dorsal/arxiv
View SchemaQuantum initial value representations using approximate Bohmian trajectories
| Authors | Eric R. Bittner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0304012 |
| URL | https://arxiv.org/abs/quant-ph/0304012 |
| DOI | 10.1063/1.1580471 |
Abstract
Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic description of quantum mechanics, are used to construct time-correlation functions in an initial value representation (IVR). The formulation is fully quantum mechanical and the resulting equations for the correlation functions are similar in form to their semi-classical analogs but do not require the computation of the stability or monodromy matrix or conjugate points. We then move to a {\em local} trajectory description by evolving the cumulants of the wave function along each individual path. The resulting equations of motion are an infinite hierarchy, which we truncate at a given order. We show that time-correlation functions computed using these approximate quantum trajectories can be used to accurately compute the eigenvalue spectrum for various potential systems.
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"abstract": "Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic\ndescription of quantum mechanics, are used to construct time-correlation\nfunctions in an initial value representation (IVR). The formulation is fully\nquantum mechanical and the resulting equations for the correlation functions\nare similar in form to their semi-classical analogs but do not require the\ncomputation of the stability or monodromy matrix or conjugate points. We then\nmove to a {\\em local} trajectory description by evolving the cumulants of the\nwave function along each individual path. The resulting equations of motion are\nan infinite hierarchy, which we truncate at a given order. We show that\ntime-correlation functions computed using these approximate quantum\ntrajectories can be used to accurately compute the eigenvalue spectrum for\nvarious potential systems.",
"arxiv_id": "quant-ph/0304012",
"authors": [
"Eric R. Bittner"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.1580471",
"title": "Quantum initial value representations using approximate Bohmian trajectories",
"url": "https://arxiv.org/abs/quant-ph/0304012"
},
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