Gutzwiller trace formula
E653526
The Gutzwiller trace formula is a semiclassical tool in quantum chaos that links the quantum energy spectrum of a system to the properties of its classical periodic orbits.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Gutzwiller trace formula canonical | 2 |
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
semiclassical approximation
ⓘ
theoretical physics concept ⓘ trace formula ⓘ |
| appliesTo |
bounded Hamiltonian systems
ⓘ
classically chaotic systems ⓘ quantum systems with chaotic classical limit ⓘ systems with discrete energy spectrum ⓘ |
| approximationMethod | stationary phase approximation ⓘ |
| approximationType | semiclassical limit ⓘ |
| assumes |
hyperbolic classical dynamics
ⓘ
isolated unstable periodic orbits ⓘ |
| basedOn | periodic orbit theory ⓘ |
| characterizes | fluctuating part of the density of states ⓘ |
| developedBy | Martin C. Gutzwiller NERFINISHED ⓘ |
| expresses | density of states as sum over periodic orbits ⓘ |
| field |
classical mechanics
ⓘ
mathematical physics ⓘ quantum chaos ⓘ quantum mechanics ⓘ semiclassical physics ⓘ |
| framework | path integral formulation of quantum mechanics ⓘ |
| generalizationOf |
Bohr–Sommerfeld quantization
NERFINISHED
ⓘ
Einstein–Brillouin–Keller quantization NERFINISHED ⓘ |
| hasComponent |
oscillatory periodic orbit sum
ⓘ
smooth Weyl term ⓘ |
| involves |
amplitudes determined by orbit stability
ⓘ
phases determined by classical action ⓘ sum over all classical periodic orbits ⓘ |
| limit | Planck constant going to zero ⓘ |
| publishedIn | Journal of Mathematical Physics NERFINISHED ⓘ |
| relatedTo |
Berry–Tabor formula
NERFINISHED
ⓘ
Selberg trace formula NERFINISHED ⓘ random matrix theory ⓘ |
| relates |
classical periodic orbits
ⓘ
quantum energy spectrum ⓘ |
| usedFor |
calculation of level density fluctuations
ⓘ
semiclassical quantization of chaotic systems ⓘ spectral statistics of quantum systems ⓘ |
| usedIn |
mesoscopic physics
ⓘ
molecular spectroscopy ⓘ nuclear physics ⓘ quantum billiards ⓘ solid-state physics ⓘ |
| usesConcept |
Lyapunov exponents
ⓘ
Maslov index NERFINISHED ⓘ classical action ⓘ stability matrix ⓘ |
| validIn | short-wavelength limit ⓘ |
| yearProposed | 1971 ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.