Questions tagged [quantum-transport]
Quantum transport is the study of transport phenomena (the exchange of mass, energy, charge, or momentum in systems out of equilibrium) governed by quantum mechanics. In particular, this includes electron transport (electrical current flow) in micro- and nano-scale systems.
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Magnetic field dependence of resistance
Experimentally, under the application of an external perpendicular magnetic field, we observe a change in the longitudinal resistance. However, in the theoretical development starting from the Drude ...
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Feynman diagrams in quantum transport theory
I'm looking to find references that describe the role that Feynman diagrams play in quantum transport theory.
I have heard discussions where it is possible to just insert a self-energy loop into an ...
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104 views
Why Kubo formula can be applied to calculate conductivity?
It seems that Kubo formula is widely adopted to calculate conductivity, or at least Hall conductivity [for example, in the famous paper by TKNN: PRL 49 405-408 (1982)].
However, the derivation of ...
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Can we add the resistivity due to different scattering mechanisms?
Suppose there's a metal in which electrons interact with themselves and with the phonons. The hamiltonian might look like this
\begin{equation}
H= \sum_{k}\epsilon_k c^\dagger_k c_k + \sum_{k}\...
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How to calculate optical conductivity from numerical eigenstates of tight-binding model?
Let's say we have a 1D spatially inhomogeneous tight-binding model that does not have momentum as a good quantum number. We can numerically diagonalize it to get the spectrum and eigenstates. But how ...
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How to include the possiblity of Umklapp Scattering into transport calculations
I'm trying to calculate transport properties of a certain model with a Hamiltonian that has electron-electron interactions. I know that, in order to use the Boltzmann equation
\begin{equation}
0=\...
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How to write down the collision integral for any interaction in the Boltzmann equation?
I'm studying the Boltzmann equation
\begin{equation}
\Big[\frac{\partial}{\partial t}+\vec{v}\cdot\nabla_{r}+\frac{1}{m}\vec{f}\cdot\nabla_{v}\Big]f(v,r,t)=\frac{df}{dt}\Bigg|_{coll}
\end{equation}
...
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Energy of band of $d$-dimensional semiconductor when voltage $V$ is applied across
Let's say we have a one-dimensional semiconductor and I apply voltage V across it, I want to calculate the energy of a parabolic band, when a source and drain voltage is applied across it. I expect it ...
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About electrode self-energy and the relation between transmission functions and Green’s functions
I am reading Electronic Transport in Mesoscopic Systems by Supriyo Datta. I got stucked when deriving some formulas.
On page 147, the book says "see exercise E.3.3" when it gives the formula (3.5.18), ...
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Peierls phase in graphene
In the introduction of the paper presented here, a derivation of the Peierls phase is presented, using a Wannier base of eigenfunctions and the Kohn-Sham Hamiltonian. After it symbolises the hopping ...
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What is the best book to read for optimal mass transportation theory for students with physics background?
I need to read optimal mass transportation theory for my research. What is the best book to read. I am from physics background. How much mathematics and what sort of mathematics required prior to ...
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Self-averaging quantities in physics
This question is about self-averaging quantities in physics. Here is a link to the wikipedia page: https://en.wikipedia.org/wiki/Self-averaging.
I'm currently studying transmission through disordered ...
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Advected Dirac comb with random number of teeth which are born and die
I'm looking for a topic which I struggle to put into words. It's a reasonable consideration which I expect has been carefully studied. I hope someone can tell me the name of it and offer some guidance ...
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1answer
83 views
Demonstration that electric current at equilibrium is zero in crystals
As it is well known, electrons at equilibrium (no external field) do not conduct electric current, i.e.
$\int_{BZ} dk\,v_{k}\,f(\epsilon_k)=0$
where $f(\epsilon_k)$ is the Fermi-Dirac distribution
$...
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1answer
104 views
Comparing the Madelung and Groenewold-Moyal pictures of quantum mechanics
We can consider a dynamical theory to be a "transport theory" if it can be described entirely by a series of continuity equations of the form:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \left({...
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Energy and momentum conservation argument for electron-phonon transitions in Bilayer Graphene
I'm reading a paper which says that the interband transitions ($\pi_1^* \rightarrow \pi_2^*$) involving phonons at $q= 0 $ and $ q = K$ in Bilayer Graphene are prohibited by energy and momentum ...
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125 views
Kubo formula derivation
In the derivation of the Kubo formula for conductivty we write the total hamiltonian as $$H_{\text{tot}}=H_0+H_{\text{ext}}$$ where $$H_{\text{tot}}=H(A_0+A_{\text{ext}}),$$ $$H_0=H(A_0)$$ and $$H_{\...
