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71.
In the present paper, we find a class of linear homogeneous differential equations of order n + 1 (n > 1) whose fundamental system of solutions is constructed from the fundamental system of solutions of a second-order differential
equation. The spectral properties of differential operators generated by these differential expressions are investigated.
In particular, sufficient conditions are obtained for the coefficients of a second-order differential equation under which
the case of maximal deficiency indices is realized.
Dedicated to the memory of B. M. Levitan 相似文献
72.
N. S. Simonović 《Few-Body Systems》2006,38(2-4):139-145
In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates
from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation
of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of
the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian
in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical
form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than
those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the
analysis of energy spectra. 相似文献
73.
On Quantum Team Games 总被引:2,自引:0,他引:2
E. Ahmed M. F. Elettreby A. S. Hegazi 《International Journal of Theoretical Physics》2006,45(5):880-886
Recently Liu and Simaan (2004) convex static multi-team classical games have been introduced. Here they are generalized to both nonconvex, dynamic and quantum games. Puu's incomplete information dynamical systems are modified and applied to Cournot team game. The replicator dynamics of the quantum prisoner's dilemma game is also studied. 相似文献
74.
We present the design and study of waveguide structures based on porous silicon where the light confinement is not due to the usual total reflection effect but to the use of photonic crystals (PCs) as confining walls. These PC are omnidirectional mirrors (OMs), consisting of the periodic repetition of two porous silicon layers with different refractive indices and thicknesses. They reflect the radiation for all angles of incidence within a frequency range called the omnidirectional band gap (OBG). We have followed the PC formalism to investigate the properties of the OM as a multimode waveguide: the number of modes within the band gap, their field spatial distribution and their confinement as a function of the frequency and the core thickness. 相似文献
75.
S. Meenakshi B.K. Godwal I. Orgzall S. Tkachev 《Journal of Physics and Chemistry of Solids》2006,67(8):1660-1667
We report the results of an X-ray diffraction study of CdAl2Se4 and of Raman studies of HgAl2Se4 and ZnAl2Se4 at room temperature, and of CdAl2S4 and CdAl2Se4 at 80 K at high pressure. The ambient pressure phase of CdAl2Se4 is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl2Se4 and ZnAl2Se4 reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl2S4 and CdAl2Se4, which shows a very weak temperature dependence of the Raman-active phonon modes. 相似文献
76.
Analytical expressions are obtained that describe the changes in the degree of coherence and in the thickness of the coherence layers occurring upon propagation of a dispersed broadband laser beam. It is found that the greater the tilting of the coherence layers with respect to the phase fronts, the more rapidly the spatial coherence is violated with increasing distance. A comparison with the case of an undispersed beam is performed. It is shown that, as the beam propagates, the decrease in the degree of coherence is accompanied by the appearance of spatial fluctuations of this parameter. The degree of mutual coherence of intersecting dispersed beams with parallel correlated coherence layers, which determines the efficiency of their coherent interaction, is investigated. The existence of spatial fluctuations of the degree of mutual coherence is established. 相似文献
77.
Benjamin J. K. Evans Susan M. Scott Antony C. Searle 《General Relativity and Gravitation》2002,34(10):1675-1684
We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time. 相似文献
78.
K. C. Shin 《Communications in Mathematical Physics》2002,229(3):543-564
We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have for all , then the eigenvalues are all positive real. We then sharpen this to a larger class of polynomial potentials.
In particular, this implies that the eigenvalues are all positive real for the potentials when with , and with the boundary conditions that decays to zero as z tends to infinity along the positive and negative real axes. This verifies a conjecture of Bessis and Zinn-Justin.
Received: 16 January 2002 / Accepted: 1 May 2002 Published online: 6 August 2002 相似文献
79.
K. Wieand 《Probability Theory and Related Fields》2002,123(2):202-224
Let U be an n × n random matrix chosen from Haar measure on the unitary group. For a fixed arc of the unit circle, let X be the number of eigenvalues of M which lie in the specified arc. We study this random variable as the dimension n grows, using the connection between Toeplitz matrices and random unitary matrices, and show that (X -E [X])/(\Var (X))1/2 is asymptotically normally distributed. In addition, we show that for several fixed arcs I
1
, ..., I
m
, the corresponding random variables are jointly normal in the large n limit.
Received: 15 November 2000 / Revised version: 27 September 2001 / Published online: 17 May 2002 相似文献
80.
E. L. Patsevich 《Journal of Mathematical Sciences》2002,110(5):3013-3015
Some estimates of derivatives are sharpened for quasiconformal reflections of a special class of simply connected plane domains. Bibliography: 2 titles. 相似文献