum mechanics.
42.	Mon, Dec 19	Room P-112	Solving problems in classical mechanics.
Final	Wed, Dec 21	8:00-10:30 AM	FINAL, P-112. Open book. Notes and textbooks are allowed. 4 problems.

Physics 540: Models solvable by Bethe Ansatz

Course description

Tentative Syllabus

Course requirements

Grading and exams

Main textbooks

Physics 540:
Models solvable by Bethe Ansatz