Edge diffraction, trace formulae and the cardioid billiard
نویسندگان
چکیده
منابع مشابه
Edge Diffraction, Trace Formulae and the Cardioid Billiard
We study the effect of edge diffraction on the semiclassical analysis of two dimensional quantum systems by deriving a trace formula which incorporates paths hitting any number of vertices embedded in an arbitrary potential. This formula is used to study the cardioid billiard, which has a single vertex. The formula works well for most of the short orbits we analyzed but fails for a few diffract...
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Trace formulae provide one of the most elegant descriptions of the classical-quantum correspondence. One side of a formula is given by a trace of a quantum object, typically derived from a quantum Hamiltonian, and the other side is described in terms of closed orbits of the corresponding classical Hamiltonian. In algebraic situations, such as the original Selberg trace formula, the identities a...
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In this note, we discuss the cardiod. We give purely geometric proofs of its well-known properties. Definitions and Basic Properties Fig. 1 The curve in Figure 1 is called a cardioid. The name is derived from the Greek word “καρδια” meaning “heart”. A cardioid has many interesting properties and very often appears in different fields of mathematics and physics. The study of geometric properties...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 1996
ISSN: 0951-7715,1361-6544
DOI: 10.1088/0951-7715/9/4/012