Fewest-Switches Surface Hopping

The qc_lab.algorithms.FewestSwitchesSurfaceHopping class implements Tully’s Fewest-Switches Surface Hopping (FSSH) dynamics algorithm according to Hammes-Schiffer 1994.

Settings

FewestSwitchesSurfaceHopping settings

Setting name (type)	Description	Default value
fssh_deterministic (bool)	If True the algorithm uses a deterministic representation of the initial state by propagating all possible initial active surfaces. If False, it samples the initial active surface according to the adiabatic populations.	False
gauge_fixing (int=0,1,2)	The level of gauge fixing to employ on the eigenvectors at each timestep. (0: adjust only the sign, 1: adjust the sign and phase using the overlap with the previous timestep, 2: adjust the sign and phase by calculating the derivative couplings.)	0

Initial State

The FSSH algorithm requires an initial diabatic wavefunction called wf_db which is a complex NumPy array with dimension sim.model.constants.num_quantum_states. For example:

sim.state.wf_db = np.array([1, 0], dtype=complex)

Output Variables

The following table lists the default output variables for the FewestSwitchesSurfaceHopping class.

FewestSwitchesSurfaceHopping Output Variables

Variable name	Description
classical_energy	Energy in the classical subsystem
quantum_energy	Energy in the quantum subsystem
dm_db	Diabatic density matrix

Example

The following example demonstrates how to run a mean-field simulation for a spin-boson model using all default settings.

import numpy as np
from qc_lab import Simulation # import simulation class
from qc_lab.models import SpinBoson # import model class
from qc_lab.algorithms import FewestSwitchesSurfaceHopping # import algorithm class
from qc_lab.dynamics import serial_driver # import dynamics driver

sim = Simulation()
sim.model = SpinBoson()
sim.algorithm = FewestSwitchesSurfaceHopping()
sim.state.wf_db= np.array([1, 0], dtype=complex)
data = serial_driver(sim)