1991 |
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| 3. | Pandey, A; Ramaswamy, R Level spacings for harmonic oscillator systems Journal Article Physical Review A, 43 (8), pp. 4237–4243, 1991. Abstract | Links | BibTeX | Tags: Quantum State @article{Pandey1991, title = {Level spacings for harmonic oscillator systems}, author = {A Pandey and R Ramaswamy }, url = {https://link.aps.org/doi/10.1103/PhysRevA.43.4237}, doi = {10.1103/PhysRevA.43.4237}, year = {1991}, date = {1991-04-01}, journal = {Physical Review A}, volume = {43}, number = {8}, pages = {4237–4243}, abstract = {From the viewpoint of eigenvalue level statistics, harmonic-oscillator systems are unusual. Although integrable, these systems are nongeneric, and a spacing distribution does not exist even as the number of levels N→∞. The origins of this pathological behavior are explored using methods of number theory and ergodic analysis. However, such nongenericity is extremely fragile, and the smallest nonlinearity asymptotically restores generic behavior. These results are of relevance to the study of molecular spectra, as well as to the quasienergy spectra of integrable quantum maps.}, keywords = {Quantum State}, pubstate = {published}, tppubtype = {article} } From the viewpoint of eigenvalue level statistics, harmonic-oscillator systems are unusual. Although integrable, these systems are nongeneric, and a spacing distribution does not exist even as the number of levels N→∞. The origins of this pathological behavior are explored using methods of number theory and ergodic analysis. However, such nongenericity is extremely fragile, and the smallest nonlinearity asymptotically restores generic behavior. These results are of relevance to the study of molecular spectra, as well as to the quasienergy spectra of integrable quantum maps. |
1989 |
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| 2. | A O Caldeira, Cerdeira H A; Ramaswamy, R Limits of weak damping of a quantum harmonic oscillator Journal Article Physical Review A, 40 (6), pp. 3438–3440, 1989. Abstract | Links | BibTeX | Tags: Quantum State @article{Caldeira1989, title = {Limits of weak damping of a quantum harmonic oscillator}, author = {A O Caldeira, H A Cerdeira and R Ramaswamy}, url = {https://link.aps.org/doi/10.1103/PhysRevA.40.3438}, doi = {10.1103/PhysRevA.40.3438}, year = {1989}, date = {1989-09-01}, journal = {Physical Review A}, volume = {40}, number = {6}, pages = {3438–3440}, abstract = {In this Brief Report we analyze the limit of very weak damping of a quantum-mechanical Brownian oscillator. It is shown that the propagator for the reduced density operator of the oscillator can be written as a double path integral of the same form as that obtained in the high-temperature limit. As a direct consequence, we can write a Fokker-Planck equation for the reduced density operator of the weakly damped oscillator (at any temperature) involving only the damping and a generalized diffusion constant in momentum space.}, keywords = {Quantum State}, pubstate = {published}, tppubtype = {article} } In this Brief Report we analyze the limit of very weak damping of a quantum-mechanical Brownian oscillator. It is shown that the propagator for the reduced density operator of the oscillator can be written as a double path integral of the same form as that obtained in the high-temperature limit. As a direct consequence, we can write a Fokker-Planck equation for the reduced density operator of the weakly damped oscillator (at any temperature) involving only the damping and a generalized diffusion constant in momentum space. |
1984 |
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| 1. | Ramaswamy, R Quasiperiodic quantum states Journal Article The Journal of Chemical Physics, 80 (12), pp. 6194–6199 , 1984, ISSN: 0021-9606. Abstract | Links | BibTeX | Tags: Perturbation, Quantum State @article{Ramaswamy1984bb, title = {Quasiperiodic quantum states}, author = {R Ramaswamy}, url = {https://pubs.aip.org/aip/jcp/article-pdf/80/12/6194/11014720/6194\_1\_online.pdf}, doi = {10.1063/1.446721}, issn = {0021-9606}, year = {1984}, date = {1984-06-15}, journal = {The Journal of Chemical Physics}, volume = {80}, number = {12}, pages = {6194–6199 }, abstract = {We show that the Hose–Taylor criterion of quantum quasiperiodicity can be recovered from low‐order nondegenerate perturbation theory. It is seen that this mnemonic, which purports to identify energy levels which can be obtained by quantizing classical quasiperiodic motions, can lead to contradictions when applied to systems which are more semiclassical than that treated previously. These discrepancies arise since the criterion is both perturbation scheme and basis set dependent: the correlation between the semiclassical quantization and such a definition of quantum quasiperiodic behavior is not straightforward. As the underlying search is for a quantum KAM‐like theory (in particular for near‐separable systems which are typical of molecular vibrational Hamiltonians) some possibilities are discussed.}, keywords = {Perturbation, Quantum State}, pubstate = {published}, tppubtype = {article} } We show that the Hose–Taylor criterion of quantum quasiperiodicity can be recovered from low‐order nondegenerate perturbation theory. It is seen that this mnemonic, which purports to identify energy levels which can be obtained by quantizing classical quasiperiodic motions, can lead to contradictions when applied to systems which are more semiclassical than that treated previously. These discrepancies arise since the criterion is both perturbation scheme and basis set dependent: the correlation between the semiclassical quantization and such a definition of quantum quasiperiodic behavior is not straightforward. As the underlying search is for a quantum KAM‐like theory (in particular for near‐separable systems which are typical of molecular vibrational Hamiltonians) some possibilities are discussed. |