Quantum magnetic billiards: boundary conditions and gauge transformations

Angelone, Giuliano; Facchi, Paolo; Lonigro, Davide

doi:10.1016/j.aop.2022.168914

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…Despite the fact that many physically observable quantities, such as the spectrum of H A , are independent of the gauge choice [50], such a choice is needed in order to perform calculations. More importantly, one should be aware that, generally, even boundary conditions depend on the gauge choice: see [51] for a detailed discussion. For the Hall strip (1)-(2), a profitable choice is the Landau gauge A = (−By, 0) , (8) which clearly satisfies equation (5).…”

Section: The Hall Hamiltonianmentioning

confidence: 99%

“…where α 0 , α 1 ∈ R (see e.g. [51] for a discussion of its physical significance); note in particular that chiral conditions reduce to Robin conditions if α 1 = 0. The above expression is manifestly invariant under longitudinal translations, which are indeed generated by the longitudinal momentum operator p x = −iℏ∂/∂ x .…”

Section: Data Availability Statementmentioning

confidence: 99%

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Boundary conditions for the quantum Hall effect

Angelone¹,

Asorey²,

Facchi³

et al. 2023

J. Phys. A: Math. Theor.

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We formulate a self-consistent model of the integer quantum Hall effect on an infinite strip, using boundary conditions to investigate the influence of finite-size effects on the Hall conductivity. By exploiting the translation symmetry along the strip, we determine both the general spectral properties of the system for a large class of boundary conditions respecting such symmetry, and the full spectrum for (fibered) Robin boundary conditions. In particular, we find that the latter introduce a new kind of states with no classical analogues, and add a finer structure to the quantization pattern of the Hall conductivity. Moreover, our model also predicts the breakdown of the quantum Hall effect at high values of the applied electric field.

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Section: The Hall Hamiltonianmentioning

confidence: 99%

Section: Data Availability Statementmentioning

confidence: 99%

Boundary conditions for the quantum Hall effect

Angelone¹,

Asorey²,

Facchi³

et al. 2023

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

Hearing the shape of a quantum boundary condition

2022

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In this paper, we study the isospectrality problem for a free quantum particle confined in a ring with a junction, analyzing all the self-adjoint realizations of the corresponding Hamiltonian in terms of a boundary condition at the junction. In particular, by characterizing the energy spectrum in terms of a spectral function, we classify the self-adjoint realizations in two classes, identifying all the families of isospectral Hamiltonians. These two classes turn out to be discerned by the action of parity (i.e. space reflection), which plays a central role in our discussion.

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Quantum magnetic billiards: boundary conditions and gauge transformations

Cited by 2 publications

References 27 publications

Boundary conditions for the quantum Hall effect

Boundary conditions for the quantum Hall effect

Hearing the shape of a quantum boundary condition

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