Influence of Geometric-Confinement Parameters on the Electronic Properties of Quantum Ring

Moskal, S.; Spisak, B. J.

doi:10.12693/aphyspola.112.101

Cited by 5 publications

(1 citation statement)

References 31 publications

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“…where g 1/2 (ϕ) = ds(ϕ) dϕ = dr(ϕ) dϕ 6 . Theoretical efforts have been focused on how deformations and external fields modify the energy spectrum of one-dimensional [28,33,103] and two-dimensional QRs [28,33,100,[104][105][106][107][108][109][110][111][112][113]. The study of deformed QRs has been concentrated mainly on elliptical deformations [104,107,109,[112][113][114][115][116], Cassini ovals [117] and limaçon-shaped [107].…”

Section: Symmetric Deformationsmentioning

confidence: 99%

Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

Monroy¹

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The problem of how to describe the effective dynamics of particles or fields confined to a lower dimensional curved space-time is of interest in many areas of physics. In the literature, several methods have been proposed to attack this problem. Recently it has been reported some experimental evidences that are consistent with the so-called confining potential approach. In light of these results, the purpose of this thesis is to construct a quantum theory for particles confined in a submanifold of a flat space-time employing the theoretical framework of the confining potential approach. The thesis is divided into two parts. The first one is dedicated exclusively to the study of quantum mechanics on a submanifold. For this purpose, we derive the effective Schrödinger, Dirac and Klein-Gordon equations on a curved submanifold, in the presence of an external electromagnetic field. We examine the singular features of these equations and present some applications to condensed matter. In the second part of this thesis, we start from the quantum mechanics on the submanifold and then we formulate the quantum field theory (QFT) on the submanifold. We will show that the "free" QFT on a submanifold can be schematically represented as a quantum theory of free fields on a curved background plus a scalar potential and an external SO(n − m) Yang-Mills field. For this theory, we compute the one-loop effective action for scalars and fermions at finite temperature and chemical potential to all orders using the Seely-DeWitt expansion. For interacting theories, we will prove that the theory known as reduced quantum electrodynamics (RQED dγ ,de) can be recovered from the confining potential approach. For a two-dimensional theory, we propose a large class of extensions of the Schwinger model, in which the interaction between fermions goes beyond the linear potential. We demonstrate that, remarkably, these extensions are exactly solvable for massless fermions and that there is no dynamical mass generation for the fermions. Furthermore, we construct a new family of exactly bosonized theories. We also show that RQED 4,2 has the necessary features to be identified as an effective field theory for graphene wires. Finally, we study the effect of an interplay of real and pseudomagnetic fields in graphene. We compute the fermion condensate, the induced vacuum charge density, the one-loop effective action and the magnetization, for this system. We will show that the presence of a non-zero pseudomagnetic field makes it possible, experimentally, to observe an induced vacuum charge density. Moreover, we will show that it is possible to have control over the magnetization as well as the dynamical mass for each valley in graphene, by straining or varying the applied magnetic field.

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