dorsal/arxiv
View SchemaWeyl's symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics
| Authors | M. I. Krivoruchenko, Amand Faessler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604075 |
| URL | https://arxiv.org/abs/quant-ph/0604075 |
| DOI | 10.1063/1.2735816 |
| Journal | J.Math.Phys.48:052107,2007 |
Abstract
The knowledge of quantum phase flow induced under the Weyl's association rule by the evolution of Heisenberg operators of canonical coordinates and momenta allows to find the evolution of symbols of generic Heisenberg operators. The quantum phase flow curves obey the quantum Hamilton's equations and play the role of characteristics. At any fixed level of accuracy of semiclassical expansion, quantum characteristics can be constructed by solving a coupled system of first-order ordinary differential equations for quantum trajectories and generalized Jacobi fields. Classical and quantum constraint systems are discussed. The phase-space analytic geometry based on the star-product operation can hardly be visualized. The statement "quantum trajectory belongs to a constraint submanifold" can be changed e.g. to the opposite by a unitary transformation. Some of relations among quantum objects in phase space are, however, left invariant by unitary transformations and support partly geometric relations of belonging and intersection. Quantum phase flow satisfies the star-composition law and preserves hamiltonian and constraint star-functions.
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"abstract": "The knowledge of quantum phase flow induced under the Weyl\u0027s association rule\nby the evolution of Heisenberg operators of canonical coordinates and momenta\nallows to find the evolution of symbols of generic Heisenberg operators. The\nquantum phase flow curves obey the quantum Hamilton\u0027s equations and play the\nrole of characteristics. At any fixed level of accuracy of semiclassical\nexpansion, quantum characteristics can be constructed by solving a coupled\nsystem of first-order ordinary differential equations for quantum trajectories\nand generalized Jacobi fields. Classical and quantum constraint systems are\ndiscussed. The phase-space analytic geometry based on the star-product\noperation can hardly be visualized. The statement \"quantum trajectory belongs\nto a constraint submanifold\" can be changed e.g. to the opposite by a unitary\ntransformation. Some of relations among quantum objects in phase space are,\nhowever, left invariant by unitary transformations and support partly geometric\nrelations of belonging and intersection. Quantum phase flow satisfies the\nstar-composition law and preserves hamiltonian and constraint star-functions.",
"arxiv_id": "quant-ph/0604075",
"authors": [
"M. I. Krivoruchenko",
"Amand Faessler"
],
"categories": [
"quant-ph",
"cond-mat.stat-mech",
"hep-th",
"math-ph",
"math.AP",
"math.CA",
"math.DS",
"math.MP"
],
"doi": "10.1063/1.2735816",
"journal_ref": "J.Math.Phys.48:052107,2007",
"title": "Weyl\u0027s symbols of Heisenberg operators of canonical coordinates and momenta as quantum characteristics",
"url": "https://arxiv.org/abs/quant-ph/0604075"
},
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