Chapter 9: More on Thermostats

Question 1

Andersen Thermostat

(Overview)

Answer 1

• system stochastically coupled to heat bath at frequency ν
  
  • selected particle experience collisions with frequency ν
  • move system from one constant energy shell to another
• collisions uncorrelated → distribution of ∆t between collisions is Poisson process

Question 2

Andersen Thermostat

(Algorithm)

Answer 2

1. Initial conditions {r^N(0),p^N(0)} → integrate for ∆t
2. Select particles with probability ν∆t to collide with heat bath
3. Selected particles get velocity drawn from Boltzmann distribution

Question 3

Andersen Thermostat

(Notes)

Answer 3

• stochastic collisions disturb dunamics → bad for measuring dynamic properties
• static properties are unaffected

Question 4

Nosé-Hoover Thermostat

(Overview)

Answer 4

• extended Lagrangian approach
• deterministic equations of motion
• s, Q parameters couple system to virtual reservoirr by extending degrees of freedom
• certain choice are made (Nosé-Hoover formalism: L = 3N) gives

Question 5

Nosé-Hoover Thermostat

(Notes)

Answer 5

• Q → ∞ gives microcanonical ensemble
• smooth, deterministic, time-reversible, but nearly periodic temperature fluctuations
• NVE safest for dunamic propertoes