Bangalore School on Statistical Physics - VIII
Course outlines

Course 2:  Critical dynamics by Uwe C Täuber (Virginia Tech, USA)

  1. Near-equilibrium critical dynamics: relaxational kinetics:
    phase transitions and critical phenomena, scaling form of free energy and correlation functions, critical exponents, critical slowing-down and dynamic scaling, relaxational models A / B for non-conserved / conserved order parameter.
     
  2. Non-equilibrium critical relaxation, coupling to conserved modes: 
    critical initial slip and aging scaling, non-equilibrium perturbations, coupling to conserved energy density (models C / D), reversible mode couplings, isotropic ferromagnets (model J): critical scaling, spin waves in ordered phase.
     
  3. Driven systems displaying generic scale invariance:
    driven lattice gas (DDS) and noisy Burgers equation, non-equilibrium phase transition in the driven Ising lattice gas (KLS model), driven interfaces and KPZ equation, roughening transition, directed polymer mapping, conserved KPZ.
     
  4. Scale invariance and phase transitions in reaction-diffusion systems:
    depletion zones in diffusion-limited pair annihilation (A + A -> 0), segregation in two-species annihilation (A + B -> 0), active-to-absorbing state transitions and directed percolation, dynamic isotropic percolation.
     
  5. Fluctuation effects and pattern formation in population dynamics:
    spatial Lotka-Volterra predator-prey competition: noise-induced structures and extinction, species coexistence in cyclic competition models, connection with complex Ginzburg-Landau equation.

References:
U.C.T., Critical dynamics - A field theory approach to equilibrium and non-equilibrium scaling behavior'', 498 pages, Cambridge University Press (Cambridge, March 2014), ISBN 9780521842235
Link

U.C.T., Phase transitions and scaling in systems far from equilibrium, Annual Review of Condensed Matter Physics 8, 14 -- 1-26 (2017)
Link

 

Course 3: Thermalization in quantum systems by Subroto Mukerjee (IISc, Bangalore)

Lecture 1: Recap of classical stat. mech: phase space, ergodicity, Boltzmannian and Gibbsian viewpoints. Relation between ergodicity and thermalization. Notion of MAcroscopic Thermal Equilibirum (MATE) and MIcroscopic Thermal Equilibirum (MITE). Quantum systems: Hilbert space as phase space, density matrices, reduced density matrices and entanglement. 

Lecture 2: Chaos in quantum systems. Integrable and non-integrable systems. Berry's conjecture(s). Random Matrix Theory (RMT) and level spacing statistics. Random energy eigenvectors and operator expectation values.

Lecture 3: Randomness and the MATE version of the Eigenstate Thermalization Hypothesis (ETH). Dephasing, operator expectation values and fluctuations. The special role of energy eigenstates in thermalization. Verification of ETH in various quantum systems.

Lecture 4: Canonical typicality and subsystems. The MITE version of ETH. Verification of MITE ETH in quantum systems. MITE implies MATE. Subsystem thermalization by entanglement with a bath. Scaling of entanglement entropy and its time evolution.

Lecture 5: Failure of ETH: Many Body Localization (MBL). Single particle (Anderson) localization vs. MBL. Localization in Fock space. Entanglement in MBL systems. Conserved charges and entanglement dynamics.

 

Course 4: Non-equilibrium statistical physics: Introductory examples by Sidney Redner (Santa Fe Institute, USA)

Topics to be covered:

  1. Aggregation Kinetics:
    Master equation, Solution of elementary models, Gelation, Scaling approach, Aggregation with input
     
  2. Adsorption Kinetics:
    Random sequential adsorption and coverage kinetics, Adsorption/desorption, Applications.
     
  3. Coarsening Kinetics:
    Time-dependent Ising model, Time-Dependeng Ginzburg-Landau equation, Lifshitz-Slyazov coarsening.
     
  4. Population Dynamics:
    Two-species reactions (competition, symbiosis, prey-predator), Epidemic models, Discrete reactions (birth & birth/death).
     
  5. Kinetic Approach to Complex Networks:
    Erdos Renyi Network, Random Recursive Tree, Preferential Attachment Networks

 

Book Reference: Paul Krapivsky, Eli Ben-Naim and Sidney Redner, “A Kinetic View of Statistical Physics”.

 

Course 5: Conformal field theory and statistical mechanics by John Cardy (UC Berkeley, USA)

Outline: Lectures on conformal invariance and statistical mechanics.

  1. Scale and conformal invariance
  • general ideas about the continuum limit of lattice models
  • scale covariance of correlation functions at a critical point
  • (naive) generalization to conformal covariance
  • finite-size scaling on the cylinder
  • operator product expansion
  1. The gaussian model
  • correlators in the gaussian model
  • Coulomb gas: electric and magnetic scaling operators
  • spectrum on the cylinder
  1. Role of the stress tensor
  • definition of the stress tensor
  • conformal Ward identity
  • spectrum on the cylinder
  • Virasoro algebra and its representations
  • null states and minimal CFTs
  1. Lattice models and coulomb gas
  • lattice O(n) and Q-state Potts models and their loop gas formu-lation
  • lattice ADE models and their loop formulation
  • mapping to Coulomb gas
  1. Schramm-Loewner Evolution
  • chordal curves and lattice exploration process
  • Loewner evolution and conformally invariant curves
  • a sample SLE computation
  • relation to CFT null states

 

Course 7: Statistical physics of active matter by Sriram Ramaswamy (IISc, Bangalore)

Lecture 1: Introduction, framework and first results

  • Definition and phenomena; why; patterns + mechanics; prehistory
  • Realisations of active matter: living, extracted, artificial
  • Building active dynamics: coupled Langevin, off-diagonal Onsager
  • Particles vs fields; scalar, polar, apolar, translational, chiral;
  • Dynamical “ensembles”: dry vs wet
  • Minimal polar active system: Vicsek’s microscopic model, LRO in d=2
  • Slow variables, Toner & Tu’s coarse-grained model: linear results

Lecture 2: Dry active matter – polar and apolar

  • Toner-Tu field theory: nonlinearities → long-range order
  • Apolar order -- the active nematic: surprises from linear theory
  • Topological defects in active nematics
  • Density instabilities and the character of the flocking transitions
  • Experiments on the flocking transition

Lecture 3: Active matter in a fluid: living liquid crystal hydrodynamics

  • The hydrodynamics of active liquid crystals
  • Consequences: modes, spontaneous flow, fluctuations, rheology
  • Some applications to living-cell biology
  • Statistical mechanics of confined active fluids

Lecture 4: Scalar active matter

  • Minimal Langevin models for active systems
  • Persistent motion → condensation without attraction
  • Pressure in active matter

Lecture 5: (a) From microscopic models to stochastic PDEs; (b) outlook

  • Self-propelled particles, motor-filament systems
  • Vicsek/Langevin → Boltzmann/Fokker-Planck → deterministic PDEs
  • Technical issues; multiplicative noise
  • Open questions

References: