684 research outputs found
Squeezing: the ups and downs
We present an operator theoretic side of the story of squeezed states
regardless the order of squeezing. For low order, that is for displacement
(order 1) and squeeze (order 2) operators, we bring back to consciousness what
is know or rather what has to be known by making the exposition as exhaustive
as possible. For the order 2 (squeeze) we propose an interesting model of the
Segal-Bargmann type. For higher order the impossibility of squeezing in the
traditional sense is proved rigorously. Nevertheless what we offer is the
state-of-the-art concerning the topic.Comment: 21 pages; improved presentation; it has been published by Proceedings
of the Royal Society
Combinatorial Physics, Normal Order and Model Feynman Graphs
The general normal ordering problem for boson strings is a combinatorial
problem. In this note we restrict ourselves to single-mode boson monomials.
This problem leads to elegant generalisations of well-known combinatorial
numbers, such as Bell and Stirling numbers. We explicitly give the generating
functions for some classes of these numbers. Finally we show that a graphical
representation of these combinatorial numbers leads to sets of model field
theories, for which the graphs may be interpreted as Feynman diagrams
corresponding to the bosons of the theory. The generating functions are the
generators of the classes of Feynman diagrams.Comment: 9 pages, 4 figures. 12 references. Presented at the Symposium
'Symmetries in Science XIII', Bregenz, Austria, 200
Squeezed States and Hermite polynomials in a Complex Variable
Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec
[J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of
coherent states, related to the Hermite polynomials in a complex variable which
are orthogonal with respect to a non-rotationally invariant measure. We
investigate relations between these coherent states and obtain the relationship
between them and the squeezed states of quantum optics. We also obtain a second
realization of the canonical coherent states in the Bargmann space of analytic
functions, in terms of a squeezed basis. All this is done in the flavor of the
classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page
- …