Vol. 53, No. 5 (2004)
2004, 53 (5): 1270-1275. doi: 10.7498/aps.53.1270
A nonNoether conserved quantity, i. e. Hojman conserved quantity constructed using the Noether symmetry for the nonholonomic mechanical system is presented. Under special infinitesimal transformations in which the time is not variable, the special Noether symmetry and Noether conserved quantity are given, and the condition under which the special Noether symmetry is a special Lie symmetry is obtained. From the special Noether symmetry, the Hojman conserved quantity of the corresponding holonomic system, the weakly Hojman conserved quantity and the strongly Hojman conserved quantity of the nonholonomic systems are obtained. An example is given to illustrate the application of the result.
2004, 53 (5): 1276-1279. doi: 10.7498/aps.53.1276
A direct extension of the known Lie algebra An-1 is presented, a new Lie algebra gl(n,C) is obtained. For the sake of application convenience, Lie algebra gl(3,C) is only considered, whose subalgebra is constructed. By the definition of the subalgebra gradation,a new loop algebra is shown. As its application, an isospectral problem is designed. It follows that a new Lax pair is obtained. By making use of Tu scheme, a family of new Liouville integrable system is resented, which possesses a biHamiltonian structure. As the reduction case of the hierarchy obtained, a new coupled generalized Schrdinger equation is obtained.
Four kinds of raising and lowering operators of three-dimensional isotropic harmonic oscillators with spin-orbit coupling
2004, 53 (5): 1280-1283. doi: 10.7498/aps.53.1280
The method of raising and lowering operator is used to solve the problem of threedimensional isotropic harmonic oscillator with Spinorbit coupling. The energy level splitting of the harmonic oscillator is analyzed and discussed.
Numerical research on critical temperature of Bose-Einstein condensation for gas with interaction in harmonic trap
2004, 53 (5): 1284-1288. doi: 10.7498/aps.53.1284
In this article we study BoseEinstein condensation of the gas with interactions in a harmonic trap using a numerical method. The distribution of the energy states was given, by which the author calculated the shift of the critical temperature and made a comparison with the situation without interactions. We have obtained a positive shift of critical temperature for systems with repulsive interaction, and a negative one for systems with attractive interaction.
Time evolution of two-atom entanglement and thermal entanglement in a generalized Jaynes-Cummings model
2004, 53 (5): 1289-1292. doi: 10.7498/aps.53.1289
In this paper, we investigate twoatom entanglement in time evolution and the thermal entanglement in a generalized JaynesCummings model by means of concurrence. The result shows that the twoatom entangled state appears with periodicity, which decreases with increasing dipoledipole coupling between the two atoms. In a finite temperature, the concurrence decreases with increasing temperature, and the thermal entanglement vanishes in this JaynesCummings model when the system temperature reaches the critical temperature, which is proportional to the dipoledipole coupling strength of the two atoms. For typical experimental data, the critical temperature is on the order of 10-5K. In addition, there exists the quantum phase transition in this JaynesCummings model
2004, 53 (5): 1293-1298. doi: 10.7498/aps.53.1293
The eigenvalue equation of the step finite strained single quantum well is deduced from Schrdinger equation, the influence of the step width on first electron energy, first hole energy, the stimulated wavelength, and the influence of the first hole energy on stimulated wavelength are studied. The results indicate that, if the In content is large, the influence of the first hole energy on the stimulated wavelength should not be neglected. The calculated value by using this model is in accord with the experiment results.
2004, 53 (5): 1299-1304. doi: 10.7498/aps.53.1299
Based on recurrence plot (RP) of chaotic time series, this paper develops the definition of cross recurrence plot (CRP) and the average length of close orbits, which reflects the similarity of two time series and is used to classify time series. By analysing the Lorenz signals, we conclude that the average length is decreased with the decrease of the similarity of two orbits. We have used our method and the crossprediction error in the detection of ECG rhythm. The results show that both methods work for rhythm with different waveforms, but our method works better for rhythms with similar waveforms than the method of cross_prediction error.
2004, 53 (5): 1305-1308. doi: 10.7498/aps.53.1305
Synchronization problem of a class of chaotic systems based on observer is proposed. In the article we propose a simple but effective method for synchronization of a class of chaotic systems by the use of state observer，and analyse the stability of the synchronization system. Numerical simulations are presented to show that the method is effective.
2004, 53 (5): 1309-1315. doi: 10.7498/aps.53.1309
We have studied the secular motion of a single ion stored in a Paul trap and sub jected to a sequence of standing laser pulses. Through theoretical analyses and numerical calculations, we obtain an exact solution of the classical motion equa tion that describes time evolution of the system. By using the exact solution we have investigated regular and chaotic motions of the system. For a weakly trapp ed ion with small confining frequency, a critical condition under which the s ys tem goes into global chaos is found. The loss of stability caused by resonanc e is shown and a method for controlling the instability is established.
Study on the relation between the dielectric properties and lattice distortions in PZT ferroelectric tetragonal phase region
2004, 53 (5): 1316-1320. doi: 10.7498/aps.53.1316
From thermodynamic theory of the lead zirconatetitanate(PZT) solid solution sy stem, we have got the basic equation between the dielectric constant εr a nd lattice distortion c/a in ferroelectric tetragonal phase region, and base d on the relative experimental data and logical deduction to physics image, we h ave established basic relations between εr and c/a. And then, from th e basic relations, we have studied in detail the physics image about lattice dis tortion c/a effect on the dielectric constant εr in ferroelectric tet ragonal phase region. A comparison with related experimental results indicates t hat the results of the basic relations are in good agreement with the conclusion s of the experiments. Finally, we have discussed the application range of the ba sic relations and the physics reason of relative warp out of application range. We would emphasize that the basic relations are essentially fitted to all perovs kite structure materials.
2004, 53 (5): 1321-1324. doi: 10.7498/aps.53.1321
From mechanics and energetics point of view, this paper proves concisely that th e pressure difference between inside and outside of a crownshaped droplet on t he surface of a condenser is different from that of a spherical droplet in the c ondenser, and indicates its disagreement with that shown in the paper by Min J C , 2002, Acta Phys. Sin. 51 2730. The reason is given in this pap er.
The application of total internal reflection fluorescence microscopy in single fluorophore molecules axial imaging
2004, 53 (5): 1325-1330. doi: 10.7498/aps.53.1325
Here we present a method of modeling fluorophore molecules as spheres in evan escent fields mathematically instead of the assumption of tophat function dist r ibution. Based on this model, we discuss that it is possible to calculate relati ve separation distances of the molecules, and their axial positions and diameters with the total internal reflection fluorescence microscopy(TIRFM) due to its uni que intensity pattern in the z direction. In the whole process, we need mere ly to change the incident angle once, that is to get only two frame imaging of TIRFM.
2004, 53 (5): 1331-1334. doi: 10.7498/aps.53.1331
This paper presents the special character of a new type of plastics sc intillator prepared for the diagnosis of the total xrays in Zpinch. The expe ri mental results in the laboratory of Beijing Synchrotron Radiation Facility (BSRF ) indicate that the scintillator has a characteristic of even energy respond in the energy region from 100eV to 1400eV, heavy restrain of visible light, fast de cay time of 6ns.
ATOMIC AND MOLECULAR PHYSICS
2004, 53 (5): 1335-1339. doi: 10.7498/aps.53.1335
Choosing the polarization of the laser,changing the wavelength of the excitation laser and the strength of an external electric field synchronously to keep scal edenergy constant,we have measured M=0 constant scaledenergy absorption spectra of barium Rydberg atoms at scaledenergy ε=-300.Fourier transfor med recurrence spectra were compared with the closedorbit calculation for hydr ogen atom in the uniform approximation.The positions of experimental recurrence peaks fit well the theoretical ones,but the peak strengths differ remarkably,esp ecially in the region of scaledaction larger than 5.This may indicate a large effect of the barium core and the electron correlation on the electron dynamics.
Generation of multi-charged ions in laser-induced ionization of methanol under intense nanosecond laser fields
2004, 53 (5): 1340-1345. doi: 10.7498/aps.53.1340
The photoionization of methanol seeded in He, N2, Ar gases by an inten se 25ns NdYAG 532nm laser has been studied by timeofflight mass spectrome try . At the laser intensity about 1011W·cm-2, strong multicharged io ns Cq+(q=2—4) and Oq+(q=2—4) appeared in the mass spectra apart from the ions coming from multiphoton ionization (MPI) process when Ar w as used as a carrier gas. From the simulation, we can find the vel ocity of multicharged ions is distributed in Gaussian shape with a FWHM of 6 4×104 m/s. From the experimental results of changing carrier gases and changi ng the delay time of the pulsed electric field, the conclusion can be drawn that th ose multicharged ions come from the Coulomb explosion of methanol cluster ions .
2004, 53 (5): 1346-1351. doi: 10.7498/aps.53.1346
Optical dipole potential in an inhomogeneous light field is an important method of realizing the laser cooling and trapping of single atoms. The optical dipole trap in the highfinesse microcavity is discussed, and different confi gur ations of optical potential composed of standing wave and vertical confined beam s are analyzed. It is shown that the submicron scale optical trap could be ob t ained in this microcavity with the potential depth of about mK. The strong cou pling of atom and the cavity mode can be realized. We also discuss the effect of laser line width on the depth of potential well.
CLASSICAL AREA OF PHENOMENOLOGY
2004, 53 (5): 1352-1356. doi: 10.7498/aps.53.1352
By means of canonicalization transformation, we study the quantization of dissi pative mesoscopic capacitance coupling circuit, and discuss the quantum fluctuat ions of charges and generalized currents in the system.
2004, 53 (5): 1357-1361. doi: 10.7498/aps.53.1357
By using the definition of generalized secondorder moments and co m plex Gaussian functions expansion of rectangular function, the analytical expres sions for the generalized M2factor and mode coherence coefficients of th e new m odel of flattopped beams introduced by Li have been derived. The mode correlat i on, mode structure, and coherentmode decomposition of flattopped beams have be en analyzed. Theory of the coherentmode decomposition of truncated flattoppe d beams is built.
2004, 53 (5): 1362-1366. doi: 10.7498/aps.53.1362
By means of a unique electrode construction and preionization burstmode switch technology, 5kW pulse average output is obtained in a transverse flow CO2 las er.
Influence of dark irradiation on transition process from self-defocusing to self-focusing in LiNbO3:Fe crystals
2004, 53 (5): 1367-1372. doi: 10.7498/aps.53.1367
We have studied the dynamic propagation of an optical beam from selfdefocusing to selffoc using in photovoltaic photorefractive crystals LiNbO3:Fe in the framework of a t wodimensional band transport model. The results show that dark irradiation pla ys an important part in the transition process. The transition occurs only when th e normalized dark irradiation is very small. We discuss also the influence of py roelectric effect on the transition process.
2004, 53 (5): 1373-1377. doi: 10.7498/aps.53.1373
This paper studies the adiabatic soliton compression of pulses in dispersion dec reasing fibers(DDF).We indicate that although high quality compressed pulse coul d be achieved from ps fundamental soliton by using DDF with linear profile,the r equired fiber length is too long to be useful.As a result,higher order soliton c ompression in DDF is proposed to achieve large compression factor and high quali ty compression with relatively short fiber lengths.
2004, 53 (5): 1378-1383. doi: 10.7498/aps.53.1378
The absorption spectra, fluorescence spectra, fluorescence lifetime and thermal stability of Er3+doped (50x)SiO2xBi2O350PbF2 (x =0, 3, 5, 8, 10, 13, 15 mol%) glasses were investigated. The intensity paramet ers Ωt (t=2,4,6) were calculated by JuddOfelt theory, and the stimulate d emission sectionsections of 4I13/2→4I15/2 transitio ns were calculated by McCumber. The results showed that the FWHM value is relate d to the Ω6 parameter, and the larger the Ω6 parameter, the broade r the FWHM. Compared with other glass hosts, the gain bandwidth property of Er 3+doped SBP3 glass is close to those of tellurite and bismuth glasses, and much greater than those of silicate, a phosphate and germanate glass, which sho ws that Er3+doped heavy metal oxyfluoride bismuth silicate glasses can b e used as host materials for broadband optical amplifier.
2004, 53 (5): 1384-1390. doi: 10.7498/aps.53.1384
In this paper, optical pulse compression using a dispersion shift fiber and a standard singlemode fiber is demonstrated both analytically and experime nta lly. The effects of fiber and input pulse parameters on the compressing quality are discussed through numerical simulation. Experimental results of compressing puls es generated from a harmonically modelocked fiber laser verify that highqual ity pulses can be obtained using this compression method.