Préface

Balian, R.; Dominicis, C. De; Gillet, V.; Messiah, A.

doi:10.1016/b978-0-444-10742-8.50005-0

Cited by 122 publications

(336 citation statements)

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“…Mesoscopic physics is usually concerned with the properties of the spectrum on an energy-scale large compared to the mean-spacing. In the spirit of the work of Balian and Bloch [54], this is the situation for which the semiclassical trace formalism is especially appropriate.…”

Section: Discussionmentioning

confidence: 99%

“…For integrable geometries however, the Berry-Tabor [52,53] or Balian-Bloch [54] trace formulae valid for integrable systems usually do not apply in the presence of a perturbing magnetic field. It will therefore be necessary, following Ozorio de Almeida [55,56], to consider the more complicated case of nearly integrable systems, which we will do in detail here.…”

Section: Overview Of This Workmentioning

confidence: 99%

“…The use of a temperature smoothed density of states Eq. (2.6a) closely follows the Balian and Bloch approach [54], where, due to the exponential proliferation of orbits and the impossibility of exchanging the infinite time and semiclassical limits, the semiclassical techniques based on trace formulae are considered meaningful only when applied to smoothed quantities. The decomposition of D(E) is depicted in Fig.…”

Section: B Canonical Ensemblementioning

confidence: 99%

“…To achieve this, it is necessary to go back to the basic equations from which the standard semiclassical trace formulae (Gutzwiller [51], Balian-Bloch [54], Berry-Tabor [53]) are derived. The density of states d(E), Eq.…”

Section: Simple Regular Geometries: the Squarementioning

confidence: 99%

“…7) and express the exact Green function G(q, q ′ ; E) in terms of the free Green function G 0 (q, q ′ ; E) as [54,51] …”

Section: A Oscillating Density Of States For Weak Fieldmentioning

confidence: 99%

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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: Discussionmentioning

confidence: 99%

Section: Overview Of This Workmentioning

confidence: 99%

Section: B Canonical Ensemblementioning

confidence: 99%

Section: Simple Regular Geometries: the Squarementioning

confidence: 99%

“…7) and express the exact Green function G(q, q ′ ; E) in terms of the free Green function G 0 (q, q ′ ; E) as [54,51] …”

Section: A Oscillating Density Of States For Weak Fieldmentioning

confidence: 99%

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Orbital magnetism in the ballistic regime: geometrical effects

1996

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Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

Koizumi¹,

Fukumoto²

1996

Int J of Quantum Chemistry

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rnWe investigate the fission process A& + Ag:, + Ag:l in order to compare total energies that calculated by the shell correction method and jellium models. A cavity potential and a Woods-Saxon-type potential are used as the shell potential for the shell correction method, with which the single-particle energy levels are calculated. Shell corrections are obtained by using the Balian-Bloch formula and by smoothing the discrete energy levels in the shell potentials. The jellium model calculations are performed in the framework of the local spin density functional approximation. The conventional jellium model and stabilized jellium model are used. Although the qualitative agreement between the shell correction method calculations and the stabilized jellium calculations is very good, an improvement of the liquid drop energy will be necessary for the satisfactory quantitative agreement.

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The first second of the Universe

2003

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The history of the Universe after its first second is now tested by high quality observations of light element abundances and temperature anisotropies of the cosmic microwave background. The epoch of the first second itself has not been tested directly yet; however, it is constrained by experiments at particle and heavy ion accelerators. Here I attempt to describe the epoch between the electroweak transition and the primordial nucleosynthesis. The most dramatic event in that era is the quark--hadron transition at 10 $\mu$s. Quarks and gluons condense to form a gas of nucleons and light mesons, the latter decay subsequently. At the end of the first second, neutrinos and neutrons decouple from the radiation fluid. The quark--hadron transition and dissipative processes during the first second prepare the initial conditions for the synthesis of the first nuclei. As for the cold dark matter (CDM), WIMPs (weakly interacting massive particles) -- the most popular candidates for the CDM -- decouple from the presently known forms of matter, chemically (freeze-out) at 10 ns and kinetically at 1 ms. The chemical decoupling fixes their present abundances and dissipative processes during and after thermal decoupling set the scale for the very first WIMP clouds.Comment: review to appear in Annalen der Physik (51 pages, 16 figures); references added (v2); typos corrected, resembles published version (v3

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Préface

Cited by 122 publications

References 0 publications

Orbital magnetism in the ballistic regime: geometrical effects

Orbital magnetism in the ballistic regime: geometrical effects

Fission of metal clusters: A comparison of jellium model calculations and shell correction method calculations

The first second of the Universe

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