On the quantum field operator dynamics: Memory dependent projected representation
The projection formalism of Zwanzig and Feshbach is used to construct the Heisenberg picture of time dependent field operators in two mutually orthogonal subspaces. A particular form of Zwanzig's generalized master equation involving time dependent Hamiltonians and Liouville superoperators is o...
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todo:paper_01661280_v433_n1-3_p19_Bochicchio2023-10-03T15:03:25Z On the quantum field operator dynamics: Memory dependent projected representation Bochicchio, R.C. Grinberg, H. Field operators Memory superoperators Partitioning technique Time evolution The projection formalism of Zwanzig and Feshbach is used to construct the Heisenberg picture of time dependent field operators in two mutually orthogonal subspaces. A particular form of Zwanzig's generalized master equation involving time dependent Hamiltonians and Liouville superoperators is obtained, from which it is verified that the emerging memory superoperator must satisfy the Volterra integral equation whose kernels involve superoperators which couple the two subspaces at a common instant of time. The subsequent development to describe the time dependence involves time-order cosine and sine projected memory superoperators. It is also shown that this projection separation admits a coupling-decoupling structure for the total (sum over the two subspaces) field operator time evolution which reveals the flux of density from one subspace to the other. The present development to obtain evolution equations for field operators allows a partition of the p-particle reduced density matrix master equation into relevant and irrelevant parts. Such a separation is exact and represents the time dependent fluctuations around the static density coming from the interference terms between the Hamiltonian states in the Liouville space. © 1998 Elsevier Science B.V. All rights reserved. Fil:Bochicchio, R.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01661280_v433_n1-3_p19_Bochicchio |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Field operators Memory superoperators Partitioning technique Time evolution |
| spellingShingle |
Field operators Memory superoperators Partitioning technique Time evolution Bochicchio, R.C. Grinberg, H. On the quantum field operator dynamics: Memory dependent projected representation |
| topic_facet |
Field operators Memory superoperators Partitioning technique Time evolution |
| description |
The projection formalism of Zwanzig and Feshbach is used to construct the Heisenberg picture of time dependent field operators in two mutually orthogonal subspaces. A particular form of Zwanzig's generalized master equation involving time dependent Hamiltonians and Liouville superoperators is obtained, from which it is verified that the emerging memory superoperator must satisfy the Volterra integral equation whose kernels involve superoperators which couple the two subspaces at a common instant of time. The subsequent development to describe the time dependence involves time-order cosine and sine projected memory superoperators. It is also shown that this projection separation admits a coupling-decoupling structure for the total (sum over the two subspaces) field operator time evolution which reveals the flux of density from one subspace to the other. The present development to obtain evolution equations for field operators allows a partition of the p-particle reduced density matrix master equation into relevant and irrelevant parts. Such a separation is exact and represents the time dependent fluctuations around the static density coming from the interference terms between the Hamiltonian states in the Liouville space. © 1998 Elsevier Science B.V. All rights reserved. |
| format |
JOUR |
| author |
Bochicchio, R.C. Grinberg, H. |
| author_facet |
Bochicchio, R.C. Grinberg, H. |
| author_sort |
Bochicchio, R.C. |
| title |
On the quantum field operator dynamics: Memory dependent projected representation |
| title_short |
On the quantum field operator dynamics: Memory dependent projected representation |
| title_full |
On the quantum field operator dynamics: Memory dependent projected representation |
| title_fullStr |
On the quantum field operator dynamics: Memory dependent projected representation |
| title_full_unstemmed |
On the quantum field operator dynamics: Memory dependent projected representation |
| title_sort |
on the quantum field operator dynamics: memory dependent projected representation |
| url |
http://hdl.handle.net/20.500.12110/paper_01661280_v433_n1-3_p19_Bochicchio |
| work_keys_str_mv |
AT bochicchiorc onthequantumfieldoperatordynamicsmemorydependentprojectedrepresentation AT grinbergh onthequantumfieldoperatordynamicsmemorydependentprojectedrepresentation |
| _version_ |
1807317410839003136 |