Quantum Spectra and Classical Orbits in Nano-Microstructure

A kind of new classical-quantum correspondence principle is proposed using the idea of closed-orbit theory. The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of one-dimensional nano-microstructure. The Fourier transformation of the quantum spectrum function is found corresponding with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some two-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science, for example, molecular reaction dynamics and quantum information.

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Classical-Quantum Correspondence in Two-Dimensional Nanomaterials

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.228-229.216 ◽

2011 ◽

Vol 228-229 ◽

pp. 216-221

Author(s):

Jun Lu

Keyword(s):

Three Dimensional ◽

Two Dimensional ◽

One Dimensional ◽

Spectrum Function ◽

Potential Applications ◽

Classical Quantum ◽

The Fourier Transform ◽

Quantum Correspondence ◽

New Evidence ◽

Quantum Spectrum

Two-dimensional nanomaterials are becoming the focus of intensive research due to their novel physical properties and the potential applications in nanodevices. We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional nanomaterials. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical orbits from one point to another for a particle in the two-dimensional nanomaterials. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some one-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science.

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Quantum Spectra and Classical Orbits in Artificial Atom

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.110-116.3316 ◽

2011 ◽

Vol 110-116 ◽

pp. 3316-3321

Author(s):

Jun Lu

Keyword(s):

Fourier Transform ◽

Two Dimensional ◽

Artificial Atom ◽

Closed Orbits ◽

Spectrum Function ◽

Classical Quantum ◽

The Fourier Transform ◽

Quantum Correspondence ◽

New Evidence ◽

Quantum Spectrum

We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional artificial atom. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical closed orbits and the classical opened orbits from one point to another. These results give new evidence about the classical-quantum correspondence.

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NEW EVIDENCE OF DISCRETE SCALE INVARIANCE IN THE ENERGY DISSIPATION OF THREE-DIMENSIONAL TURBULENCE: CORRELATION APPROACH AND DIRECT SPECTRAL DETECTION

International Journal of Modern Physics C ◽

10.1142/s0129183103004632 ◽

2003 ◽

Vol 14 (04) ◽

pp. 459-470 ◽

Cited By ~ 11

Author(s):

WEI-XING ZHOU ◽

DIDIER SORNETTE ◽

VLADILEN PISARENKO

Keyword(s):

Energy Dissipation ◽

Three Dimensional ◽

Energy Dissipation Rate ◽

Corrections To Scaling ◽

Developed Turbulence ◽

Pairwise Correlations ◽

Spectral Detection ◽

Simple Variant ◽

High Reynolds ◽

New Evidence

We extend the analysis of Ref. 16 showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number (≈ 2500) of three-dimensional fully developed turbulence. First, we develop a simple variant of the canonical averaging method using a rephasing scheme between different samples based on pairwise correlations that confirms Zhou and Sornette's previous results. The second analysis uses a simpler local spectral approach and then performs averages over many local spectra. This yields stronger evidence of the existence of underlying log-periodic undulations, with the detection of more than 20 harmonics of a fundamental logarithmic frequency f = 1.434 ± 0.007 corresponding to the preferred scaling ratio γ = 2.008 ± 0.006.

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