Publications (2)0.93 Total impact
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ABSTRACT: In this paper, we study a class of Jacobi matrices with very rapidly decreasing weights. It is shown that the Weyl function (the matrix element of the resolvent of the operator) for the class under study can be expressed as the ratio of two entire transcendental functions of order zero. It is shown that the coefficients in the expansion of these functions in Taylor series are proportional to the generating functions of the number of integral solutions defined by certain Diophantine equations. An asymptotic estimate for the eigenvalues is obtained.Mathematical Notes 08/2003; 74(3):425437. DOI:10.1023/A:1026171122104 · 0.26 Impact Factor 
Article: Energy spectrum of the Hamiltonian of the JaynesCummings model without rotatingwave approximation
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ABSTRACT: The energy spectrum of the Hamiltonian of the JaynesCummings model without a rotatingwave approximation is studied. The trajectories of eigenvalues as functions of the dimensionless coupling constant are constructed. It is shown that the spectrum approaches the equidistant spectrum, i.e., the oscillator spectrum, as the coupling constant increases. As a result, each energy level becomes doubly degenerate.Optics and Spectroscopy 11/2001; 91(6):899902. DOI:10.1134/1.1429703 · 0.67 Impact Factor
Publication Stats
11  Citations  
0.93  Total Impact Points  
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Institutions

2003

Saint Petersburg State University
 Department of Higher Mathematics
SanktPeterburg, St.Petersburg, Russia


2001

Vavilov State Optical Institute
SanktPeterburg, St.Petersburg, Russia
