Magnetic moment and perturbation theory with singular magnetic fields

Comtet, Alain; Mashkevich, Stefan; Ouvry, Stéphane

doi:10.1103/physrevd.52.2594

Cited by 19 publications

(30 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…r i are the positions of the vortices in the plane : they are uncorrelated random variables (Poisson distribution). The δ interactions (coupling to the magnetic field) are necessary in order to define properly the model [131,163,175,33,63]. By comparison with scalar impurities discussed in the introduction, the magnetic nature of the scatterers gives rise to rather different properties 38 : it was shown in ref.…”

Section: Occupation Time and Local Time Distribution On A Graphmentioning

confidence: 99%

Functionals of Brownian motion, localization and metric graphs

Comtet¹,

Desbois²,

Texier³

2005

J. Phys. A: Math. Gen.

Self Cite

View full text Add to dashboard Cite

We review several results related to the problem of a quantum particle in a random environment.In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization).Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues).Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schrödinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated.Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.

show abstract

Section: Occupation Time and Local Time Distribution On A Graphmentioning

confidence: 99%

Functionals of Brownian motion, localization and metric graphs

Comtet¹,

Desbois²,

Texier³

2005

J. Phys. A: Math. Gen.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The solution for Λ(ℓ), the exact low energy eigenvalues E n=0,ℓ and the normalisation constant N (ℓ) are given by, In this case the eigenvalues and eigenfunctions for higher Landau levels can also be solved as in Ref. [16]. The full spectrum is given by E n,ℓ = 2n + ℓ 2 + 2λ 2 1/2 − ℓ + 1 ω c , n = 0, 1, 2 .…”

Section: B Inverse Square Potentialmentioning

confidence: 99%

“…To obtain the appropriate Hamiltonian [16], we perform a singular gauge transformation in the relative coordinate on the Hamiltonian (5). To be precise we perform the gauge transformation e iαφ He −iαφ with φ = tan −1 y x , with y and x the components of the relative coordinates.…”

Section: Singular Magnetic Fieldsmentioning

confidence: 99%

See 1 more Smart Citation

Interactions and non-commutativity in quantum Hall systems

Scholtz¹,

Chakraborty²,

Gangopadhyay³

et al. 2005

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general renormalize the non-commutative parameter away from the non-interacting value 1 B. The effective non-commutative parameter is in general also angular momentum dependent. An heuristic argument, based on the non-commutative coordinates, is given to find the filling fractions at incompressibilty, which are in general renormalized by the interactions, and the results are consistent with known results in the case of singular magnetic fields.

show abstract

“…While the results of this discussion are generally known and were mentioned in the literature in various contexts [6], there is no published work that we know of, which contains a systematic and complete treatment. Thus we present it here for completeness and to set the stage for the discussion of the relativistic case.…”

Section: Introductionmentioning

confidence: 99%

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Shikakhwa

Pak

2003

Phys. Rev. D

View full text Add to dashboard Cite

A partial wave analysis using the basis of the total angular momentum operator J3 is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm (AB) potential. It is demonstrated that the s-partial wave contributes to the scattering amplitude in contrast to the case with scalar non-relativistic particles. We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.

show abstract

Magnetic moment and perturbation theory with singular magnetic fields

Cited by 19 publications

References 23 publications

Functionals of Brownian motion, localization and metric graphs

Functionals of Brownian motion, localization and metric graphs

Interactions and non-commutativity in quantum Hall systems

Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

Contact Info

Product

Resources

About