Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

EPJ Web of Conferences

The Feynman-Vernon Influence Functional Approach in QED

Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

Published Jan 1, 2016• 1 citation
Publisher

Abstract

In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.

DOI
10.1051/epjconf/201612505016

Related papers

Discription of the Dinamics of Fermions by the Influence Functional Method

А.А. Бирюков, Марк Александрович Шлеенков

Abstract We consider a system of interacting spinor and electromagnetic fields. We describe the quantum state of the fields by a statistical density matrix. We present the equation of evolution of the density matrix of the field system in the method of integration over trajectories. The evolution equation for the density matrix of the fermion field is obtained as an averaging of the functional of the influence of the electromagnetic field. An explicit form of the functional of the influence of the electromagnetic field is found. We present the equations of motion for the fermion field taking into account the influence of the vacuum of the electromagnetic field.

Moscow University Physics Bulletin•Dec 1, 2025•0 citations

The influence functional method to the description of the dynamics of quantum systems interacting with the laser radiation

Alexander Alexandrovich Biryukov, Александр Александрович Бирюков, Марк Александрович Шлеенков +1 more

The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

Вестник Самарского государственного технического университета Серия Физико-математические науки•Jun 15, 2013•0 citations

Описание динамики квантовых систем, взаимодействующих с лазерным излучением, методом функционала влияния

Александр Александрович Бирюков, Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков +1 more

The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

Вестник Самарского государственного технического университета Серия Физико-математические науки•Jan 1, 2013•0 citations

The Influence Functional approach to the quantum systems dynamics

Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков

We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.

International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP)•Apr 14, 2014•5 citations

Описание динамики многоуровневых квантовых систем в сильных лазерных полях методом функционала влияния

Александр Александрович Бирюков, Шлеенков Марк Александрович

We describe multilevel quantum systems dynamics in electromagnetic fields using the influence functional approach in path integration formalism. We obtain equations for the statistical density matrix and the probability of transitions of quantum systems induced by the electromagnetic field. The explicit form of the quantized electromagnetic field influence functional is concretized. Spontaneous transition of the quantum systems, the Rabi oscillations and their fluctuations are obtained. The two#photon photoelectric effect is explained.

Известия Самарского научного центра Российской академии наук•Jan 1, 2012•0 citations

Canonical derivation of the fermionic influence superoperator

Mauro Cirio, Po-Chen Kuo, Yueh-Nan Chen +2 more

The Feynman-Vernon influence functional is a powerful result, based on path integrals, for describing the reduced state of a system interacting with a Gaussian environment. Here, the authors derive in detail a canonical (i.e., operatorial) form of the influence functional for fermionic environments, and show how it can be used to compute the dynamics under arbitrary parity-symmetry initial conditions as well as to derive generalized versions of the Lindblad master equation and the hierarchical equations of motion.

Physical review. B./Physical review. B•Jan 13, 2022•24 citations
In the path integral approach we describe evolution of interacting electromagnetic and fermionic fields by the use of density matrix formalism. The equation for density matrix and transitions probability for fermionic field is obtained as average of electromagnetic field influence functional. We obtain a formula for electromagnetic field influence functional calculating for its various initial and final state. We derive electromagnetic field influence functional when its initial and final states are vacuum. We present Lagrangian for relativistic fermionic field under influence of electromagnetic field vacuum.
Abstract We consider a system of interacting spinor and electromagnetic fields. We describe the quantum state of the fields by a statistical density matrix. We present the equation of evolution of the density matrix of the field system in the method of integration over trajectories. The evolution equation for the density matrix of the fermion field is obtained as an averaging of the functional of the influence of the electromagnetic field. An explicit form of the functional of the influence of the electromagnetic field is found. We present the equations of motion for the fermion field taking into account the influence of the vacuum of the electromagnetic field.
The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for singleand multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.
The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.
We study the dynamics of multi-level quantum systems under the influence of electromagnetic field.Basing on the path integral approach to the quantum density matrix and transitions probability we represent functional averaging electromagnetic field influence.We demonstrate that the transition probability can be written as a path integral of real functional (the product of exponent and cosine).The numerical integration algorithm of the transitions probability in energy representation was developed.The numerical simulations of the quantum system dynamics under electromagnetic field action describe the well-known Rabi oscillations, their fluctuations and multi-photon quantum transitions.
We describe multilevel quantum systems dynamics in electromagnetic fields using the influence functional approach in path integration formalism. We obtain equations for the statistical density matrix and the probability of transitions of quantum systems induced by the electromagnetic field. The explicit form of the quantized electromagnetic field influence functional is concretized. Spontaneous transition of the quantum systems, the Rabi oscillations and their fluctuations are obtained. The two#photon photoelectric effect is explained.
The Feynman-Vernon influence functional is a powerful result, based on path integrals, for describing the reduced state of a system interacting with a Gaussian environment. Here, the authors derive in detail a canonical (i.e., operatorial) form of the influence functional for fermionic environments, and show how it can be used to compute the dynamics under arbitrary parity-symmetry initial conditions as well as to derive generalized versions of the Lindblad master equation and the hierarchical equations of motion.