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1.
A. Teğmen T. Altanhan B. S. Kandemir 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,41(2):397-402
We calculate the Wigner distribution function for the
Calogero-Sutherland system which consists of harmonic and
inverse-square interactions. The Wigner distribution function is
separated out into two parts corresponding to the relative and
center-of-mass motions. A general expression for the relative
Wigner function is obtained in terms of the Laguerre polynomials
by introducing a new identity between Hermite and Laguerre
polynomials. 相似文献
2.
K. Weibert J. Main G. Wunner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2002,19(3):379-388
In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical
trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the
technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order
? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical
eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system,
as a prototype of a chaotic system.
Received 10 September 2001 and Received in final form 3 January 2002 相似文献
3.
Using the trial-function method, the general solution of the Schrödinger equation for the time-dependent linear potential is obtained. Based on the Heisenberg correspondence principle, the solution of the classical equation of motion is derived from the quantum matrix elements. 相似文献
4.
Analysis of edge-state energies in the integer quantum
Hall effect is carried out within the semiclassical approximation.
When the system is wide so that each edge can be considered
separately, this problem is equivalent to that of a one dimensional
harmonic oscillator centered at x = xc and an infinite wall at
x = 0, and appears in numerous physical contexts. The eigenvalues
En(xc) for a given quantum number n are solutions of the
equation S(E,xc)=π[n+ γ(E,xc)] where S is the WKB
action and 0 < γ < 1 encodes all the information on the
connection procedure at the turning points.
A careful implication of the WKB connection formulae results in an
excellent approximation to the exact energy eigenvalues. The
dependence of γ[En(xc),xc] ≡γn(xc)
on xc is analyzed between its two extreme values
as xc ↦-∞ far inside the sample
and as xc ↦∞ far outside the sample.
The edge-state energiesEn(xc) obey an almost exact scaling
law of the form
and the scaling function f(y) is explicitly elucidated. 相似文献
5.
K. Weibert J. Main G. Wunner 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,12(3):381-401
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit
orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic
orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision.
Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized
in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal
tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: firstly,
the periodic orbit quantization will be extended to include higher order corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly
reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard,
whose periodic orbits and quantum eigenvalues can easily be obtained.
Received 24 February 2000 and Received in final form 22 May 2000 相似文献
6.
Three different families of short periodic orbits in the semiclassical SU(3) nuclear model were studied and their stability calculated. Then, knowing the shortest periodT
min of the closed trajectories, the long-range behaviour of the
3 statistic was determined.The authors are greatly indebted to Prof. G. Benettin for many enlightening discussions and to Mr. G. Salmaso for his valuable computational assistance. This work has been partially supported by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica (MURST). 相似文献
7.
S. Gao G. C. Yang S. L. Lin M. L. Du 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,42(2):189-196
Photo-detached electrons of negative hydrogen ion in
parallel electric and magnetic fields show quite complicated classical
dynamical behavior, and a sequence of bifurcation and anti-bifurcation
occurs. We investigate the effects of bifurcations on the flux distribution
of photo-detached electrons by using position and momentum diagrams.
Detached-electron flux distributions are calculated based on a uniform
semi-classical theory. The flux distributions exhibit patterns with multiple
rings. The bright rings correspond to special points in the diagrams. The
flux distributions can be controlled by adjusting the magnetic field
strength while fixing the electric field. 相似文献
8.
P. Gosselin A. Bérard H. Mohrbach 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,58(2):137-148
It has been recently found that the equations of motion of several
semiclassical systems must take into account terms arising from Berry phases
contributions. Those terms are responsible for the spin Hall effect in
semiconductor as well as the Magnus effect of light propagating in
inhomogeneous media. Intensive ongoing research on this subject seems to
indicate that a broad class of quantum systems may be affected by Berry
phase terms. It is therefore important to find a general procedure allowing
for the determination of semiclassical Hamiltonian with Berry Phase
corrections. This article presents a general diagonalization method at order
ħ for a large class of quantum Hamiltonians directly inducing Berry
phase corrections. As a consequence, Berry phase terms on both coordinates
and momentum operators naturally arise during the diagonalization procedure.
This leads to new equations of motion for a wide class of semiclassical
system. As physical applications we consider here a Dirac particle in an
electromagnetic or static gravitational field, and the propagation of a
Bloch electrons in an external electromagnetic field. 相似文献
9.
F. Svensson S. Jonsell C. M. Dion 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,48(2):235-240
We extend the theory for laser cooling in a near-resonant
optical lattice to include multiple excited hyperfine
states. Simulations are performed treating the external degrees of
freedom of the atom, i.e., position and momentum, classically, while
the internal atomic states are treated quantum mechanically,
allowing for arbitrary superpositions. Whereas theoretical
treatments including only a single excited hyperfine state predict
that the temperature should be a function of lattice depth only,
except close to resonance, experiments have shown that
the minimum temperature achieved depends also on the detuning from
resonance of the lattice light. Our results resolve this
discrepancy. 相似文献
10.
We study wave equations with energy-dependent potentials. Simple analytical models are found useful to illustrate difficulties
encountered with the calculation and interpretation of observables. A formal analysis shows under which conditions such equations
can be handled as evolution equation of quantum theory with an energy-dependent potential. Once these conditions are met,
such theory can be transformed into ordinary quantum theory.
This work was supported by the agreement between IN2P3 and ASCR (collaboration no. 97-13) and by the Grant Agency of ASCR
(J.M., grant No.A1048305). 相似文献
11.
A. Popa 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,54(3):575-583
In previous papers we proved that, for stationary systems, the geometric elements of the wave described by the Schrödinger equation, namely the characteristic surfaces and their normals, are periodic solutions of the Hamilton-Jacobi equation. In this paper we prove that the Hamilton-Jacobi equation admits periodic solutions with the same geometrical symmetries as the wave function of the system in the case of the beryllium, boron, carbon and oxygen atoms. The above property is a reflection of the fact that for a multielectron atomic system the energetically most favorable geometric configuration minimizes the electron electron repulsion, and it leads to a general semiclassical calculation method, which is in principle valid for more complex systems. We show that this property can be used to compute the energetic atomic values, with the help of the central field method which we developed in previous publications. The relative error of our method is of the order 3×10-3, compared with experimental data for the atoms mentioned above. The accuracy of our method is revealed by a comparison between our theoretical data and values resulting from Hartree-Fock methods. 相似文献
12.
M. Schreier K. Richter G.-L. Ingold R.A. Jalabert 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,3(3):387-396
We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical
trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal with the case
where tunneling is present. Peaks in the Fourier transform of the energy-dependent transmission and reflection spectra exhibit
a nonmonotonic behaviour as a function of the barrier height in the quantum mechanical numerical calculations. Semiclassical
analysis provides a simple qualitative explanation of this behaviour, as well as a quantitative agreement with the exact calculations.
The experimental relevance of the classical trajectories in mesoscopic and microwave systems is discussed.
Received: 23 October 1997 / Received in final form and Accepted: 11 March 1998 相似文献
13.
Dehua Wang Kaiyun Huang Shenglu Lin 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,54(3):699-706
The ionization of Rydberg hydrogen atoms near a metal surface at different scaled energies above the classical saddle point
energy has been discussed by using the semiclassical method. The results show that the atoms ionize by emitting a train of
electron pulses. In order to reveal the chaotic and escape dynamical properties of this system in detail, the sensitive dependence
of the ionization rate upon the scaled energy is discussed. As the scaled energy is close to the saddle point energy, the
ionization process of the hydrogen atom is nearly the same as the case of hydrogen atom in an electric field. There is only
a single pulse of electrons, with an exponentially decaying tail. With the increase of the scaled energy, the ionization rates
are similar to the case of the hydrogen atom in parallel electric and magnetic field, a series of electron pulses appear in
the ionization process. This is caused by classical chaos, which occurs for the metal surface. Our studies also suggest that
the metal surface can play the role of both the electric and the magnetic fields. Our theoretical analysis will be useful
for guiding experimental studies of the ionization of atoms near the metal surface. 相似文献
14.
15.
A recent investigation of the possibility of having a
-symmetric periodic potential in an optical lattice stimulated the urge to generalize non-hermitian quantum mechanics beyond
the case of commutative space. We thus study non-hermitian quantum systems in non-commutative space as well as a
-symmetric deformation of this space. Specifically, a
-symmetric harmonic oscillator together with an iC(x
1+x
2) interaction are discussed in this space, and solutions are obtained. We show that in the
deformed non-commutative space the Hamiltonian may or may not possess real eigenvalues, depending on the choice of the non-commutative
parameters. However, it is shown that in standard non-commutative space, the iC(x
1+x
2) interaction generates only real eigenvalues despite the fact that the Hamiltonian is not
-symmetric. A complex interacting anisotropic oscillator system also is discussed. 相似文献
16.
Alexander J. Silenko 《The European Physical Journal C - Particles and Fields》2008,57(3):595-599
The exact solution of the Corben–Schwinger equations is obtained for spin-1 particles without an anomalous magnetic moment
in a uniform magnetic field. The exact Hamiltonian in the Foldy–Wouthuysen representation is derived. The conservation of
projections of the polarization operator onto four directions is proved. The approximate conservation of projections of this
operator onto the horizontal axes of the cylindrical coordinate system is established. For spin-1 particles with the anomalous
magnetic moment, the Hamiltonian in the Foldy–Wouthuysen representation is deduced within first order terms in the Planck
constant. Dynamics of spin-1 particles with the anomalous magnetic moment and their spins in the strong uniform magnetic field
are calculated. 相似文献
17.
A. E. Bernardini 《The European Physical Journal C - Particles and Fields》2008,56(4):545-556
We point out some incompatibilities which appear when one applies the stationary phase method for deriving phase times to
obtain the spatial localization of wave packets scattered by a unidimensional potential barrier. We concentrate on the above
barrier diffusion problem where the wave packet collision implies the possibility of multiple reflected and transmitted wave
packets, which, depending on the boundary conditions, can overlap or stand in relative separation in space. We demonstrate
that the indiscriminate use of the method for such a particular configuration leads to paradoxical results for which the correct
interpretation, confirmed by analytical/numerical calculations, imposes the necessity of the appearance of multiple peaks
as a consequence of multiple reflections by the barrier steps.
Also at Instituto de Física Gleb Wataghin, UNICAMP, PO Box 6165, 13083-970 Campinas, SP, Brazil. 相似文献
18.
H. Y. Li X. Zhao S. Gao X. Y. Xu H. Zhou S. L. Lin 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,49(1):1-6
By using the closed-orbit theory including the effect of Coulomb scattering together with an electrical image potential approach,
the recurrence spectra and the dynamical behaviours of the Rydberg hydrogen atom near a metal surface are presented. Theoretical
analysis and numerical simulation reveal that the impacts of the image potential contributing to the recurrence spectrum are
qualitatively analogous to that of the parallel electrical and magnetic fields on the Rydberg atom. The recurrence spectra
are computed for a few selected scaled energies and the results demonstrate that the scaled energy dominates the dynamical
properties of system. With the increase of the scaled energy e from small to large, the whole trend of spectral structure
is from simple to complex,and then simple. 相似文献
19.
The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative.
We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and
for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative
space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem. 相似文献
20.
G. Grawert 《Zeitschrift für Physik A Hadrons and Nuclei》1994,348(4):293-300
Experimental results of the 1st rank analyzing power for elastic scattering of6Li and7Li could be only understood when including coupling to inelastic channels in the calculations. This finding — established for some time — yet presents some open questions regarding the energy dependence of the spin and polarization effects. Semiclassical calculations presented here might clarify the relevant physical background of the earlier quantummechanically exact results. 相似文献