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1.
We construct and discusss explicitly time dependent integrals of the motion of non-autonomous quantum systems. Such integrals may exist even when the classical limit of the dynamics is non-integrable. 相似文献
2.
Farhan Saif 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,39(1):87-91
We investigate recurrence phenomena in coupled two degrees of
freedom systems.
It is shown that an initial well localized wave packet displays recurrences
even in the presence of coupling in these systems. We discuss the interdependence
of time scales namely classical period and quantum revival time and
explain the significance of initial conditions. 相似文献
3.
D. Braun 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(1):3-12
I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation
reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator,
if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical
strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently
many times the formulae become entirely classical, and powerful classical trace formulae apply.
Received 7 October 1999 相似文献
4.
A. Casado T. Marshall R. Risco-Delgado E. Santos 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,13(1):109-119
We continue the study of parametric down conversion within the framework of the Wigner representation, by using a Maxwellian
approach developed in a recent paper [A. Casado et al., Eur. Phys. J. D 11, 465 (2000)]. This gives a mechanism, inside the crystal, for the production of the down-converted radiation. We obtain the
electric field to second order in the coupling constant by using the Green's function method, and compare our treatment with
the standard Hamiltonian approach. The spectrum of the down-converted radiation is calculated as a function of the parameters
of the nonlinear crystal (in particular the length) and the radius of the pumping beam.
Received 15 May 2000 相似文献
5.
An investigation is undertaken of semiclassical time-evolutions and their classical limit with the intent of getting insights into the classical–quantum frontier. We deal with a system that represents the interaction between matter and a given field, and our main research tool is the so-called q-complexity quantifier, for which two different versions are considered. The probability distribution associated with the time-evolution process is determined by recourse to the Bandt–Pompe symbolic technique [C. Bandt, B. Pompe, Permutation entropy: a natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102:1–174102:4]. The most salient details of the quantum–classical transition turn out to be described not only well, but also in a better fashion than that of previous literature. 相似文献
6.
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
7.
We study the evolution of the dynamics across a generic first-order quantum phase transition in an interacting boson model of nuclei. The dynamics inside the phase coexistence region exhibits a very simple pattern. A classical analysis reveals a robustly regular dynamics confined to the deformed region and well separated from a chaotic dynamics ascribed to the spherical region. A quantum analysis discloses regular bands of states in the deformed region, which persist to energies well above the phase-separating barrier, in the face of a complicated environment. The impact of kinetic collective rotational terms on this intricate interplay of order and chaos is investigated. 相似文献
8.
A. Casado A. Fernández-Rueda T. Marshall J. Martínez R. Risco-Delgado E. Santos 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2000,11(3):465-472
The theory of parametric down conversion within the framework of the Wigner representation has been treated recently in a
series of papers using the standard model Hamiltonian. Here we take a more fundamental point of view studying the mechanism,
inside the crystal, for the production of the signal and idler beams. We begin from the evolution equations for the quantum
field operators, pass to the Wigner function and solve the resulting (Maxwell) equations with the use of the Green's function
method. We derive the time dependence of the coincidence detection probability as a function of the parameters of the nonlinear
crystal (in particular the length) the radius of the pumping beam, and the bandwidth of the filters in front of the detectors.
Received 24 January 2000 and Received in final form 24 March 2000 相似文献
9.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):61-82
We study the relaxation of a test particle immersed
in a bath of field particles interacting via weak long-range
forces. To order 1/N in the N→+∞ limit, the
velocity distribution of the test particle satisfies a
Fokker-Planck equation whose form is related to the Landau and
Lenard-Balescu equations in plasma physics. We provide explicit
expressions for the diffusion coefficient and friction force in the
case where the velocity distribution of the field particles is
isotropic. We consider (i) various dimensions of space d=3,2 and
1; (ii) a discret spectrum of masses among the particles; (iii)
different distributions of the bath including the Maxwell
distribution of statistical equilibrium (thermal bath) and the step
function (water bag). Specific applications are given for
self-gravitating systems in three dimensions, Coulombian systems in
two dimensions and for the HMF model in one dimension. 相似文献
10.
I.?Jakusjina Linn?us K.-E.?Thylwe 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2009,53(3):283-288
The radial Schrödinger equation with an effective potential containing a single well and a single barrier is treated with an improved uniform semiclassical method. The improved quantization formula for complex energies (or resonances) contains a correction term that originates from a uniform treatment of the classically forbidden region near the origin in addition to the more familiar uniform treatment of the barrier region. In the present case the origin has a second-order pole, due to the centrifugal barrier potential term, and/or a Coulomb-type singularity, and these terms dominate the region inside the innermost classical turning point.Numerical results for first-order and third-order approximate complex resonance energies are compared with those of a standard (first- and third-order) barrier-uniform semiclassical method and also with those of ‘exact’ numerical computations.The improved quantization formula provides results in significantly better agreement with the exact results as the angular momentum quantum number l approaches zero. 相似文献
11.
Ahmed S. Hassan 《Physics letters. A》2010,374(21):2106-4771
In this Letter a conventional method of statistical physics and quantum mechanics is used to calculate the effective area and the expansion energy for trapped Bose gas in a combined optical-magnetic potential. Correction due to the finite number of particles, interatomic interaction and the deepness of the lattice potential are given simultaneously. It is found that the system possess two different phases which are superfluid phase and Mott insulator phase. The critical temperature which separate these two phases is calculated. In the superfluid phase both the effective area and expansion energy is sensitive to the variation of temperature and lattice depth. Mott insulator phase is characterized by vanishing of the condensed fraction and freezing of the effective area at the value which corresponding to BEC transition temperature. So these parameters can serve as a practical thermometer for such system. The expansion energy shows that the lack of expansion in any direction is due to the strong anisotropy of the trapping potential in this direction. The obtained results provide a solid theoretical foundation for the current experiments. 相似文献
12.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(1):47-59
We present first elements of kinetic theory appropriate
to the inhomogeneous phase of the Hamiltonian Mean Field (HMF)
model. In particular, we investigate the case of strongly
inhomogeneous distributions for T→0 and exhibit
curious behaviour of the force auto-correlation function and
friction coefficient. The temporal correlation function of the
force has an oscillatory behaviour which averages to zero over a
period. By contrast, the effects of friction accumulate with time
and the friction coefficient does not satisfy the Einstein
relation. On the contrary, it presents the peculiarity to increase
linearly with time. Motivated by this result, we provide analytical
solutions of a simplified kinetic equation with a time dependent
friction. Analogies with self-gravitating systems and other systems
with long-range interactions are also mentioned. 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.
S. Jonsell C. M. Dion M. Nylén S. J.H. Petra P. Sjölund A. Kastberg 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2006,37(1):67-74
We develop a semi-classical method to simulate the motion of
atoms in a dissipative optical lattice. Our method treats the
internal states of the atom quantum mechanically, including all
nonadiabatic couplings, while position and momentum are treated as
classical variables. We test our method in the one-dimensional
case. Excellent agreement with fully quantum mechanical simulations is
found. Our results are much more accurate than those of earlier
semi-classical methods based on the adiabatic approximation. 相似文献
15.
C.P. Sun D.L. Zhou S.X. Yu X.F. Liu 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2001,13(1):145-155
Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum
decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic
limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized
as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large
system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments
[e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can
be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system
respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a
coherent initial state, three illustrations are presented with their explicit solutions in this paper.
Received 26 February 2000 and Received in final form 14 July 2000 相似文献
16.
Distribution of eigenfrequencies for vibrating plates 总被引:2,自引:0,他引:2
P. Bertelsen C. Ellegaard E. Hugues 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,15(1):87-96
Acoustic spectra of free plates with a chaotic billiard shape have been measured, and all resonance frequencies in the range
0-500 kHz have been identified. The spectral fluctuations are analyzed and compared to predictions of the Gaussian Orthogonal
Ensemble (GOE) of random matrices. The best agreement is found with a superposition of two independent GOE spectra with equal
density which indicates that two types of eigenmodes contribute to the same extent. To explain and predict these results a
detailed theoretical analysis is carried out below the first cut-off frequency where only flexural and in-plane vibrations
are possible. Using three-dimensional plate dispersion relations and two-dimensional models for flexural and in-plane vibrations
we obtained two first terms of the asymptotic expansion of the counting function of these eigenmodes. The contribution of
edge modes is also discussed. The results are in a very good agreement with the experimentally measured number of modes. The
analysis shows that the two types of modes have almost equal level density in the measured frequency interval, and this explains
the observed spectral statistics. For a plate with broken symmetry in the up-down direction (where flexural and in-plane modes
are strongly coupled) experimentally observed spectral fluctuations correspond to a single GOE spectrum. Above the first cut-off
frequency a greater complexity of the spectral fluctuations is expected since a larger number of types of modes will contribute
to the spectrum.
Received 5 January 1999 and Received in final form 5 September 1999 相似文献
17.
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
18.
Peter A. Braun Stefan Heusler Sebastian Müller Fritz Haake 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):189-206
Employing symbolic dynamics for geodesic motion on the tesselated pseudosphere, the so-called Hadamard-Gutzwiller model, we
construct extremely long periodic orbits without compromising accuracy. We establish criteria for such long orbits to behave
ergodically and to yield reliable statistics for self-crossings and avoided crossings. Self-encounters of periodic orbits
are reflected in certain patterns within symbol sequences, and these allow for analytic treatment of the crossing statistics.
In particular, the distributions of crossing angles and avoided-crossing widths thus come out as related by analytic continuation.
Moreover, the action difference for Sieber-Richter pairs of orbits (one orbit has a self-crossing which the other narrowly
avoids and otherwise the orbits look very nearly the same) results to all orders in the crossing angle. These findings may
be helpful for extending the work of Sieber and Richter towards a fuller understanding of the classical basis of quantum spectral
fluctuations.
Received 17 July 2002 Published online 29 November 2002 相似文献
19.
We study the optical absorptions of an exciton in a quantum ring. The quantum ring is described as a circular quantum dot with a repulsive core. The advantage of our methodology is that one can investigate the influence of the repulsive core by varying two parameters in the confinement potential. The linear, third-order nonlinear and total optical absorption coefficients have been examined with the change of the confinement potential. The results show that the optical absorptions are strongly affected by the repulsive core. Moreover, the repulsive core can influence the oscillation in the resonant peak of the absorption coefficients. 相似文献
20.
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