dorsal/arxiv
View SchemaOn the positivity of Bloch-Boltzmann equations
| Authors | Stanislaw Kryszewski, Justyna Czechowska |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0412139 |
| URL | https://arxiv.org/abs/quant-ph/0412139 |
Abstract
In a large variety of spectroscopical applications Bloch-Boltzmann equations (BBE) play an essential role. They describe the evolution of the reduced density operator of an active atom which is coupled to radiation (Bloch part) and which interacts collisionally with the perturber gas (Boltzmann part). The standard approach to the collisional part is well-known from the literature. It preserves hermiticity and normalization, but the question whether it preserves positivity seems to remain open. The completely positive BBE were recently derived via the general master equation techniques. These two approaches are applied for a model of n-level nondegenerate atom. We show that within this model both approaches to the collisional part of BBE are equivalent -- give the same physical predictions. The approach based upon master equation techniques guarantees the preservation of hermiticity, normalization and positivity. The proven equivalence ascertains that the standard approach also preserves positivity. Moreover, some aspects of the standard derivation (which atomic states do contribute to the evolution) are clarified by the established equivalence.
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"abstract": "In a large variety of spectroscopical applications Bloch-Boltzmann equations\n(BBE) play an essential role. They describe the evolution of the reduced\ndensity operator of an active atom which is coupled to radiation (Bloch part)\nand which interacts collisionally with the perturber gas (Boltzmann part). The\nstandard approach to the collisional part is well-known from the literature. It\npreserves hermiticity and normalization, but the question whether it preserves\npositivity seems to remain open. The completely positive BBE were recently\nderived via the general master equation techniques. These two approaches are\napplied for a model of n-level nondegenerate atom. We show that within this\nmodel both approaches to the collisional part of BBE are equivalent -- give the\nsame physical predictions. The approach based upon master equation techniques\nguarantees the preservation of hermiticity, normalization and positivity. The\nproven equivalence ascertains that the standard approach also preserves\npositivity. Moreover, some aspects of the standard derivation (which atomic\nstates do contribute to the evolution) are clarified by the established\nequivalence.",
"arxiv_id": "quant-ph/0412139",
"authors": [
"Stanislaw Kryszewski",
"Justyna Czechowska"
],
"categories": [
"quant-ph"
],
"title": "On the positivity of Bloch-Boltzmann equations",
"url": "https://arxiv.org/abs/quant-ph/0412139"
},
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