Preserving threshold resonances and avulsion of eigenvalues from the threshold of the continuous spectrum of quantum waveguides

2021 ◽  
Vol 212 (7) ◽  
Author(s):  
Sergei Aleksandrovich Nazarov
Keyword(s):  
Continuous Spectrum ◽  
Quantum Waveguides ◽  
Threshold Resonances

scholarly journals Mathematical scattering theory in quantum waveguides

2019 ◽  
Vol 489 (2) ◽  
pp. 142-146
Author(s):  
B. A. Plamenevskii ◽  
A. S. Poretskii ◽  
O. V. Sarafanov
Keyword(s):  
Continuous Spectrum ◽  
Scattering Theory ◽  
Scattering Matrix ◽  
Stationary Problem ◽  
Variable Coefficients ◽  
Scattering Operator ◽  
Wave Operators ◽  
Order Elliptic Operator ◽  
The Laplace Operator ◽  
Quantum Waveguides

A waveguide occupies a domain G with several cylindrical ends. The waveguide is described by a nonstationary equation of the form it f = Af ,where A is a selfadjoint second order elliptic operator with variable coefficients (in particular, for A = -, where stands for the Laplace operator, the equation coincides with the Schrodinger equation). For the corresponding stationary problem with spectral parameter, we define continuous spectrum eigenfunctions and a scattering matrix. The limiting absorption principle provides expansion in the continuous spectrum eigenfunctions. We also calculate wave operators and prove their completeness. Then we define a scattering operator and describe its connections with the scattering matrix.

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

scholarly journals Nontrivial topology in the continuous spectrum of a magnetized plasma

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Jeffrey B. Parker ◽  
J. W. Burby ◽  
J. B. Marston ◽  
Steven M. Tobias
Keyword(s):  
Continuous Spectrum ◽  
Magnetized Plasma ◽  
Nontrivial Topology

α-Adrenoceptor agonists and the Ca2+-dependence of smooth muscle contraction: evidence for subtypes of receptors or for agonist-dependent differences in the agonist-receptor interaction?

1985 ◽  
Vol 68 (s10) ◽  
pp. 55s-63s ◽  
Author(s):  
John C. McGrath
Keyword(s):  
Smooth Muscle ◽  
Muscle Contraction ◽  
Continuous Spectrum ◽  
Contractile Response ◽  
Nitrilotriacetic Acid ◽  
Smooth Muscle Contraction ◽  
Receptor Type ◽  
Receptor Interaction ◽  
Initial Transient ◽  
Adrenoceptor Agonists

1. The effects of varying [Ca2+]o on the contraction of smooth muscle by different α-adrenoceptor agonists were examined on rat isolated anococcygeus muscle. Agonists were tested in the presence of various [Ca2+]o or ‘Ca2+-re-addition curves’ were constructed. In some experiments the [Ca2+]free was buffered with EGTA and nitrilotriacetic acid. The components of the response which were revealed were further analysed by using drugs which modify Ca2+ mobilization. 2. Three separate elements in the contractile response were identified: (i) an initial transient contraction, due to intracellular Ca2+ release could be isolated with [Ca2+]o between 1 nmol/l and 3 μmol/l (this could be obtained only with noradrenaline, phenylephrine and amidephrine); (ii) a nifedipine-sensitive response requiring [Ca2+]o of 3 μmol/l or more; (iii) a nifedipine-resistant response requiring [Ca2+]o of 100 μmol/l or more. Presumably (ii) and (iii) involve the entry of Ca2+o: they could be obtained with all agonists tested, including these above, methoxamine, indanidine and xylazine. 3. The results are discussed in relation to the possibility of distinct types of response and their relationship to subgroups of receptors or agonists. It is concluded that there is a continuous spectrum of activity across the agonist range and that this is likely to correlate with ‘efficacy’ at a single α1 receptor type.

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