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Perturbation theory of a many-fermion system

Robert William Jones, Franz Mohling, Richard L. Becker

Nuclear Physics AFeb 1, 197416 citations

Field moment expansion method for interacting bosonic systems

Andrew Eberhardt, Michael Kopp, Alvaro Zamora +1 more

We introduce a numerical method and python package, chimes, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum break time of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and the growth of the higher order moments must be hierarchical.We introduce a numerical method and python package, chimes, that simulates quantum systems initially well approximated by mean field theory using a second order extension of the classical field approach. We call this the field moment expansion method. In this way, we can accurately approximate the evolution of first and second field moments beyond where the mean field theory breaks down. This allows us to estimate the quantum break time of a classical approximation without any calculations external to the theory. We investigate the accuracy of the field moment expansion using a number of well studied quantum test problems. Interacting bosonic systems similar to scalar field dark matter are chosen as test problems. We find that successful application of this method depends on two conditions: the quantum system must initially be well described by the classical theory, and the growth of the higher order moments must be hierarchical.

arXiv:2108.08849Physical review. D/Physical review. D.Oct 5, 20216 citations

Perturbation theory of a many-fermion system

Robert William Jones, Franz Mohling

Nuclear Physics AAug 1, 197021 citations

Pairing in Cold Atoms and other Applications for Quantum Monte Carlo methods

Michal Bajdich, Jindřich Kolorenč, Luboš Mitáš +1 more

We discuss the importance of the fermion nodes for the quantum Monte Carlo (QMC) methods and find two cases of the exact nodes. We describe the structure of the generalized pairing wave functions in Pfaffian antisymmetric form and demonstrate their equivalency with certain class of configuration interaction wave functions. We present the QMC calculations of a model fermion system at unitary limit. We find the system to have the energy of E=0.425Efree and the condensate fraction of α=0.48. Further we also perform the QMC calculations of the potential energy surface and the electric dipole moment along that surface of the LiSr molecule. We estimate the vibrationally averaged dipole moment to be 〈D〉ν=0=−0.4(2).We discuss the importance of the fermion nodes for the quantum Monte Carlo (QMC) methods and find two cases of the exact nodes. We describe the structure of the generalized pairing wave functions in Pfaffian antisymmetric form and demonstrate their equivalency with certain class of configuration interaction wave functions. We present the QMC calculations of a model fermion system at unitary limit. We find the system to have the energy of E=0.425Efree and the condensate fraction of α=0.48. Further we also perform the QMC calculations of the potential energy surface and the electric dipole moment along that surface of the LiSr molecule. We estimate the vibrationally averaged dipole moment to be 〈D〉ν=0=−0.4(2).

Physics ProcediaFeb 1, 20102 citations

Inertial Moment of Large Many-Fermion Systems with Repulsive Interactions

Ronald M. Rockmore

The interaction effects on the moment of inertia of a large many-body fermion system moving under periodic boundary conditions have been explicitly derived in the second order of particle-particle coupling for the case of nonsingular repulsive interparticle forces. The derivation is facilitated by the use of a new Hamiltonian constructed by canonical transformation. This transformation is determined by requiring that it remove the compensating effects of pair excitation and that the new interaction operators of first and second order in the cranking field be also of first order in particle-particle coupling. A graphical analysis is presented in which those classes of diagrams which yield corrections vanishing relative to the rigid moment in the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$ are distinguished. Some remarks on the related problem of diamagnetism are made. The possible application of the method of canonical transformation to related many-body problems is indicated.The interaction effects on the moment of inertia of a large many-body fermion system moving under periodic boundary conditions have been explicitly derived in the second order of particle-particle coupling for the case of nonsingular repulsive interparticle forces. The derivation is facilitated by the use of a new Hamiltonian constructed by canonical transformation. This transformation is determined by requiring that it remove the compensating effects of pair excitation and that the new interaction operators of first and second order in the cranking field be also of first order in particle-particle coupling. A graphical analysis is presented in which those classes of diagrams which yield corrections vanishing relative to the rigid moment in the limit $L\ensuremath{\rightarrow}\ensuremath{\infty}$ are distinguished. Some remarks on the related problem of diamagnetism are made. The possible application of the method of canonical transformation to related many-body problems is indicated.

Physical ReviewDec 15, 19605 citations

Calculation of ground states for many-Fermion systems

Theoretical Physics

Annals of PhysicsMar 1, 19891 citation

Theory and Applications of Moment Methods in Many-Fermion Systems

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