Lorentz-Bath driver¶

Warning

This is a beta feature and may change in future versions.

The Lorentz-Bath driver implements a classical bright harmonic oscillator coupled to a bath of classical dark oscillators. It is provided by maxwelllink.mxl_drivers.python.models.LorentzBathModel and ships with MaxwellLink for reduced polaritonic-chemistry models where a collective molecular bright mode exchanges energy with dark molecular modes.

Note

The Lorentz-Bath driver advances the bright coordinate \(q_B\), its conjugate momentum \(p_B\), and bath coordinates \(q_j, p_j\) generated by the Hamiltonian

\[H = \frac{1}{2}\left(p_B - \sum_j k_j q_j\right)^2 + \frac{1}{2}\omega_0^2 q_B^2 - \mu_0 q_B\,\bigl(\widetilde{\mathbf{E}}(t)\cdot\mathbf{e}_i\bigr) + \sum_j\left(\frac{1}{2}\omega_j^2 q_j^2 + \frac{1}{2}p_j^2\right).\]

Here \(\mathbf{e}_i\) denotes the selected dipole orientation, \(k_j\) are bright-dark coupling coefficients, and \(\omega_j\) are bath-mode frequencies. The emitted dipole current returned to Maxwell’s equations is evaluated by:

\[\frac{d}{dt}\langle\boldsymbol{\mu}\rangle = \mu_0\left(p_B - \sum_j k_j q_j\right)\mathbf{e}_i.\]

Requirements¶

No additional packages are required beyond MaxwellLink’s dependencies.

Usage¶

Socket mode¶

mxl_driver --model lorentz_bath --port 31415 \
  --param "omega=0.242, mu0=187, orientation=2, num_bath=101, \
           bath_width=0.05, bath_form=lorentzian, bath_dephasing=0.002, \
           checkpoint=false, restart=false"

Non-socket mode¶

mxl.Molecule(
    driver="lorentz_bath",
    driver_kwargs={
        "omega": 0.242,
        "mu0": 187.0,
        "orientation": 2,
        "num_bath": 101,
        "bath_width": 0.05,
        "bath_form": "lorentzian",
        "bath_dephasing": 0.002,
    },
    # ...
)

Parameters¶

Name	Description
`omega`	Bright oscillator frequency \(\omega_0\) in atomic units. Default: `2.4188843e-1`, corresponding to `1.0` in Meep units when `time_units_fs=0.1`.
`mu0`	Dipole-coordinate coupling prefactor \(\mu_0\) in atomic units, so that the instantaneous bright-mode dipole is \(\mu(t)=\mu_0 q_B(t)\); scales the emitted source amplitude. Default: `1.870819866e2`, corresponding to `0.1` in Meep units when `time_units_fs=0.1`.
`orientation`	Dipole orientation: `0` couples to `E_x`, `1` to `E_y`, `2` to `E_z`. Default: `2`.
`num_bath`	Number of bath oscillators used by the convenient bath builder. Must be greater than `1`. Used only when `omega_bath` and `k_bath` are not both provided.
`bath_width`	Frequency width of the convenient bath distribution in atomic units. The bath frequencies are placed uniformly from `omega - 0.5bath_width` to `omega + 0.5bath_width`.
`bath_form`	Coupling-envelope form for the convenient bath builder. Supported values: `uniform`, `gaussian`, and `lorentzian`.
`bath_dephasing`	Bright-to-dark dephasing scale in atomic units used by the convenient bath builder to set the coupling coefficients \(k_j\). Default: `0.0`.
`bath_relaxation`	Direct bath-momentum relaxation rate in atomic units. When positive, bath momenta are damped by `exp(-bath_relaxation*dt)` each time step. Default: `0.0`.
`omega_bath`	Direct list of bath oscillator frequencies in atomic units. When supplied together with `k_bath`, this direct definition has priority over `num_bath`/`bath_width`/`bath_form`.
`k_bath`	Direct list of bright-dark coupling coefficients in atomic units. Must have the same length as `omega_bath`.
`p_initial`	Initial bright-mode momentum \(p_B\) in atomic units. Default: `0.0`.
`q_initial`	Initial bright-mode position \(q_B\) in atomic units. Default: `0.0`.
`p_bath_initial`	Initial bath momenta as a list with the same length as the bath. Defaults to zeros.
`q_bath_initial`	Initial bath positions as a list with the same length as the bath. Defaults to zeros.
`langevin_tau_au`	Optional Langevin thermostat damping time in atomic units. The thermostat is enabled during initialization when this value is provided and `temperature_au > 0`. Default: `None`.
`initializer`	Optional initializer. Supported value: `maxwell_boltzmann`, which samples bright and bath coordinates and momenta using `temperature_au`.
`temperature_au`	Temperature in atomic units used by the Langevin thermostat and `maxwell_boltzmann` initializer. Default: `0.0`.
`random_seed`	Random seed used by the initializer and thermostat. Default: `114514`.
`checkpoint`	When `True` write `lorentz_bath_checkpoint_id_<n>.npz` after each step. Default: `False`.
`restart`	When `True` resume from the latest checkpoint if present. Default: `False`.
`verbose`	When `True` print field values and oscillator diagnostics each step. Default: `False`.

Returned data¶

time_au - Simulation time in atomic units.
energy_au - Total half-step Hamiltonian energy in atomic units.
energy_lorentz_au - Bright oscillator contribution, including the bright-bath momentum-shift terms, in atomic units.
energy_bath_au - Bath oscillator energy in atomic units.
mux_au, muy_au, muz_au - Half-step dipole vector components (non-zero along the selected orientation) in atomic units.
mux_m_au, muy_m_au, muz_m_au - Full-step bright-mode dipole vector components in atomic units.
p_au - Full-step bright-mode momentum \(p_B\) in atomic units.
q_au - Full-step bright-mode position \(q_B\) in atomic units.

Notes¶

A bath definition is required. Provide either direct omega_bath and k_bath lists, or the convenient builder parameters num_bath, bath_width, and bath_form.
Direct omega_bath/k_bath settings have priority over the convenient bath builder.
The convenient bath builder currently places bath frequencies on an evenly spaced grid and supports uniform, Gaussian, and Lorentzian coupling envelopes. Use direct bath arrays for custom spectral densities.
This driver is a reduced classical model intended for studying bright-mode dephasing into dark molecular modes. For atomistic molecular dynamics, prefer the LAMMPS, DFTB+, or ASE drivers.