Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula
Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Quantum Reports |
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| Online Access: | https://www.mdpi.com/2624-960X/4/4/40 |
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| author | Alfredo M. Ozorio de Almeida |
| author_facet | Alfredo M. Ozorio de Almeida |
| author_sort | Alfredo M. Ozorio de Almeida |
| collection | DOAJ |
| description | Oscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints that coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. It is shown here that the probability density is the double Fourier transform of this trace, and that the closed compound orbits emulate the role played by the periodic orbits in Gutzwiller’s trace formula in its semiclassical evaluation. The phase of the oscillations with the energies or the evolution parameters agree with those previously obtained, whereas the amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl–Wigner representation in which the calculation was carried out. |
| first_indexed | 2024-03-09T15:54:56Z |
| format | Article |
| id | doaj.art-e5328601bace49bfaab4915be5fb8806 |
| institution | Directory Open Access Journal |
| issn | 2624-960X |
| language | English |
| last_indexed | 2024-03-09T15:54:56Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Quantum Reports |
| spelling | doaj.art-e5328601bace49bfaab4915be5fb88062023-11-24T17:42:53ZengMDPI AGQuantum Reports2624-960X2022-11-014455856510.3390/quantum4040040Energy Transition Density of Driven Chaotic Systems: A Compound Trace FormulaAlfredo M. Ozorio de Almeida0Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, BrazilOscillations in the probability density of quantum transitions of the eigenstates of a chaotic Hamiltonian within classically narrow energy ranges have been shown to depend on closed compound orbits. These are formed by a pair of orbit segments, one in the energy shell of the original Hamiltonian and the other in the energy shell of the driven Hamiltonian, with endpoints that coincide. Viewed in the time domain, the same pair of trajectory segments arises in the semiclassical evaluation of the trace of a compound propagator: the product of the complex exponentials of the original Hamiltonian and of its driven image. It is shown here that the probability density is the double Fourier transform of this trace, and that the closed compound orbits emulate the role played by the periodic orbits in Gutzwiller’s trace formula in its semiclassical evaluation. The phase of the oscillations with the energies or the evolution parameters agree with those previously obtained, whereas the amplitude of the contribution of each closed compound orbit is more compact and independent of any feature of the Weyl–Wigner representation in which the calculation was carried out.https://www.mdpi.com/2624-960X/4/4/40quantum energy transitionssemiclassical trace formulaecompound classical trajectories |
| spellingShingle | Alfredo M. Ozorio de Almeida Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula Quantum Reports quantum energy transitions semiclassical trace formulae compound classical trajectories |
| title | Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula |
| title_full | Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula |
| title_fullStr | Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula |
| title_full_unstemmed | Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula |
| title_short | Energy Transition Density of Driven Chaotic Systems: A Compound Trace Formula |
| title_sort | energy transition density of driven chaotic systems a compound trace formula |
| topic | quantum energy transitions semiclassical trace formulae compound classical trajectories |
| url | https://www.mdpi.com/2624-960X/4/4/40 |
| work_keys_str_mv | AT alfredomozoriodealmeida energytransitiondensityofdrivenchaoticsystemsacompoundtraceformula |