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name: "dynamics-and-solvers" description: "QuTiP time-evolution, steady-state, time-dependent coefficient, and solver workflows." metadata: disco-role: operating disable-model-invocation: true license: BSD 3-Clause

Dynamics and solvers

Use this subskill when the task is about evolving states, solving master equations, computing steady states, building time-dependent coefficients, or choosing among QuTiP's solver families.

Read this subskill when the prompt mentions

• sesolve, mesolve, mcsolve, nm_mcsolve, ssesolve, smesolve
• steadystate, propagator, correlation, spectrum, floquet
• QobjEvo, coefficient, string coefficients, or runtime-compiled coefficients
• parallel_map, serial_map, loky_pmap, mpi_pmap
• solver options, QUTIP_NUM_PROCESSES, integrators, or time-dependent Hamiltonians and collapse operators

What to decide first

1. Is the system pure-state or density-matrix based?
2. Is the task time evolution, steady state, or a derived quantity such as a spectrum or correlation?
3. Is the Hamiltonian time-independent, list-form, or built with QobjEvo or coefficient?
4. Does the task need optional parallel helpers or accelerated steady-state backends?

Core workflow

• Start with the simplest solver that matches the physics: sesolve for pure states, mesolve for density matrices, steadystate for stationary solutions.
• Add collapse operators only when the model is open.
• Use QobjEvo or coefficient when the model has explicit time dependence.
• Check solver options and expected data types before increasing model size.
• If the task moves into PIQS, HEOM, transfer-tensor, or bath-model construction, hand it to specialized-open-systems.

Typical success signals

• The solver returns the expected Result or state object.
• Observables have the expected time-series length.
• Time-dependent coefficients evaluate numerically in the active environment.
• Optional parallel helpers fall back cleanly when extras are absent.

Boundaries

Use this subskill for solver mechanics and ordinary dynamics. Do not use it as the main route for:

• Basic Qobj construction or tensor algebra before the model exists; start in core-objects.
• PIQS, HEOM, transfer-tensor, or explicit bath/environment model design; switch to specialized-open-systems.
• Plotting or saving the solver result; switch to analysis-and-io after the solve.

Answer shape

When responding from this subskill, give:

1. The solver choice and why it matches the physics.
2. The expected forms of H, initial state, tlist, c_ops, e_ops, and args.
3. A minimal executable code snippet.
4. The validation signal, such as expectation-vector length, trace, or coefficient value.
5. The optional dependency or backend note when the route uses Cython, Loky, MPI, or MKL.

Validation hints

• Start with a two-level or tiny Hilbert-space example before scaling up.
• Check that time-dependent arguments are passed consistently through args.
• Compare against serial_map or a one-worker map when debugging parallel helpers.

Reference files

• references/api-reference.md for solver families, signatures, and the main option families.
• references/workflows.md for small end-to-end evolution and steady-state recipes.
• references/troubleshooting.md for coefficient compilation, solver-option, and backend issues.

Helper script

• scripts/solver_smoke.py runs a tiny evolution, steady-state, coefficient, and parallel-map smoke check.