Fermion-like coherent states are obtained as projections from the Glauber coherent states for a boson field, and the two sets of states have an interesting correspondence. It is shown that because of the correspondence the equation of motion of the density operator for a fermion interacting with a radiation field maps into a classical-like transport equation in a hypothetical boson phase space. Besides being useful in the description of systems of fermions involved in cooperative phenomena, it is shown that the use of the continuous basis offers some unique advantages even for systems which are essentially Markovian. As an illustration, the method is applied to the description of the time evolution of a two-level atom interacting with a blackbody radiation field.Fermion-like coherent states are obtained as projections from the Glauber coherent states for a boson field, and the two sets of states have an interesting correspondence. It is shown that because of the correspondence the equation of motion of the density operator for a fermion interacting with a radiation field maps into a classical-like transport equation in a hypothetical boson phase space. Besides being useful in the description of systems of fermions involved in cooperative phenomena, it is shown that the use of the continuous basis offers some unique advantages even for systems which are essentially Markovian. As an illustration, the method is applied to the description of the time evolution of a two-level atom interacting with a blackbody radiation field.

International Journal of Quantum ChemistryJun 18, 20097 citations

On the low density limit of Boson models

Luigi Accardi, Yun Gang Lu

Lecture notes in mathematicsJan 1, 19902 citations

Boson description of fermion systems

B. Sørensen

Physics LettersOct 1, 19669 citations

Effective Dynamics for the Bose Polaron in the Large-Volume Mean-Field Limit

Jonas Lampart, Peter Pickl, Siegfried Spruck

We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $ρ$ and large volume $Λ$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $Λ^3 \ll ρ$ , the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $ρ$ and large volume $Λ$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $Λ^3 \ll ρ$, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.

arXiv:2604.11976Apr 13, 20260 citations

Effective dynamics for the Bose polaron in the large-volume mean-field limit

Jonas Lampart, Peter Pickl, Siegfried Spruck

We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\rho$ and large volume $\Lambda$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\Lambda^3\ll\rho$ , the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\rho$ and large volume $\Lambda$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\Lambda^3\ll\rho$, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.

Jan 1, 20260 citations

We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of

N

bosons evolving in

\mathbb{R}^3

in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density

ρ

and large volume

Λ

of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint

Λ^3 \ll ρ

, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.

We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of

N

bosons evolving in

\mathbb{R}^3

in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density

\rho

and large volume

\Lambda

\Lambda^3\ll\rho

, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.