Resonances| Resonances |
In General > s.a. solar
planets; chaos; oscillator.
* In particle physics:
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 Γ and lifetime τ are related by
Γ = \(\hbar\)/τ; > s.a. quantum mechanics.
* Relativistic, theory: A pole
of the S-matrix at a complex value sR
of the energy squared s.
* Descriptions: One can use
Gamow vectors, the S-matrix, or the Green function; They are usually associated
with time asymmetry.
@ Mechanical and general resonances: Rosas-Ortiz et al AIP(08)-a0902 [primer];
Bleck-Neuhaus a1811 [mechanical, history].
@ In particle physics:
Mosini SHPMP(00) [history];
Bohm & Sato PRD(05) [general theory, properties];
de la Madrid AIP(07)qp/06 [rigged-Hilbert-space description];
Hatano et al Pra(09)-a0904-proc [probabilistic interpretation];
Gluskin et al a1003 [graphical convolution approach];
Bohm RPMP(11),
Gadella & Kielanowski RPMP(11) [formalism].
@ Decay: Rotter a0710 [Feshbach-projector description];
de la Madrid NPA(15)-a1505 [decay widths, constants and branching fractions];
Baumgärtel a1706 [mathematical];
Wyrzykowski a1801 [transition to non-exponential decay].
Gamow States / Vectors > s.a. quantum state evolution
[decay of unstable states]; types of quantum states [unstable].
* Idea: Generalized eigenvectors of
a quantum Hamiltonian with complex eigenvalues that describe exponentially decaying
(or growing) states and can be used to model irreversibility in quantum theory.
@ General references: Bohm et al AJP(89)dec;
Bollini et al PLB(96);
Gaioli et al IJTP(99) [and time asymmetry];
de la Madrid & Gadella AJP(02)jun-qp [intro];
Castagnino et al JPA(01)qp/02,
PLA(01)qp/02;
Civitarese & Gadella PRP(04);
Kaldass ht/05-conf;
de la Madrid JMP(12)-a1210 [rigged-Hilbert-space approach];
> 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].
Special Types and Related Topics
* Parametric resonance: A resonance
that arises when the parameters on which an oscillating system depends are varied
periodically, and the driving frequency goes through special values;
Example: An LC circuit with characteristic frequency ω
= (LC)−1/2 in which the capacitance
C is varied periodically.
* Stochastic resonance:
The amplification of a periodic signal applied to a non-linear system
obtained by adding noise.
* Feshbach resonance: A scattering resonance
that occurs when the energy of an unbound state of a two-body system matches the energy of
an excited state of the compound system; Recognized long ago as an important feature in
nuclear, atomic, and molecular scattering, and in photoionization and photodissociation,
they have assumed new importance in ultracold atomic systems.
@ 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)dec [Faraday waves].
@ Stochastic resonance: Marchesoni Phy(09) [in mechanical system and Bose-Einstein condensates].
@ Related topics: Bohm & Harshman NPB(00)hp,
Bohm et al ht/01 [mass and width];
Kleefeld ht/03-conf [formulation];
Stefanov mp/04 [Complex Absorbing Potential method];
de la Madrid et al CzJP(05)qp [resonance expansions];
Chin et al RMP(10) [Feshbach resonances in ultracold gases].
Applications > see particle effects.
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– abbreviations
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– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 18 jan 2020