Source code for qutip.solver.mesolve

"""
This module provides solvers for the Lindblad master equation and von Neumann
equation.
"""

__all__ = ['mesolve', 'MESolver']

import numpy as np
from time import time
from .. import (Qobj, QobjEvo, isket, liouvillian, ket2dm, lindblad_dissipator)
from ..core import stack_columns, unstack_columns
from ..core.data import to
from .solver_base import Solver, _solver_deprecation
from .sesolve import sesolve, SESolver
from ._feedback import _QobjFeedback, _DataFeedback


[docs]def mesolve(H, rho0, tlist, c_ops=None, e_ops=None, args=None, options=None, **kwargs): """ Master equation evolution of a density matrix for a given Hamiltonian and set of collapse operators, or a Liouvillian. Evolve the state vector or density matrix (``rho0``) using a given Hamiltonian or Liouvillian (``H``) and an optional set of collapse operators (``c_ops``), by integrating the set of ordinary differential equations that define the system. In the absence of collapse operators the system is evolved according to the unitary evolution of the Hamiltonian. The output is either the state vector at arbitrary points in time (``tlist``), or the expectation values of the supplied operators (``e_ops``). If e_ops is a callback function, it is invoked for each time in ``tlist`` with time and the state as arguments, and the function does not use any return values. If either ``H`` or the Qobj elements in ``c_ops`` are superoperators, they will be treated as direct contributions to the total system Liouvillian. This allows the solution of master equations that are not in standard Lindblad form. **Time-dependent operators** For time-dependent problems, ``H`` and ``c_ops`` can be a :obj:`.QobjEvo` or object that can be interpreted as :obj:`.QobjEvo` such as a list of (Qobj, Coefficient) pairs or a function. **Additional options** Additional options to mesolve can be set via the ``options`` argument. Many ODE integration options can be set this way, and the ``store_states`` and ``store_final_state`` options can be used to store states even though expectation values are requested via the ``e_ops`` argument. Notes ----- When no collapse operator are given and the `H` is not a superoperator, it will defer to :func:`sesolve`. Parameters ---------- H : :obj:`.Qobj`, :obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format. Possibly time-dependent system Liouvillian or Hamiltonian as a Qobj or QobjEvo. List of [:obj:`.Qobj`, :obj:`.Coefficient`] or callable that can be made into :obj:`.QobjEvo` are also accepted. rho0 : :obj:`.Qobj` initial density matrix or state vector (ket). tlist : *list* / *array* list of times for :math:`t`. c_ops : list of (:obj:`.QobjEvo`, :obj:`.QobjEvo` compatible format) Single collapse operator, or list of collapse operators, or a list of Liouvillian superoperators. None is equivalent to an empty list. e_ops : list of :obj:`.Qobj` / callback function, optional Single operator or list of operators for which to evaluate expectation values or callable or list of callable. Callable signature must be, `f(t: float, state: Qobj)`. See :func:`expect` for more detail of operator expectation. args : dict, optional dictionary of parameters for time-dependent Hamiltonians and collapse operators. options : dict, optional Dictionary of options for the solver. - | store_final_state : bool | Whether or not to store the final state of the evolution in the result class. - | store_states : bool, None | Whether or not to store the state vectors or density matrices. On `None` the states will be saved if no expectation operators are given. - | normalize_output : bool | Normalize output state to hide ODE numerical errors. - | progress_bar : str {'text', 'enhanced', 'tqdm', ''} | How to present the solver progress. 'tqdm' uses the python module of the same name and raise an error if not installed. Empty string or False will disable the bar. - | progress_kwargs : dict | kwargs to pass to the progress_bar. Qutip's bars use `chunk_size`. - | method : str ["adams", "bdf", "lsoda", "dop853", "vern9", etc.] | Which differential equation integration method to use. - | atol, rtol : float | Absolute and relative tolerance of the ODE integrator. - | nsteps : int | Maximum number of (internally defined) steps allowed in one ``tlist`` step. - | max_step : float | Maximum lenght of one internal step. When using pulses, it should be less than half the width of the thinnest pulse. Other options could be supported depending on the integration method, see `Integrator <./classes.html#classes-ode>`_. Returns ------- result: :obj:`.Result` An instance of the class :obj:`.Result`, which contains a *list of array* ``result.expect`` of expectation values for the times specified by ``tlist``, and/or a *list* ``result.states`` of state vectors or density matrices corresponding to the times in ``tlist`` [if ``e_ops`` is an empty list of ``store_states=True`` in options]. """ options = _solver_deprecation(kwargs, options) H = QobjEvo(H, args=args, tlist=tlist) c_ops = c_ops if c_ops is not None else [] if not isinstance(c_ops, (list, tuple)): c_ops = [c_ops] c_ops = [QobjEvo(c_op, args=args, tlist=tlist) for c_op in c_ops] use_mesolve = len(c_ops) > 0 or (not rho0.isket) or H.issuper if not use_mesolve: return sesolve(H, rho0, tlist, e_ops=e_ops, args=args, options=options) solver = MESolver(H, c_ops, options=options) return solver.run(rho0, tlist, e_ops=e_ops)
[docs]class MESolver(SESolver): """ Master equation evolution of a density matrix for a given Hamiltonian and set of collapse operators, or a Liouvillian. Evolve the density matrix (`rho0`) using a given Hamiltonian or Liouvillian (`H`) and an optional set of collapse operators (`c_ops`), by integrating the set of ordinary differential equations that define the system. If either `H` or the Qobj elements in `c_ops` are superoperators, they will be treated as direct contributions to the total system Liouvillian. This allows the solution of master equations that are not in standard Lindblad form. Parameters ---------- H : :obj:`.Qobj`, :obj:`.QobjEvo` Possibly time-dependent system Liouvillian or Hamiltonian as a Qobj or QobjEvo. List of [:obj:`.Qobj`, :obj:`.Coefficient`] or callable that can be made into :obj:`.QobjEvo` are also accepted. c_ops : list of :obj:`.Qobj`, :obj:`.QobjEvo` Single collapse operator, or list of collapse operators, or a list of Liouvillian superoperators. None is equivalent to an empty list. options : dict, optional Options for the solver, see :obj:`MESolver.options` and `Integrator <./classes.html#classes-ode>`_ for a list of all options. Attributes ---------- stats: dict Diverse diagnostic statistics of the evolution. """ name = "mesolve" _avail_integrators = {} solver_options = { "progress_bar": "", "progress_kwargs": {"chunk_size":10}, "store_final_state": False, "store_states": None, "normalize_output": True, 'method': 'adams', } def __init__(self, H, c_ops=None, *, options=None): _time_start = time() if not isinstance(H, (Qobj, QobjEvo)): raise TypeError("The Hamiltonian must be a Qobj or QobjEvo") c_ops = c_ops or [] c_ops = [c_ops] if isinstance(c_ops, (Qobj, QobjEvo)) else c_ops for c_op in c_ops: if not isinstance(c_op, (Qobj, QobjEvo)): raise TypeError("All `c_ops` must be a Qobj or QobjEvo") self._num_collapse = len(c_ops) rhs = H if H.issuper else liouvillian(H) rhs += sum(c_op if c_op.issuper else lindblad_dissipator(c_op) for c_op in c_ops) Solver.__init__(self, rhs, options=options) def _initialize_stats(self): stats = super()._initialize_stats() stats.update({ "solver": "Master Equation Evolution", "num_collapse": self._num_collapse, }) return stats
[docs] @classmethod def StateFeedback(cls, default=None, raw_data=False, prop=False): """ State of the evolution to be used in a time-dependent operator. When used as an args: ``QobjEvo([op, func], args={"state": MESolver.StateFeedback()})`` The ``func`` will receive the density matrix as ``state`` during the evolution. Parameters ---------- default : Qobj or qutip.core.data.Data, default : None Initial value to be used at setup of the system. prop : bool, default : False Set to True when computing propagators. The default with take the shape of the propagator instead of a state. raw_data : bool, default : False If True, the raw matrix will be passed instead of a Qobj. For density matrices, the matrices can be column stacked or square depending on the integration method. """ if raw_data: return _DataFeedback(default, open=True, prop=prop) return _QobjFeedback(default, open=True, prop=prop)