Details of PH5114 (Autumn 2026)
| Level: 5 | Type: Theory | Credits: 4.0 |
| Course Code | Course Name | Instructor(s) |
|---|---|---|
| PH5114 | Nonequilibrium Quantum Dynamics | Rangeet Bhattacharyya |
| Preamble |
|---|
| This course will introduce the theoretical, experimental, and computational tools used in general nonequilibrium quantum dynamics. Examples are drawn from magnetic resonance
techniques. |
| Syllabus |
|---|
| 1. Review of essential concepts: SU(2) algebra; Spin-1/2 and higher spins; Pauli matrices
and angular momentum operators; Tensor products and composite spin systems; Spin Hamiltonians: Zeeman interaction; Dipolar interaction; Hyperfine interaction; Time-dependent drive Hamiltonians. 2. Density Matrix Formalism: Pure vs mixed states; Liouville-von Neumann equation; Liouville space representation; Superoperators. 3. Two-Level Systems: Rabi oscillations; Rotating frame transformation; Interaction picture; Rotating wave approximation (RWA) 4. System-Bath Models: Environment as harmonic oscillator bath; Spin-boson model; Reduced density matrix; Partial trace; 5. Derivation of Quantum Master Equations: Born approximation; Markov approximation; Coarse-grained methods 6. Lindblad Equation: Completely positive trace-preserving maps; Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form; Physical interpretation of jump operators 7. Applications to Spin Systems: Relaxation ($T_1$); Dephasing ($T_2$); Amplitude damping; Pure dephasing; Steady states 8. Redfield Equation: Secular approximation; Comparison with Lindblad; Spectral densities; Validity regimes 9. Stochastic approaches: Quantum trajectories; Monte Carlo wavefunction method; Stochastic Liouville equation |
| Prerequisite |
|---|
| Intermediate and advanced quantum mechanics, Intermediate Mathematical Methods |
| References |
|---|
| References:
1. C. P. Slichters Principles of Magnetic Resonance 2. A. Abrahams Principles of Magnetic Resonance 3. Lidars notes on Open Quantum Systems |
Course Credit Options
| Sl. No. | Programme | Semester No | Course Choice |
|---|---|---|---|
| 1 | IP | 1 | Not Allowed |
| 2 | IP | 3 | Elective |
| 3 | MP | 1 | Not Allowed |
| 4 | MP | 3 | Not Allowed |
| 5 | MR | 1 | Not Allowed |
| 6 | MR | 3 | Not Allowed |
| 7 | MS | 3 | Not Allowed |
| 8 | MS | 5 | Not Allowed |
| 9 | MS | 7 | Not Allowed |
| 10 | MS | 9 | Elective |
| 11 | RS | 1 | Elective |
| 12 | RS | 2 | Elective |