Flowchart of qrate/solvers.py

This document outlines the main data flow in qrate.solvers.

Flowchart

graph TD
    subgraph "Solver Construction"
        SS["solve_system"]
        SS_IN["Inputs: hamiltonian, leads, temperature, parity_op, system_parameters, lead_parameters"]
        MAT["Materialize Hamiltonian and lead matrices"]
        PD["parity_diag"]
        TM["compute_t_matrices"]
        OUT["Output: conductance function"]

        SS_IN --> SS
        SS --> MAT
        MAT --> PD
        PD --> TM
        TM --> OUT
    end

    subgraph "Runtime Evaluation"
        BIAS["biases"]
        GM["g_matrix"]
        CUR["current solver closure"]
        RATES["compute_rates"]
        MEQ["solve_master_equation"]
        G["conductance tensor"]

        BIAS --> GM
        GM --> CUR
        CUR --> RATES
        RATES --> MEQ
        MEQ --> CUR
        CUR --> GM
        GM --> G
    end

    OUT -.-> GM

Function Descriptions

solve_system

Constructs a callable conductance solver from a Hamiltonian, lead coupling matrices, temperature, and parity operator. The Hamiltonian and leads may be arrays or callables; callable inputs receive matching keys from system_parameters and lead_parameters.

The returned function maps a bias grid with shape (S, L) to a conductance tensor with shape (S, L, L).

parity_diag

Jointly diagonalizes the Hamiltonian and parity operator, preserving parity sectors before sorting states by energy.

compute_t_matrices

Transforms lead coupling matrices into the Hamiltonian eigenbasis and returns the removal and addition tunneling matrices.

compute_rates

Computes lead-resolved addition and removal rates for every bias point using Fermi-Dirac occupations.

solve_master_equation

Solves the steady-state rate equation for each bias point and returns occupations, currents, and the total transition matrix.

g_matrix

Computes the conductance tensor with central finite differences of the current solver.