We review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be on transport coefficients, such as conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a non-equilibrium almost-stationary state (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual double-commutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately defined spin conductivities, which are still explicit but more involved. Certain “Kubo-like” terms in these formulas are also shown to agree with the corresponding contributions to the spin conductance. In addition to that, we employ similar techniques to show a new result, namely that even in systems with non-conserved spin, there is no generation of spin torque, that is, the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field.

From charge to spin: Analogies and differences in quantum transport coefficients / Marcelli, Giovanna; Monaco, Domenico. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 63:7(2022), p. 072102. [10.1063/5.0089786]

From charge to spin: Analogies and differences in quantum transport coefficients

Giovanna Marcelli
;
Domenico Monaco
2022

Abstract

We review some recent results from the mathematical theory of transport of charge and spin in gapped crystalline quantum systems. The emphasis will be on transport coefficients, such as conductivities and conductances. As for the former, those are computed as appropriate expectations of current operators in a non-equilibrium almost-stationary state (NEASS), which arises from the perturbation of an equilibrium state by an external electric field. While for charge transport the usual double-commutator Kubo formula is recovered (also beyond linear response), we obtain formulas for appropriately defined spin conductivities, which are still explicit but more involved. Certain “Kubo-like” terms in these formulas are also shown to agree with the corresponding contributions to the spin conductance. In addition to that, we employ similar techniques to show a new result, namely that even in systems with non-conserved spin, there is no generation of spin torque, that is, the spin torque operator has an expectation in the NEASS which vanishes faster than any power of the intensity of the perturbing field.
2022
Quantum hall effect; adiabatic process; spin-orbit interactions; linear response
01 Pubblicazione su rivista::01a Articolo in rivista
From charge to spin: Analogies and differences in quantum transport coefficients / Marcelli, Giovanna; Monaco, Domenico. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - 63:7(2022), p. 072102. [10.1063/5.0089786]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1650822
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