Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Müller, Markus

doi:10.1088/0305-4470/32/6/014

Cited by 24 publications

(42 citation statements)

References 38 publications

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“…Higher order terms beyond the Poisson bracket contribution are functions of derivatives of F jk . This series coincides structurally with that recently obtained [22] by Müller.…”

Section: Introduction and Overviewsupporting

confidence: 91%

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Symplectic areas, quantization, and dynamics in electromagnetic fields

Karasev

Osborn

2002

Journal of Mathematical Physics

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A gauge invariant quantization in a closed integral form is developed over a linear phase space endowed with an inhomogeneous Faraday electromagnetic tensor. An analog of the Groenewold product formula (corresponding to Weyl ordering) is obtained via a membrane magnetic area, and extended to the product of N symbols. The problem of ordering in quantization is related to different configurations of membranes: a choice of configuration determines a phase factor that fixes the ordering and controls a symplectic groupoid structure on the secondary phase space. A gauge invariant solution of the quantum evolution problem for a charged particle in an electromagnetic field is represented in an exact continual form and in the semiclassical approximation via the area of dynamical membranes.

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“…Higher order terms beyond the Poisson bracket contribution are functions of derivatives of F jk . This series coincides structurally with that recently obtained [22] by Müller.…”

Section: Introduction and Overviewsupporting

confidence: 91%

“…In the case where F is restricted to be the pure magnetic form (1.2a), then the series above is equivalent to the one derived in [22]. The formula (3.2) is still not presented in a completely symplectic manner.…”

Section: Exponential Formula For Magnetic Productmentioning

confidence: 97%

Symplectic areas, quantization, and dynamics in electromagnetic fields

Karasev

Osborn

2002

Journal of Mathematical Physics

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“…For simulation purposes, the spin Vlasov equations (35)- (36) are much easier to solve numerically than the corresponding Wigner equations (23)- (24), mainly because the former are local in space while the latter are not. The Vlasov approximation is valid when quantum effects in the orbital dynamics are small.…”

Section: Semiclassical Limit and Spin Vlasov Modelmentioning

confidence: 99%

Phase-space methods for the spin dynamics in condensed matter systems

Hurst

Hervieux

Manfredi

2017

Phil. Trans. R. Soc. A.

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“…It has first been proposed by Müller in 1999 [19] in a non-rigorous fashion. Independently, Măntoiu and Purice [20] as well as Iftimie, Măntoiu and Purice [14] have laid the mathematical foundation.…”

Section: Magnetic ψDo and Weyl Calculusmentioning

confidence: 99%

Applications of Magnetic Ψdo Techniques to Sapt

Nittis

Lein

2011

Rev. Math. Phys.

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In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic ΨDO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [24] to a more general class of magnetic fields: we consider a single particle moving in a periodic potential which is subjectd to a weak and slowly-varying electromagnetic field. In addition to the semiclassical parameter ε ≪ 1 which quantifies the separation of spatial scales, we explore the influence of an additional parameter λ that allows us to selectively switch off the magnetic field.We find that even in the case of magnetic fields with components in C ∞ b (R d ), e. g. for constant magnetic fields, the results of Panati, Spohn and Teufel hold, i. e. to each isolated family of Bloch bands, there exists an associated almost invariant subspace of L 2 (R d ) and an effective hamiltonian which generates the dynamics within this almost invariant subspace. In case of an isolated non-degenerate Bloch band, the full quantum dynamics can be approximated by the hamiltonian flow associated to the semiclassical equations of motion found in [24].

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Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding centre motion

Cited by 24 publications

References 38 publications

Symplectic areas, quantization, and dynamics in electromagnetic fields

Symplectic areas, quantization, and dynamics in electromagnetic fields

Phase-space methods for the spin dynamics in condensed matter systems

Applications of Magnetic Ψdo Techniques to Sapt

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