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.
@ References: Mosini SHPMP(00) [history]; Bohm & Sato PRD(05) [general theory, properties]; de la Madrid AIP(07)qp/06 [rigged-Hilbert-space description]; Rosas-Ortiz et al AIP(08)-a0902 [primer]; 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]; Baungärtel a1706 [mathematical].

Gamow States / Vectors > s.a. quantum effects [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 resonances 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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