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Merge pull request #119 from nwlambert/fix-dead-link
Update heom 5b deadlink to resolve markdown test failure
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tutorials-v4/time-evolution/002_larmor-precession.md

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This notebook guides you through the process of setting up a Schrödinger
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equation in QuTiP and using the corresponding solver to obtain the time
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evolution. We will investigate the example of the Larmor precession to
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explore the functionality of [`qutip.sesolve()`](https://qutip.readthedocs.io/en/latest/apidoc/functions.html?highlight=sesolve#module-qutip.sesolve).
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explore the functionality of [`qutip.sesolve()`](https://qutip.readthedocs.io/en/latest/apidoc/solver.html#module-qutip.solver.sesolve).
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You can also find more on time evolutions with QuTiP [here](https://qutip.readthedocs.io/en/latest/guide/guide-dynamics.html).
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## Simulation with varying magnetic field
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Above we passed a constant Hamiltonian to `sesolve`. In QuTiP these constant operators are represented by `Qobj`. However, `sesolve` can also take time-dependent operators as an argument, which are represented by [`QobjEvo`](https://qutip.readthedocs.io/en/latest/apidoc/classes.html?highlight=qobjevo#qutip.QobjEvo) in QuTiP. In this section we define the magnetic field with a linear and a periodic field strength, and observe the changes in the expecation value of $\sigma_y$.
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Above we passed a constant Hamiltonian to `sesolve`. In QuTiP these constant operators are represented by `Qobj`. However, `sesolve` can also take time-dependent operators as an argument, which are represented by [`QobjEvo`](https://qutip.readthedocs.io/en/latest/apidoc/time_dep.html#qutip.core.cy.qobjevo.QobjEvo) in QuTiP. In this section we define the magnetic field with a linear and a periodic field strength, and observe the changes in the expecation value of $\sigma_y$.
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You can find more information on `QobjEvo` in [this notebook](https://nbviewer.jupyter.org/github/qutip/qutip-notebooks/blob/master/examples/qobjevo.ipynb).
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We start by defining two functions for the field strength of the magnetic field. To be passed on to `QobjEvo` the functions need two arguments: the times and optional arguments.

tutorials-v4/time-evolution/003_qubit-dynamics.md

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### Introduction
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In this notebook we will explore the dynamics of a single-qubit interacting with an environment. The evolution of the qubit state is governed by the Master equation. We will make use of the master equation solver `qutip.mesolve` implemented in qutip, to obtain the time-evolution of the qubit for different settings.
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You can read more about the master equation solver (and the theory behind it) in the [QuTiP docs](https://qutip.readthedocs.io/en/latest/apidoc/functions.html?highlight=sesolve#module-qutip.sesolve).
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You can read more about the master equation solver (and the theory behind it) in the [QuTiP docs](https://qutip.readthedocs.io/en/latest/apidoc/time_dep.html#qutip.core.cy.qobjevo.QobjEvo).
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### Import
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Here we import the required modules for this example.

tutorials-v5/heom/heom-5b-fermions-discrete-boson-model.md

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Here we model a single fermion coupled to two electronic leads or reservoirs (e.g., this can describe a single quantum dot, a molecular transistor, etc), also coupled to a discrete bosonic (vibronic) mode.
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Note that in this implementation we primarily follow the definitions used by Christian Schinabeck in his Dissertation https://opus4.kobv.de/opus4-fau/files/10984/DissertationChristianSchinabeck.pdf and related publications. In particular this example reproduces some results from https://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.201407
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Note that in this implementation we primarily follow the definitions used by Christian Schinabeck in his Dissertation https://open.fau.de/items/36fdd708-a467-4b59-bf4e-4a2110fbc431 and related publications. In particular this example reproduces some results from https://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.201407
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Notation:
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tutorials-v5/time-evolution/002_larmor-precession.md

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This notebook guides you through the process of setting up a Schrödinger
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equation in QuTiP and using the corresponding solver to obtain the time
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evolution. We will investigate the example of the Larmor precession to
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explore the functionality of [`qutip.sesolve()`](https://qutip.readthedocs.io/en/latest/apidoc/functions.html?highlight=sesolve#module-qutip.sesolve).
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explore the functionality of [`qutip.sesolve()`](https://qutip.readthedocs.io/en/latest/apidoc/solver.html#module-qutip.solver.sesolve).
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You can also find more on time evolutions with QuTiP [here](https://qutip.readthedocs.io/en/latest/guide/guide-dynamics.html).
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## Simulation with varying magnetic field
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Above we passed a constant Hamiltonian to `sesolve`. In QuTiP these constant operators are represented by `Qobj`. However, `sesolve` can also take time-dependent operators as an argument, which are represented by [`QobjEvo`](https://qutip.readthedocs.io/en/latest/apidoc/classes.html?highlight=qobjevo#qutip.QobjEvo) in QuTiP. In this section we define the magnetic field with a linear and a periodic field strength, and observe the changes in the expecation value of $\sigma_y$.
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Above we passed a constant Hamiltonian to `sesolve`. In QuTiP these constant operators are represented by `Qobj`. However, `sesolve` can also take time-dependent operators as an argument, which are represented by [`QobjEvo`](https://qutip.readthedocs.io/en/latest/apidoc/time_dep.html#qutip.core.cy.qobjevo.QobjEvo) in QuTiP. In this section we define the magnetic field with a linear and a periodic field strength, and observe the changes in the expecation value of $\sigma_y$.
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You can find more information on `QobjEvo` in [this notebook](https://nbviewer.jupyter.org/github/qutip/qutip-notebooks/blob/master/examples/qobjevo.ipynb).
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We start by defining two functions for the field strength of the magnetic field. To be passed on to `QobjEvo` the functions need two arguments: the times and optional arguments.

tutorials-v5/time-evolution/003_qubit-dynamics.md

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### Introduction
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In this notebook we will explore the dynamics of a single-qubit interacting with an environment. The evolution of the qubit state is governed by the Master equation. We will make use of the master equation solver `qutip.mesolve` implemented in qutip, to obtain the time-evolution of the qubit for different settings.
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You can read more about the master equation solver (and the theory behind it) in the [QuTiP docs](https://qutip.readthedocs.io/en/latest/apidoc/functions.html?highlight=sesolve#module-qutip.sesolve).
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You can read more about the master equation solver (and the theory behind it) in the [QuTiP docs](https://qutip.readthedocs.io/en/latest/guide/dynamics/dynamics-master.html).
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### Import
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Here we import the required modules for this example.

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