Riv. Mat. Univ. Parma, Vol. 15, No. 1, 2024

Luigi Barletti[a]

Quantum corrections to drift-diffusion equations in graphene with smoothed energy-band

Pages: 91-106
Received: 7 June 2023
Accepted in revised form: 12 december 2023
Mathematics Subject Classification: 76Y05, 35Q40, 82D37.
Keywords: Graphene, quantum diffusion, subleading corrections.
Author address:
[a]: Università degli Studi di Firenze, Dipartimento di Matematica e Informatica ''U. Dini'', Viale Morgagni 67/A, Firenze, 50134, Italia

This research was partially supported by GNFM-INdAM (National Group for Mathematical Physics).

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Abstract: Quantum corrections to the semiclassical drift-diffusion equation are obtained for electrons in graphene with a regularized energy-band. The derivation starts from the single-particle, single-band Wigner equation and exploits the quantum maximum entropy principle together with the classical Chapman-Enskog method. The functional calculus in phase-phase space is then used to expand the model to second order in the scaled Planck's constant. The model is shown to be singular in the limit where the regularization parameter goes to zero.

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