Применение двойного квантования в диамагнетизме Ландау

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И.Н. Алиев, М.Ю. Докукин, З.А. Самедова
26 ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 4
APPLICATION OF DOUBLE QUANTIZATION IN LANDAU DIAMAGNETISM
I.N. Aliev
Dokukin
Z.A. Samedova
Bauman Moscow State Technical University, Moscow, Russian Federation
Abstract Keywords
For the calculation of the diamagnetic permeability is consi-
dered a set of noninteracting electrons in a finite, sufficiently
large amount of magnetic. The Hamiltonian of the considered
structure with one-electron functions, involving the operators
of birth and destruction is reduced to conjunction operators,
the first of which is simply the kinetic energy of the electrons,
and the other two are considered as small perturbations. Using
the procedure of perturbation theory is calculated the energy of
the magnetic field in the first and second order. It is shown that
the amendment of the first order equal to zero and the second
order is computed by using the introduction of the Fermi mo-
mentum in the case of temperatures close to zero. The result for
the energy is represented in the form of a number from quad-
ratic in the vector potential terms. Further tying together the
result is a representation of energy using the current density of
electrons able to find the connection between the components
of the current density and the corresponding components of the
vector potential. A similar relationship obtained by using Fouri-
er transform of Maxwell's equations. When comparing the
obtained ratios obtained an expression for diamagnetic perme-
ability, which is accurate to dimensional multipliers, associated
with the choice of system of units, coincides with the classical
result obtained by a different method
Vector potential, Hamilton opera-
tor, Hermitian conjugate operators,
Kronecker symbols, Schrödinger
equation, perturbation theory,
operators of birth and destruction,
Fermi momentum, diamagnetic
susceptibility
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