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jTWA.integrate

jTWA.integrate#

jTWA.integrate comprises all functionality that is required to evolve the system of interest in time.

jTWA.integrate.obtain_evolution(samples, hamiltonian, spin_operators, cfg)#

Stepper functionality to integrate the coupled equations of motion given by the Hamiltonian to the final time specified in cfg. First, the flow that is generated by the Hamiltonian is computed. Then, the samples are integrated along their flow lines using jTWA.integrate.integrate(). At times of interest that are separated by the interval cfg["simulationParameters"]["dtObs"], observables are read out and stored to a dictionary. This dictionary is returned once the final integration time is reached.

Args:

  • samples: A list of samples. The array should be of shape (\(N_{samples}\), \(N_{wells}\), \(N_{internal}\)).

  • hamiltonian: A function that returns the energy of a given single sample, given its complex conjugate, the sample itself as well as cfg.

  • spin_operators: A dictionary of the matrices that describe spin observables of interest along with their names.

  • cfg: The dictionary that contains the settings of the current run.

Returns:

  • obs: Dictionary that holds observables at specified times of interest.

jTWA.integrate.integrate(samples, flow, dt)#

(Compiled) Integrator that propagates the samples along their flow lines by the time step dt using a 4-th order RK-scheme described in integrate_single_sample().

Args:

  • samples: A list of samples. The array should be of shape (\(N_{samples}\), \(N_{wells}\), \(N_{internal}\)).

  • flow: The flow that is induced by the Hamiltonian.

  • dt: A small time step.

Returns:

  • samples: The propagated samples.

jTWA.integrate.integrate_single_sample(sample, flow, dt)#

4-th order RK-integrator that propagates a single sample along its flow by the time step dt.

Args:

  • sample: A single sample. The array should be of shape (\(N_{wells}\), \(N_{internal}\)).

  • flow: The flow that is induced by the Hamiltonian.

  • dt: A small time step.

Returns:

  • sample: The propagated sample.

jTWA.integrate.append_observables(key_to_use, samples, hamiltonian, spin_operators, stored_observables, t, cfg)#

Append observables to an existing array of observables in stored_observables.

Args:

  • key_to_use: A jax.random.PRNGKey that is used to mix each sample with Gaussian noise to simulate simultaneous readout.

  • samples: A list of samples. The array should be of shape (\(N_{samples}\), \(N_{wells}\), \(N_{internal}\)).

  • hamiltonian: The hamiltonian function that describes the system. Used to obtain energy expectation values.

  • spin_operators: A dictionary of the matrices that describe spin observables of interest along with their names.

  • stored_observables: A dictionary that is either empty or contains observable values from previous time steps.

  • t: The current simulation time.

  • cfg: The dictionary that contains the settings of the current run.

Returns:

  • stored_observables: The dictionary to which the new observables have been added.

jTWA.integrate.check_obs_save_condition(t, cfg, eps=0.1)#

Check whether observables should be computed and stored at the current time step.

Args:

  • t: The current simulation time.

  • cfg: The dictionary that contains the settings of the current run.

Returns:

  • A boolean indicating whether observables should be computed and stored or not.

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