Geometrical properties of Maslov indices in the semiclassical trace formula for the density of states

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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“…[80] and Sec. III in [81]). Although a priori q 1 and q 2 play a similar role, their non-symmetrical appearance on the right hand side of Eq.…”

Section: Appendix C: Calculation Of G E For a Ring Billiardmentioning

confidence: 99%

Orbital magnetism in the ballistic regime: geometrical effects

1996

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“…to be quantized in a WKB fashion, but not allowing for any interference between those orbits. It has been shown that it is enough, for our very simple purposes, 25,26 to simply use a WKB formula, with a correct zero-point energy ͑or Maslov angle 45,51 ͒, to find the approximate energies of the main resonances. Since we are dealing with an open system, the dynamics explores the phase space structure in the strong interaction region only for a short amount of time ͑of the order of 100 fs, that is, a few vibrational periods͒.…”

Section: B Semiclassical Descriptionmentioning

confidence: 99%

A quantum and semiclassical study of dynamical resonances in the C+NO→CN+O reaction

Abrol

Wiesenfeld

Lambert

et al. 2001

The Journal of Chemical Physics

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Accurate quantum mechanical reactive scattering calculations were performed for the collinear CϩNO→CNϩO reaction using a polynomial-modified London Eyring Polanyi Sato ͑PQLEPS͒ potential energy surface ͑PES͒, which has a 4.26 eV deep well in the strong interaction region, and a reference LEPS PES, which has no well in that region. The reaction probabilities obtained for both PESs show signatures for resonances. These resonances were characterized by calculating the eigenvalues and eigenvectors of the collision lifetime matrix as a function of energy. Many resonances were found for scattering on both PESs, indicating that the potential well in the PQLEPS PES does not play the sole role in producing resonances in this relatively heavy atom system and that Feshbach processes occur for both PESs. However, the well in the PQLEPS PES is responsible for the differences in the energies, lifetimes, and compositions of the corresponding resonance states. These resonances are also interpreted in terms of simple periodic orbits supported by both PESs ͑using the WKB formalism͒, to further illustrate the role played by that potential well on the dynamics of this reaction. The existence of the resonances is associated with the dynamics of the long-lived CNO complex, which is much different than that of systems having an activation barrier. Although these results were obtained for a collinear model of the reaction, its collinearly-dominated nature suggests that related resonant behavior may occur in the real world.

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“…of the orbits. The Maslov indices were obtained by the method developed in [45] (see Ref. [27] for practical recipes).…”

Section: Semiclassical Calculation Of the Coarse-grained Resonancementioning

confidence: 99%

Periodic orbit theory for the Hénon-Heiles system in the continuum region

2004

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We investigate the resonance spectrum of the Hénon-Heiles potential up to twice the barrier energy. The quantum spectrum is obtained by the method of complex coordinate rotation. We use periodic orbit theory to approximate the oscillating part of the resonance spectrum semiclassically and Strutinsky smoothing to obtain its smooth part. Although the system in this energy range is almost chaotic, it still contains stable periodic orbits. Using Gutzwiller's trace formula, complemented by a uniform approximation for a codimension-two bifurcation scenario, we are able to reproduce the coarse-grained quantum-mechanical density of states very accurately, including only a few stable and unstable orbits.05.45.Mt,03.65.Sq

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Geometrical properties of Maslov indices in the semiclassical trace formula for the density of states

Cited by 133 publications

References 17 publications

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism in the ballistic regime: geometrical effects

A quantum and semiclassical study of dynamical resonances in the C+NO→CN+O reaction

Periodic orbit theory for the Hénon-Heiles system in the continuum region

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