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

arXiv:1412.8506 · Physical Review A

Statistical properties of states in QED with unstable vacuum

Sergei P. Gavrilov, Dmitri M Gitman, A. A. Shishmarev

Published May 11, 2015• 10 citations
arXivHTMLPDF

Abstract

We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al. [Gavrilov, Gitman, and Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. We consider the so-called $T$-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration.

DOI
10.1103/physreva.91.052106

Related papers

States of charged quantum fields and their statistical properties in the presence of critical potential steps

Sergei P. Gavrilov, Dmitri M Gitman, A. A. Shishmarev

The evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct density operators of the quantum fields with different initial conditions. Then we study some reductions of the density operators, for example, reductions to electron or positron subsystems, reduction induced by measurements, and spatial reduction to the left or to the right subsystems of final particles. We calculate von Neumann entropy for the corresponding reduced density operators, estimating in such a way an information loss. We illustrate the obtained results by calculations in a specific background of a strong constant electric field between two infinite capacitor plates separated by a finite distance $L$.

arXiv:1901.01217•Physical Review A•May 20, 2019•3 citations

Vacuum photon emission and mean electromagnetic field in pair-creating external backgrounds

I. A. Aleksandrov, E. V. Perelygin, D. V. Chubukov

We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order $α$, reproduces the known vertex and tadpole mechanisms, while the complete order-$α^2$ correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order $e^3$, including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.

hep-thCross-listedarXiv:2606.12547•Jun 12, 2026

Spatial Decoherence in QED

Bruno Bellomo, G. Compagno, Francesco Petruccione

We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various effects, such as free spreading, vacuum dressing and vacuum and thermal decoherence, in the wave packet width and coherence length evolution.

Open Systems & Information Dynamics•Nov 15, 2006•0 citations

Loss of coherence and dressing in QED

Bruno Bellomo, G. Compagno, Francesco Petruccione

The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature $T$, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.

arXiv:quant-ph/0612192•Physical Review A•Nov 22, 2006•6 citations

Entanglement between smeared field operators in the Klein-Gordon vacuum

Magdalena Zych, Fabio Costa, Johannes Kofler +1 more

Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.

arXiv:1003.3354•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jun 24, 2010•19 citations

Decoherence in quantum electrodynamics and quantum gravity

Claus Kiefer

We treat the interaction of a semiclassical electromagnetic field with a complex scalar field as a continuous measurement process through which certain interference terms between electromagnetic field states may become suppressed---they "decohere." The formal framework is the functional Schr\"odinger picture for scalar QED. The reduced density matrix for the electromagnetic field is discussed in detail. We calculate the remaining coherence width for realistic laboratory field strengths. The back reaction of the scalar field on the electromagnetic state is discussed with the help of the Wigner function and is explicitly calculated. We compare our results with the corresponding case in quantum gravity where the radius of the Universe is "measured" by inhomogeneous scalar field modes. We propose to render the decoherence factor finite by summing over a set of rescaled field modes.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Aug 15, 1992•116 citations
We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al. [Gavrilov, Gitman, and Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. We consider the so-called TTT-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration.
The evolution of charged quantum fields under the action of constant nonuniform electric fields is studied. To this end we construct density operators of the quantum fields with different initial conditions. Then we study some reductions of the density operators, for example, reductions to electron or positron subsystems, reduction induced by measurements, and spatial reduction to the left or to the right subsystems of final particles. We calculate von Neumann entropy for the corresponding reduced density operators, estimating in such a way an information loss. We illustrate the obtained results by calculations in a specific background of a strong constant electric field between two infinite capacitor plates separated by a finite distance LLL.
We develop a perturbative description of vacuum radiative processes in quantum electrodynamics with a prescribed external electromagnetic background capable of producing electron-positron pairs. Since the initial vacuum is then unstable and the in- and out-vacua are inequivalent, radiative observables require a real-time formulation beyond the ordinary in-out approach of vacuum-stable QED. Using the Keldysh-Schwinger-Fradkin nonequilibrium technique, we derive the mean number density of emitted photons through the second nonvanishing order in the fine-structure constant. The leading term, of order ααα, reproduces the known vertex and tadpole mechanisms, while the complete order-α2α^2α2 correction contains interference, loop, and induced-current contributions. We also give an independent derivation based on the spectral decomposition of the identity operator in the in-Fock space, where the photon number density is represented as a sum of squared transition amplitudes and vacuum-disconnected terms are canceled by the optical theorem generalized to an unstable vacuum. In addition, we compute the mean electromagnetic field through order e3e^3e3, including the electromagnetic dressing of the induced vacuum current, and verify it using the corresponding Schwinger-Dyson equations. The final formulas are expressed in terms of exact solutions and propagators of the Dirac equation in the external background and apply to general spacetime-dependent field configurations.
We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various effects, such as free spreading, vacuum dressing and vacuum and thermal decoherence, in the wave packet width and coherence length evolution.
The dynamics of a free charged particle, initially described by a coherent wave packet, interacting with an environment, i.e., the electromagnetic field characterized by a temperature TTT, is studied. Using the dipole approximation, the exact expressions for the evolution of the reduced density matrix both in momentum and configuration space and the vacuum and the thermal contribution to decoherence are obtained. The time behavior of the coherence lengths in the two representations are given. Through the analysis of the dynamic of the field structure associated with the particle the vacuum contribution is shown to be linked to the birth of correlations between the single momentum components of the particle wave packet and the virtual photons of the dressing cloud.
Quantum field theory is the application of quantum physics to fields. It provides a theoretical framework widely used in particle physics and condensed matter physics. One of the most distinct features of quantum physics with respect to classical physics is entanglement or the existence of strong correlations between subsystems that can even be spacelike separated. In quantum fields, observables restricted to a region of space define a subsystem. While there are proofs on the existence of local observables that would allow a violation of Bell's inequalities in the vacuum states of quantum fields as well as some explicit but technically demanding schemes requiring an extreme fine-tuning of the interaction between the fields and detectors, an experimentally accessible entanglement witness for quantum fields is still missing. Here we introduce smeared field operators which allow reducing the vacuum to a system of two effective bosonic modes. The introduction of such collective observables is motivated by the fact that no physical probe has access to fields in single spatial (mathematical) points but rather smeared over finite volumes. We first give explicit collective observables whose correlations reveal vacuum entanglement in the Klein-Gordon field. We then show that the critical distance between the two regions of space above which two effective bosonic modes become separable is of the order of the Compton wavelength of the particle corresponding to the massive Klein-Gordon field.
We treat the interaction of a semiclassical electromagnetic field with a complex scalar field as a continuous measurement process through which certain interference terms between electromagnetic field states may become suppressed---they "decohere." The formal framework is the functional Schr\"odinger picture for scalar QED. The reduced density matrix for the electromagnetic field is discussed in detail. We calculate the remaining coherence width for realistic laboratory field strengths. The back reaction of the scalar field on the electromagnetic state is discussed with the help of the Wigner function and is explicitly calculated. We compare our results with the corresponding case in quantum gravity where the radius of the Universe is "measured" by inhomogeneous scalar field modes. We propose to render the decoherence factor finite by summing over a set of rescaled field modes.