Resonances| Resonances |
In General > s.a. solar
planets; chaos; oscillator.
* In hep: A resonance
is an unstable particle whose existence is inferred from a peak in the invariant
mass distribution
of other sets of particles into which
it
decays; The peak width 
and
lifetime 
are related
by =
/; > s.a. quantum
mechanics.
* Relativistic, theory:
A pole of the S-matrix at a complex value
sR of the energy squared s.
* Descriptions: Can use Gamow vectors, the S-matrix, or the Green
function; Usually associated with time asymmetry.
@ References: Mosini SHPMP(00)
[history]; Bohm & Sato PRD(05)
[general theory, properties]; de la Madrid qp/06-in
[rigged Hilbert space description]; Rotter a0710 [and decay, Feshbach projector
description].
Gamow Vectors
@ General references: Bohm et al AJP(89);
Bollini et al PLB(96);
de la Madrid & Gadella AJP(02)qp [intro];
Castagnino et al JPA(01)qp/02,
PLA(01)qp/02;
Civitarese & Gadella PRP(04);
Kaldass ht/05-in; > s.a. Friedrichs
Model.
@ Relativistic: Antoniou et al JMP(98);
Kielanowski IJTP(03).
@ Special systems: Antoniou et al JMP(98)
[degenerate scattering resonances], JPA(03)
[models], IJTP(03)
[exactly solvable].
@ Related topics: Gaioli et al IJTP(99)
[and time asymmetry]; Castagnino et al JPA(02) [decay prcesses].
Special Types and Related Topics
* Parametric resonances: Resonances
that arise when the paremeters on which an oscillating system depends are varied
periodically, and the driving frequency goes through special values; Example:
An LC circuit with characteristic frequency 
=
(LC)–1/2 in which the capacitance C is
varied periodically.
@ Parametric: Weigert JPA(02)qp/01 [quantum];
Berges & Serreau PRL(03)hp/02 [in
quantum field theory]; Leroy et al EJP(06)
[Hamiltonian approach].
@ Parametric wave excitation: Bechhoefer & Johnson AJP(96) [Faraday
waves].
@ Related topics: Bohm & Harshman NPB(00)hp,
Bohm et al ht/01 [mass
and width];
Kleefeld ht/03-in
[formulation]; Stefanov mp/04 [Complex
Absorbing Potential method]; de la Madrid et al CzJP(05)qp [resonance
expansions].
Applications > see particle effects.
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
25 may 2008