1973
DOI: 10.1070/rm1973v028n01abeh001397
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J-EXPANDING MATRIX FUNCTIONS AND THEIR ROLE IN THE ANALYTICAL THEORY OF ELECTRICAL CIRCUITS

Abstract: Non-relativistic rates for the decay of 2s hydrogen atoms to the ground state by single-photon and two-photon emission in the presence of a homogeneous magnetic field of arbitrary strength (0 4.7 x lo6 T) are calculated by variational procedures. Over the whole range of B, two-photon emission is the dominant process. As the magnetic field grows, the two-photon decay rate increases. It is found that the Markov approximation can be applied to the two-photon decay for magnetic fields of strength B 3 4.7 x lo3 T. B Show more

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Cited by 65 publications
(36 citation statements)
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“…Under this condition, the cascade matrix is considered to be a J-unitary matrix [6]. By calculating the determinants of the two sides, we obtain |AD−BC| 2 = 1 (6.3a) This can be generally rewritten as…”
Section: Cascade Matrix Representing Lossless Reciprocal Circuitmentioning
confidence: 99%
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“…Under this condition, the cascade matrix is considered to be a J-unitary matrix [6]. By calculating the determinants of the two sides, we obtain |AD−BC| 2 = 1 (6.3a) This can be generally rewritten as…”
Section: Cascade Matrix Representing Lossless Reciprocal Circuitmentioning
confidence: 99%
“…A two-terminal pair circuit having reactances [2] is lossless, and this condition is generalized as follows [6].…”
Section: Cascade Matrix Representing Lossless Reciprocal Circuitmentioning
confidence: 99%
See 1 more Smart Citation
“…, N (matrices A k are assumed to have real entries), due to their relation to electrical circuits. He proved that such functions constitute the class (let us denote it by RB n×n N ) of characteristic matrix functions of passive 2n-poles, where impedances of elements (resistances, capacitances, inductances and ideal transformers are allowed) are considered as independent variables (let us note, that in the analytic theory of electrical circuits it is customary to consider characteristic matrices as functions of frequency, e.g., see [16,19,12,17]). It is easy to verify that any f ∈ RB n×n N satisfies the following properties: = {f (z) = zA : A = A * ≥ 0}, where z ∈ C and A is an n × n matrix with real (resp., complex) entries, thus this case is trivial.…”
Section: Introductionmentioning
confidence: 99%
“…The circle and line cases were studied in a unified way in [5]. We mention also the earlier papers [36,23] that inspired much of ivestigation of these and other classes of rational matrix-valued functions with symmetries.…”
Section: Introductionmentioning
confidence: 99%