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

Physical Review B

Dynamic many-body theory: Multiparticle fluctuations and the dynamic structure of He4

C. E. Campbell, E. Krotscheck, T. Lichtenegger

Published May 14, 2015• 35 citations
Publisher

Abstract

We present further progress in a systematic approach to the microscopic understanding of the dynamics of strongly interacting quantum fluids. Employing the concept of dynamic multiparticle fluctuations, we derive equations of motion for fluctuating $n$-body densities. We apply the theory to calculate the dynamic structure function of liquid $^{4}\mathrm{He}$ as a function of density and find, without any phenomenological input, overall excellent agreement with both experiments and, as far as available, simulation data.

DOI
10.1103/physrevb.91.184510

Related papers

Dynamic many-body theory: Pair fluctuations in bulk H4e

C. E. Campbell, E. Krotscheck

Dynamical excitations in bulk liquid $^{4}\text{H}\text{e}$ are investigated by using a manifestly microscopic theory of excitations that includes multiple-phonon scattering. The wave function of the dynamic system is represented in terms of one- and two-body excitation amplitudes. Equations of motion for the linear response of boson liquids to a scalar external field are then derived from a stationarity principle. For a consistent treatment of long- and short-wavelength properties of the excitation amplitudes we derive and solve three sets of generic ``hypernetted chain'' equations determining the basic ingredients of the theory. From those ingredients, we calculate a dynamic structure function for $^{4}\text{H}\text{e}$ at saturation density. It is shown that the complete solution of the hypernetted chain equations leads, partly by the cancellation of errors, to an insignificantly improved theoretical prediction for the dynamic structure function compared with approximations introduced by Jackson, Feenberg, and Campbell. The implications of this result and the need for including higher-order multiparticle fluctuations are discussed.

Physical Review B•Nov 2, 2009•21 citations

Dynamic many-body theory: Dynamics of strongly correlated Fermi fluids

Helga M. Böhm, Robert A. Holler, E. Krotscheck +1 more

We develop a systematic theory of multiparticle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced implementation, quantitative predictions for the dynamic structure function in the whole experimentally accessible energy/momentum regime. Our view is that the same physical effects, namely, fluctuations of the wave function at an atomic length scale are responsible for the correct energetics of the excitations in both Bose and Fermi fluids. Besides a comprehensive derivation of the fermion version of the theory and discussion of the approximations made, we present results for homogeneous $^{3}\text{H}\text{e}$ and electrons in three dimensions. We find indeed a significant lowering of the zero-sound mode in $^{3}\text{H}\text{e}$ and a broadening of the collective mode due to the coupling to two-particle--two-hole excitations in good agreement with experiments. The most visible effect in electronic systems is the appearance of a ``double-plasmon'' excitation.

arXiv:1010.1816•Physical Review B•Dec 6, 2010•28 citations

Dynamic Many-Body Theory: The dynamics of atomic impurities in $^4$He

E. Krotscheck

We implement manifestly microscopic many-body methods to study the dynamics of atomic impurities in a host quantum fluid, specifically $^4$He. Our investigations are motivated by experiments of muonium atoms within $^4$He with the goal of testing the universality of free fall by neutral bound states using unstable particles. Structure calculations are performed using standard semi-analytic methods; we extend here the calculations of our previos work (Journal of Low Temperature Physics {\bf 93}, 415-449 (1993)) to muonic \he4, antiprotonic \he4 and mounium atoms within \he4. We find that the muonium impurity probes, due to its large zero-point motion, the atomic interaction at rather short distances. Its chemical potential is estimated to be about 19 meV. Antiprotonic \he4 has, on the other hand, a negative chemical potential. Dynamics is treated by making all correlation functions time-dependent. In analogy to the derivation of the dynamics of the background liquid, we derive a working formula for the impurity self-energy that includes the most relevant physical effects. Results for the effective mass of \he3 and hydrogen atoms agree well with available experiments. The dispersion relations of muonic \he4 and antiprotonic \he4 pass through under the roton minimum.

arXiv:2605.17069•May 16, 2026•0 citations

Fluctuating quantum kinetic theory

T. R. Kirkpatrick, D. Belitz

We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an $H$ theorem for the nonlinear Landau kinetic equation.

arXiv:2203.05521•Physical review. B./Physical review. B•Jun 29, 2022•5 citations

Quantum fluctuations approach to the nonequilibrium GW approximation: Density correlations and dynamic structure factor

Erik Schroedter, Björn Jakob Wurst, Jan‐Philip Joost +1 more

The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGFs) or reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle self-energy or decoupling of the BBGKY-hierarchy, respectively. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. In a recent paper [E. Schroedter, J.-P. Joost, and M. Bonitz, Condens. Matter Phys. 25, 23401 (2022)] we presented a different approach in which, instead of equations of motion for the many-particle NEGF (or density operators), equations for the correlation functions of fluctuations are analyzed. In particular, we derived the stochastic $GW$ and polarization approximations that are closely related to the nonequilibrium $GW$ approximation. Here, we extend this approach to the computation of two-time observables depending on the specific ordering of the underlying operators. In particular, we apply this extension to the calculation of the density correlation function and dynamic structure factor of correlated Hubbard clusters in and out of equilibrium.

arXiv:2305.18956•Physical review. B./Physical review. B•Nov 6, 2023•6 citations

Dynamic correlations in electron liquids. I. General formalism

Aiichiro Nakano, Setsuo Ichimaru

Time-dependent multiparticle correlation functions and response functions are formulated with the functional derivatives in the grand-canonical ensemble. Equations for the single-particle Green's functions are the Dyson equations describing scattering of the single particles by density-fluctuation excitations. Equations for the density-fluctuation excitations are truncated with a dynamic version of the convolution approximation to triple correlations. A closed set of equations for the Green's functions and excitations are thereby obtained, which constitutes a dynamic hypernetted-chain scheme for the degenerate electron liquids. The formalism is extended also to the description of the spin-dependent response and correlations.

Physical review. B, Condensed matter•Mar 15, 1989•21 citations
We present further progress in a systematic approach to the microscopic understanding of the dynamics of strongly interacting quantum fluids. Employing the concept of dynamic multiparticle fluctuations, we derive equations of motion for fluctuating nnn-body densities. We apply the theory to calculate the dynamic structure function of liquid 4He^{4}\mathrm{He}4He as a function of density and find, without any phenomenological input, overall excellent agreement with both experiments and, as far as available, simulation data.
Dynamical excitations in bulk liquid 4He^{4}\text{H}\text{e}4He are investigated by using a manifestly microscopic theory of excitations that includes multiple-phonon scattering. The wave function of the dynamic system is represented in terms of one- and two-body excitation amplitudes. Equations of motion for the linear response of boson liquids to a scalar external field are then derived from a stationarity principle. For a consistent treatment of long- and short-wavelength properties of the excitation amplitudes we derive and solve three sets of generic ``hypernetted chain'' equations determining the basic ingredients of the theory. From those ingredients, we calculate a dynamic structure function for 4He^{4}\text{H}\text{e}4He at saturation density. It is shown that the complete solution of the hypernetted chain equations leads, partly by the cancellation of errors, to an insignificantly improved theoretical prediction for the dynamic structure function compared with approximations introduced by Jackson, Feenberg, and Campbell. The implications of this result and the need for including higher-order multiparticle fluctuations are discussed.
We develop a systematic theory of multiparticle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced implementation, quantitative predictions for the dynamic structure function in the whole experimentally accessible energy/momentum regime. Our view is that the same physical effects, namely, fluctuations of the wave function at an atomic length scale are responsible for the correct energetics of the excitations in both Bose and Fermi fluids. Besides a comprehensive derivation of the fermion version of the theory and discussion of the approximations made, we present results for homogeneous 3He^{3}\text{H}\text{e}3He and electrons in three dimensions. We find indeed a significant lowering of the zero-sound mode in 3He^{3}\text{H}\text{e}3He and a broadening of the collective mode due to the coupling to two-particle--two-hole excitations in good agreement with experiments. The most visible effect in electronic systems is the appearance of a ``double-plasmon'' excitation.
Dynamic Many-Body Theory: The dynamics of atomic impurities in 4^44He
We implement manifestly microscopic many-body methods to study the dynamics of atomic impurities in a host quantum fluid, specifically 4^44He. Our investigations are motivated by experiments of muonium atoms within 4^44He with the goal of testing the universality of free fall by neutral bound states using unstable particles. Structure calculations are performed using standard semi-analytic methods; we extend here the calculations of our previos work (Journal of Low Temperature Physics {\bf 93}, 415-449 (1993)) to muonic \he4, antiprotonic \he4 and mounium atoms within \he4. We find that the muonium impurity probes, due to its large zero-point motion, the atomic interaction at rather short distances. Its chemical potential is estimated to be about 19 meV. Antiprotonic \he4 has, on the other hand, a negative chemical potential. Dynamics is treated by making all correlation functions time-dependent. In analogy to the derivation of the dynamics of the background liquid, we derive a working formula for the impurity self-energy that includes the most relevant physical effects. Results for the effective mass of \he3 and hydrogen atoms agree well with available experiments. The dispersion relations of muonic \he4 and antiprotonic \he4 pass through under the roton minimum.
We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an HHH theorem for the nonlinear Landau kinetic equation.
The quantum dynamics of correlated fermionic or bosonic many-body systems following external excitation can be successfully studied using nonequilibrium Green functions (NEGFs) or reduced density matrix methods. Approximations are introduced via a proper choice of the many-particle self-energy or decoupling of the BBGKY-hierarchy, respectively. These approximations are based on Feynman's diagram approaches or on cluster expansions into single-particle and correlation operators. In a recent paper [E. Schroedter, J.-P. Joost, and M. Bonitz, Condens. Matter Phys. 25, 23401 (2022)] we presented a different approach in which, instead of equations of motion for the many-particle NEGF (or density operators), equations for the correlation functions of fluctuations are analyzed. In particular, we derived the stochastic GWGWGW and polarization approximations that are closely related to the nonequilibrium GWGWGW approximation. Here, we extend this approach to the computation of two-time observables depending on the specific ordering of the underlying operators. In particular, we apply this extension to the calculation of the density correlation function and dynamic structure factor of correlated Hubbard clusters in and out of equilibrium.
Time-dependent multiparticle correlation functions and response functions are formulated with the functional derivatives in the grand-canonical ensemble. Equations for the single-particle Green's functions are the Dyson equations describing scattering of the single particles by density-fluctuation excitations. Equations for the density-fluctuation excitations are truncated with a dynamic version of the convolution approximation to triple correlations. A closed set of equations for the Green's functions and excitations are thereby obtained, which constitutes a dynamic hypernetted-chain scheme for the degenerate electron liquids. The formalism is extended also to the description of the spin-dependent response and correlations.