"""Prepared population imbalance on a two-state rate matrix.
Approach to equilibrium and adaptive kinetic Monte Carlo are the same
experiment on different generators. This module propagates the rate matrix.
A cluster has no box length, so the decay time is not turned into a
conductivity.
"""
import math
# eV/K. The same constant the tunnelling rates use.
K_B = 8.617333262145177e-5
[docs]
def arrhenius_rate(barrier_eV, temperature_K, prefactor_hz=1.0e12):
"""Harmonic transition-state rate in Hz."""
if temperature_K <= 0.0 or prefactor_hz <= 0.0 or barrier_eV < 0.0:
raise ValueError("a rate needs a positive temperature, a positive prefactor, and a non-negative barrier")
return prefactor_hz * math.exp(-barrier_eV / (K_B * temperature_K))
[docs]
def prepared_imbalance(forward_rate, reverse_rate):
"""Decay time, in seconds, of a prepared population imbalance.
The two-state generator relaxes as ``exp(-t/tau)`` with
``tau = 1/(k_f + k_b)``.
"""
total = forward_rate + reverse_rate
if not total > 0.0 or not math.isfinite(total):
raise ValueError("a two-state gap needs a positive total rate")
return 1.0 / total
[docs]
def survival(time_s, decay_time_s):
"""Remaining imbalance ``exp(-t/tau)``."""
if decay_time_s <= 0.0 or time_s < 0.0:
raise ValueError("survival needs a positive decay time and a non-negative time")
return math.exp(-time_s / decay_time_s)
[docs]
def recurrence_time(rate):
"""Mean return time of a saddle that comes back to the same basin.
That process has no population mode.
"""
if not rate > 0.0 or not math.isfinite(rate):
raise ValueError("a recurrence needs a positive rate")
return 1.0 / rate
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