quantum_operator

Quantum operators (position moments, position, IPR) for dynamics simulations.

mqed.Lindblad.quantum_operator.excited_population_norm(state, *, Nmol: int) → float

Total excited-manifold population (sum over sites |1>...|N|).

mqed.Lindblad.quantum_operator.ipr_callable(t, state, *, Nmol)

Inverse participation ratio (IPR) at time t for a state (ket or density matrix).

\[\mathrm{IPR} = \frac{\sum_j |c_j|^4}{\left(\sum_j |c_j|^2\right)^2},\]

where c_j are site amplitudes (or populations for a density matrix) over the excited subspace.

mqed.Lindblad.quantum_operator.position_operator(dim: int, d_nm: float, Nmol: int, init_site_index: int) → qutip.Qobj

Position operator (single excitation), centered at the initial site x0.

\[\langle x \rangle = \mathrm{Tr}\big[(X - x_0 I) \, \rho\big].\]

mqed.Lindblad.quantum_operator.position_square_operator(dim: int, d_nm: float, Nmol: int, init_site_index: int) → qutip.Qobj

Second moment of position operator (single-excitation manifold).

\[ \begin{align}\begin{aligned}Basis: \quad |0\rangle \text{ (ground)}, \quad |1\rangle,...,|N\rangle \text{ (sites)}.\\Positions: \quad \text{ground}=0, \quad \text{site } j \text{ at } j \cdot d.\\\langle x^2 \rangle = \mathrm{Tr}\big[(X - x_0 I)^2 \, \rho\big].\end{aligned}\end{align} \]

mqed.Lindblad.quantum_operator.site_population_operator(dim: int, site: int) → qutip.Qobj

Projector onto site site (single excitation).

\[P_j = \quad |j\rangle \langle j|, \quad j=1,...,N\]

mqed.Lindblad.quantum_operator.x_shift2_conditional_callable(t, state, *, X_shift2: qutip.Qobj, Nmol: int) → float

Conditional <(X-x0I)^2> / P_exc, where P_exc is excited population.

mqed.Lindblad.quantum_operator.x_shift_conditional_callable(t, state, *, X_shift: qutip.Qobj, Nmol: int) → float

Conditional <X-x0I> / P_exc, where P_exc is excited population.