dorsal/arxiv
View SchemaExact time evolution and master equations for the damped harmonic oscillator
| Authors | Robert Karrlein, Hermann Grabert |
|---|---|
| Categories | |
| ArXiv ID | physics/9610001 |
| URL | https://arxiv.org/abs/physics/9610001 |
| DOI | 10.1103/PhysRevE.55.153 |
| Journal | Phys.Rev. E55 (1997) 153-164 |
Abstract
Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact non-stationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact new master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time-evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude and weak coupling cases. The connection with earlier work is discussed.
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"abstract": "Using the exact path integral solution for the damped harmonic oscillator it\nis shown that in general there does not exist an exact dissipative Liouville\noperator describing the dynamics of the oscillator for arbitrary initial bath\npreparations. Exact non-stationary Liouville operators can be found only for\nparticular preparations. Three physically meaningful examples are examined. An\nexact new master equation is derived for thermal initial conditions. Second,\nthe Liouville operator governing the time-evolution of equilibrium correlations\nis obtained. Third, factorizing initial conditions are studied. Additionally,\none can show that there are approximate Liouville operators independent of the\ninitial preparation describing the long time dynamics under appropriate\nconditions. The general form of these approximate master equations is derived\nand the coefficients are determined for special cases of the bath spectral\ndensity including the Ohmic, Drude and weak coupling cases. The connection with\nearlier work is discussed.",
"arxiv_id": "physics/9610001",
"authors": [
"Robert Karrlein",
"Hermann Grabert"
],
"categories": [
"physics.atom-ph",
"quant-ph"
],
"doi": "10.1103/PhysRevE.55.153",
"journal_ref": "Phys.Rev. E55 (1997) 153-164",
"title": "Exact time evolution and master equations for the damped harmonic oscillator",
"url": "https://arxiv.org/abs/physics/9610001"
},
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