Electron interactions, classical integrability, and level statistics in quantum dots

Meza-Montes, L.; Ulloa, Sergio; Pfannkuche, Daniela

doi:10.1016/s1386-9477(97)00059-3

Cited by 11 publications

(4 citation statements)

References 31 publications

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“…This type of dot systems has also attracted interest in the field of quantum control of orbital wave functions due to their simplicity and tunability. 21,22,23,24 As we will see here they are also well-suited for applications involving control of the spin degrees of freedom since they allow a great deal of control over the Rashba and Dresselhaus Hamiltonians. In this paper we study the influence of the Rashba and Dresselhaus spin-orbit Hamiltonians on the electronic structure of quasi-1D QDs, akin to those formed in semiconductor nanorods.…”

Section: Introductionmentioning

confidence: 93%

Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures

2005

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We investigate theoretically how the spin-orbit Dresselhaus and Rashba effects influence the electronic structure of quasi-one-dimensional semiconductor quantum dots, similar to those that can be formed inside semiconductor nanorods. We calculate electronic energy levels, eigen-functions, and effective g-factors for coupled, double dots made out of different materials, especially GaAs and InSb. We show that by choosing the form of the lateral confinement, the contributions of the Dresselhaus and Rashba terms can be tuned and suppressed, and we consider several possible cases of interest. We also study how, by varying the parameters of the double-well confinement in the longitudinal direction, the effective g-factor can be controlled to a large extent.PACS numbers: 73.21. La,

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Section: Introductionmentioning

confidence: 93%

Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures

2005

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“…The recent development in high technology has fabricated nano-scale quantum dots [1][2][3][4][5][6][7][8][9]. However, closer correspondence between the classical chaos and the quantum chaos in those systems has not been investigated well.…”

Section: Introductionmentioning

confidence: 99%

“…regular, mixed, or chaotic character, reflects on some of the quantum properties of the systems, particularly in the energy level statistics. In this context, a number of studies on the quantum chaos of systems containing a few electrons in quantum dots have been reported [1][2][3][4][5][6][7][8][9]. However, closer correspondence between the classical chaos and the quantum chaos in those systems has not been investigated well.…”

Section: Introductionmentioning

confidence: 99%

Quantum and classical chaos of a two-spinless-fermion system in a quantum wire

Masuda¹,

Sawada²,

Shimizu³

2013

J. Phys. A: Math. Theor.

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We study classical and quantum dynamics of two spinless particles confined in a quantum wire with repulsive or attractive Coulomb interaction. The interaction induces irregular dynamics in classical mechanics, which reflects on the quantum properties of the system in the energy level statistics (the signatures of quantum chaos). We investigate especially closer correspondence between the classical and quantum chaos. The present classical dynamics has some scaling property, which the quantum counterpart does not have. However, we demonstrate that the energy level statistics implies the existence of the corresponding scaling property even in the quantum system. Instead of ordinary maximum Lyapunov exponent (MLE), we introduce a novel kind of MLE,which is shown to be suitable measure of chaotic irregularity for the present classical system. We show that tendency of the energy dependence of the Brody parameter, which characterizes the energy level statistics in the quantum system, is consistent with that of the novel kind of MLE.

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“…The statistical properties of the energy spectrum have been studied before in Ref. [9]. In the weakly perturbed case, the level spacing distribution is Poisson-like.…”

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confidence: 99%

Quantum-Classical Correspondence for Two Interacting Particles in a One-Dimensional Box

Meza-Montes

Izrailev

Ulloa

2000

phys. stat. sol. (b)

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We study the model of two interacting particles moving in a 1D box, paying main attention to the quantum-classical correspondence for the average shape of quantum eigenstates and for the local density of states (LDOS). We show that if the classical motion is chaotic, in a deep semi-classical region of a quantum system, both the shape of eigenstates and of the LDOS coincide with their classical analogs, on average. However, individual eigenstates exhibit quite large fluctuations which may not be treated as statistical ones. Thus, comparison of quantum quantities to the classical ones allows one to detect quantum effects of localization which for conservative systems emerge in the energy space.Recently, a novel approach has been developed for a model of two-body random interactions with a finite number of Fermi particles [1 to 3]. The goal of this approach is to study the relation between the average shape of chaotic eigenstates on the one hand, and the distribution of occupation numbers for single-particle levels, on the other hand. As shown before, there is no need to know exactly the eigenstates of a (chaotic) system since only the shape of eigenfunctions (SEF) in a proper basis comes into play, provided that the unperturbed density of states is also known. The important point is that in some cases, the SEF can be found analytically from the off-diagonal matrix elements of the Hamiltonian matrix. Moreover, if a quantum system has a well-defined classical counterpart, and in the classical limit the total Hamiltonian (of a correspondent dynamical system) is chaotic, then one can use the quantum-classical correspondence for the SEF, thus introducing a new kind of semi-quantum approach. Similar to the SEF, one can define the classical analog of the so-called local density of states (LDOS) which is of great importance in the study of quantum complex systems such as many-electron atoms, heavy nuclei, atomic clusters, and solid-state models [4].In this paper, we extend the above approach to a specific dynamical model of two interacting particles in a one-dimensional box, in a way similar to that used recently in Refs. [5,6] for two interacting spin-particles. The aim of this study is two-fold. First, we demonstrate how the generic approach suggested in Refs. [7,8] can be extended to dynamical models. Second, using the quantum-classical analogy for the SEF and LDOS, we study quantum effects of localization in energy space. We would like to stress that the notion of the quantum localization for conservative systems is quite different from L. Meza-Montes et al.: Two Interacting Particles in a 1D Box

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Electron interactions, classical integrability, and level statistics in quantum dots

Cited by 11 publications

References 31 publications

Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures

Level structure and spin-orbit effects in quasi-one-dimensional semiconductor nanostructures

Quantum and classical chaos of a two-spinless-fermion system in a quantum wire

Quantum-Classical Correspondence for Two Interacting Particles in a One-Dimensional Box

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