Realizability, Kramers-Kronig relations and Fuoss-Kirkwood dielectric

✍ Scribed by H. Pelzer

• Publisher: Elsevier Science
• Year: 1956
• Weight: 333 KB
• Volume: 22
• Category: Article
• ISSN: 0031-8914
• DOI: 10.1016/s0031-8914(56)80014-1

✦ Synopsis

Synopsis

A recent statement by Brachman and Macdonald that the commonly accepted conditions of realizability are too stringent and are not fulfilled for the Fuoss-Kirkwood dielectric is not correct. On the other hand, the usual formulation could be somewhat amplified when dealing with an admittance function which is analytically multivalued. In this case only the principal value of the function has physical significance and the "lower sheets" of its Riemann surface are to be discarded (poles in them do not matter, even if they lie in a normally "forbidden" half plane) and the branch cuts become line singularities of a now univalued physical function. This is in line with the genesis of such functions from infinite continued fractions corresponding to a ladder structure.