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- W4297890307 abstract "We consider non-interacting particles subject to a fixed external potential $V$ and a self-generated magnetic field $B$. The total energy includes the field energy $beta int B^2$ and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter $beta$ tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical asymptotics, $hto0$, of the total ground state energy $E(beta, h, V)$. The relevant parameter measuring the field strength in the semiclassical limit is $kappa=beta h$. We are not able to give the exact leading order semiclassical asymptotics uniformly in $kappa$ or even for fixed $kappa$. We do however give upper and lower bounds on $E$ with almost matching dependence on $kappa$. In the simultaneous limit $hto0$ and $kappatoinfty$ we show that the standard non-magnetic Weyl asymptotics holds. The same result also holds for the spinless case, i.e. where the Pauli operator is replaced by the Schrodinger operator." @default.
- W4297890307 created "2022-10-01" @default.
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- W4297890307 date "2011-05-03" @default.
- W4297890307 modified "2023-10-18" @default.
- W4297890307 title "Stability and semiclassics in self-generated fields" @default.
- W4297890307 doi "https://doi.org/10.48550/arxiv.1105.0506" @default.
- W4297890307 hasPublicationYear "2011" @default.
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