Chaotic dynamics and the GOE-GUE transition

Bohigas, O.; Giannoni, M.J.; Almeida, Alfredo M. Ozorio de; Schmit, C.

doi:10.1088/0951-7715/8/2/005

Cited by 76 publications

(98 citation statements)

References 21 publications

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“…Therefore, in this regime we will use for τ M and g E the values τ 0 M and g 0 E at zero field and consider the first order correction δS to the unperturbed action S 0 M . A general result in classical mechanics [56,69] states that the change (at constant energy) in the action integral along a closed orbit under the effect of a parameter λ of the Hamiltonian is given by…”

Section: A Oscillating Density Of States For Weak Fieldmentioning

confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of multiply-connected geometries. We concentrate on the geometric effects by studying confinement by perfect (disorder free) potentials stressing the importance of the underlying classical dynamics. We demonstrate that in a constrained geometry the standard Landau diamagnetic response is always present, but is dominated by finite-size corrections of a quasi-random sign which may be orders of magnitude larger. These corrections are very sensitive to the nature of the classical dynamics. Systems which are integrable at zero magnetic field exhibit larger magnetic response than those which are chaotic. This difference arises from the large oscillations of the density of states in integrable systems due to the existence of families of periodic orbits. The connection between quantum and classical behavior naturally arises from the use of semiclassical expansions. This key tool becomes particularly simple and insightful at finite temperature, where only short classical trajectories need to be kept in the expansion. In addition to the general theory for integrable systems, we analyze in detail a few typical examples of experimental relevance: circles, rings and square billiards. In the latter, extensive numerical calculations are used as a check for the success of the semiclassical analysis. We study the weak-field regime where classical trajectories remain essentially unaffected, the intermediate field regime where we identify new oscillations characteristic for ballistic mesoscopic structures, and the high-field regime where the typical de Haas-van Alphen oscillations exhibit finite-size corrections. We address the comparison with experimental data obtained in high-mobility semiconductor microstructures discussing the differences between individual and ensemble measurements, and the applicability of the present model. 03.65.Sq,05.45.+b,05.30.Fk,73.20.Dx

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Section: A Oscillating Density Of States For Weak Fieldmentioning

confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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“…The parameter γ may be related to the magnetic flux Φ through a twodimensional dot having area A [15,16]:…”

Section: Introductionmentioning

confidence: 99%

Andreev conductance of chaotic and integrable quantum dots

2000

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We examine the voltage V and magnetic field B dependent Andreev conductance of a chaotic quantum dot coupled via point contacts to a normal metal and a superconductor. In the case where the contact to the superconductor dominates, we find that the conductance is consistent with the dot itself behaving as a superconductor-it appears as though Andreev reflections are occurring locally at the interface between the normal lead and the dot. This is contrasted against the behaviour of an integrable dot, where for a similar strong coupling to the superconductor, no such effect is seen. The voltage dependence of the Andreev conductance thus provides an extremely pronounced quantum signature of the nature of the dot's classical dynamics. For the chaotic dot, we also study non-monotonic re-entrance effects which occur in both V and B.

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“…A single-particle semiclassical estimate of the correlation field B c gives an expression similar to (12). For a stadium in a uniform magnetic field, the correlation flux is Φ c ≈ 0.3 Φ 0 [31,23], which is below the experimental value of ≈ 0.8 Φ 0 . This indicates that the singleparticle picture is inadequate for estimating the correlation field.…”

Section: Parametric Correlationsmentioning

confidence: 85%

Chaos and Interactions in Quantum Dots

Alhassid

2001

Quantum Chaos Y2K

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Quantum dots are small conducting devices containing up to several thousand electrons. We focus here on closed dots whose single-electron dynamics are mostly chaotic. The mesoscopic fluctuations of the conduction properties of such dots reveal the effects of one-body chaos, quantum coherence and electron-electron interactions. I. QUANTUM DOTSRecent advances in materials science have made possible the fabrication of quantum dots, submicron-scale conducting devices containing up to several thousand electrons [1]. A 2D electron gas is created at the interface region of a semiconductor heterostructure (e.g., GaAs/AlGaAs) and the electrons are further confined to a small region by applying a voltage to metal gates, depleting the electrons under them. Insofar as the motion of the electrons is restricted in all three dimensions, a quantum dot may be considered a zero-dimensional system. The transport properties of the dot, i.e., its conductance, can be measured by connecting it to external leads. A micrograph of a quantum dot is shown in Fig. 1(a).At low temperatures, the electron preserves its phase over distances that are longer than the system's size, i.e., L φ > L, where L φ is the coherence length and L is the linear size of the system. Such systems are called mesoscopic. Elastic scatterings of the electron from impurities generally preserve phase coherence, while inelastic scatterings, e.g., from other electrons or phonons, result in phase breaking When the mean free path ℓ is much smaller than L, transport across the dot is dominated by diffusion, and the system is called diffusive. In the late 1980s it became possible to fabricate devices with little disorder where ℓ > L. In these so-called ballistic dots, transport is dominated by scattering of the electrons from the boundaries. A schematic illustration of a ballistic dot is shown in Fig. 1(b).In small dots (with typically less than ∼ 20 electrons), the confining potential is often harmonic-like, leading to regular dynamics of the electron and shell structure that can be observed in the addition spectrum (i.e., the energy required to add an electron to the dot). Maxima in the 1

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Chaotic dynamics and the GOE-GUE transition

Cited by 76 publications

References 21 publications

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism in the ballistic regime: geometrical effects

Andreev conductance of chaotic and integrable quantum dots

Chaos and Interactions in Quantum Dots

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