1. Fluctuation-Induced Force as constrained probability
• Review of Gaussian probability distributions
• Correlations in free field theory
• Dipole-dipole FIF in three dimensions
• Different approaches to FIF in one dimension
  • Zeta-function regularization
  • Table of zeta-functions and derivatives
• Quantum Casimir force in one dimension
• Thermal Casimir force in two dimensions
• Thermal Casimir force in three dimensions
• Quantum Casimir force in three dimensions
2. A plethora of FIF:
• Casimir force in QED: Theory & Experiment
• Casimir force of Critical fluctuations: Oil-water mixtures
• Casimir force of Goldstone modes: Superfluid films
• Membranes inclusions: Forces between inclusions

(Notes for lectures 1-2)

1. Scaling of   FIF with shape and dimension
• Casimir and Casimir-Polder interactions
• General compact shapes
• Scattering approach
• Cylinder-plate force
• Scale-Invariant Shapes: Wedges and cones
2. Entropic force from polymers
• Polymer force on conical tip:  Attractive and repulsive surfaces, and universal amplitudes
• Phantom polymers: Exact results for force amplitude at and beyond adsorption transition
• Self-avoiding polymers: Numerical results, ε-expansions, star polymers
• Scale-free boundary conditions
3. Casimir and Casimir-Polder interaction

• Stiction in MEMS
• Repulsion/Levitation(?) Boundary effects (fluids, meta-materials, ...)
• Repulsion/Levitation? Shapes (spheres, pistons, ...) 
• Earnshaw's theorem in electrostatics and for fluctuation-induced forces

(Notes for lectures 3-4)

1. Origins of scale invariance
• Tuning to criticality
• Goldstone modes of broken continuous symmetry
• Conservation laws in non-equilibrium dynamics
2. Generic scale invariance
• Anisotropy
• Fluctuations in confinement
3. Assumption of local equilibrium
• Stochastic hydrodynamics
• Diffusive pressure

(Notes for lecture 5)

1. Transient FIF in active matter
• Examples of active particles
• Model B dynamics for conserved density
• Transient force between plates
• Transient force between spheres
2. Simulations
• Active Brownian particles
• Forces from mean density variations
• Force from fluctuations
3. Non-equilibrium Quantum Electrodynamics
• Breakdown of Stefan-Boltzmann law & Rytov's "fluctuational QED"
• Heat radiation and transfer: The near field regime
• Nonequilibrium force: Force, levitation and propulsion 
4. Motion and fluctuations
• Dynamic phenomena: Rotating object
• Anomalous wandering of classical particle in a quantum bath

(Notes for lecture 6)

Last update 8/31/18 by M. Kardar