Commit ae060e78 by Adel Kara Slimane

### Update tutorial

parent c32ffee0
 ... ... @@ -4,7 +4,7 @@ Tutorial: Energy and heat transport The aim of this tutorial is to show how to simulate energy and heat transport with tKwant. The corresponding theoretical framework can be found in Ref [1] <#references>__. Readers who are not familiar with t-Kwant are invited to visit its documentation webpage _ first. Theory ------ ... ... @@ -12,7 +12,7 @@ In the following, we take :math:e=\hbar=1. In the presence of time-dependent electromagnetic fields (described by an electromagnetic scalar potential :math:V(\vec r, t) and an electromagnetic vector potential :math:\vec A(\vec r, t)), the Hamiltonian's expectation value is (in general) gauge dependent i.e. an electromagnetic gauge transformation does not leave its expectation value invariant. The gauge invariant energy operator :math:\hat ε is defined as being the kinetic energy operator plus any eventual stationary and physical scalar potential that is present from the remote past. The local energy density operator :math:\hat ε_i on site :math:i reads: The gauge invariant energy operator :math:\hat ε is defined as being the kinetic energy operator plus any stationary physical scalar potential that is present from the remote past. The local energy density operator :math:\hat ε_i on site :math:i reads: .. math:: ... ... @@ -114,11 +114,19 @@ We want to calculate the time dependent energy density on the site lat(0) (t lead[lat(0)] = 0 lead[lat.neighbors()] = - γ added_sites_left = builder.attach_lead(lead, add_cells=1) # Attach the left lead and add the first cell of the lead # (i.e. the site lat(-2)) to the central system. The added site # is returned by attach_lead() and stored in added_sites_left added_sites_left = builder.attach_lead(lead, add_cells=1) # Append lat(-1) to the list, to calculate the heat current between lat(-1) and lat(0) added_sites_left.append(lat(-1)) # Attach the right lead and add the first cell of the lead # (i.e. the site lat(2)) to the central system. The added site # is returned by attach_lead() and stored in added_sites_right added_sites_right = builder.attach_lead(lead.reversed(), add_cells=1) # Append lat(1) to the list, to calculate the heat current between lat(1) and lat(0) added_sites_right.append(lat(1)) ... ... @@ -144,8 +152,7 @@ The system is thus the following .. jupyter-execute:: #kwant.plotter.set_engine("matplotlib") kwant.plot(builder) kwant.plot(builder); The lists of sites added_sites_left and added_sites_right are used when declaring ~tkwantoperator.LeadHeatCurrent operator instances by giving them to the added_lead_sites parameter: ... ... @@ -267,9 +274,8 @@ Which gives the following plots: A python file containing all the above lines of code is available: :download:quantum_dot.py . It can be ran in parallel to shorten the simulation time, as explained in :ref:parallel-calculations References ---------- Reference --------- [1] A. Kara Slimane, P. Reck, G. Fleury, Simulating time-dependent thermoelectric transport in quantum systems __ ... ...
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