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:2605.17069

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

E. Krotscheck

Published May 16, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2605.17069

Related papers

Properties of 4He in one dimension

E. Krotscheck, Michael David Miller

It has been suggested recently that ${}^{4}\mathrm{He}$ can be prepared and studied as a quasi-one-dimensional quantum fluid. In this paper we calculate the static and dynamic properties of one-dimensional ${}^{4}\mathrm{He}$ using variational methods based upon the Jastrow-Feenberg wave function and its extension to dynamic systems with time-dependent, correlated wave functions. We calculate the zero temperature equation of state and show that in one dimension ${}^{4}\mathrm{He}$ is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 ${\mathrm{\AA{}}}^{\ensuremath{-}1}.$ We calculate the Feynman excitation spectrum and corrections that contain multiphonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a ${}^{3}\mathrm{He}$ impurity and calculate the zero concentration chemical potential as a function of ${}^{4}\mathrm{He}$ linear density. We also compute the ${}^{3}\mathrm{He}$-${}^{3}\mathrm{He}$ effective interaction in the ${}^{4}\mathrm{He}$ background and compute the energy of dimerization.

Physical review. B, Condensed matter•Nov 1, 1999•33 citations

Properties of4He in one dimension

E. Krotscheck, Michael David Miller

It has been suggested recently that 4 He can be prepared and studied as a quasi one-dimensional quantum fluid. We calculate the static and dynamic properties of one-dimensional 4 He using variational methods based upon the Jastrow-Feenberg wavefunction and its extension to dynamic systems with time-dependent, correlated wavefunctions. The zero temperature equation of state shows that in one-dimension 4 He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 A -1 . We also calculate the excitation spectrum including corrections that contain multi-phonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a 3 He impurity and calculate the zero concentration chemical potential as a function of He linear density. We also compute the 3 He- 3 He effective interaction in the 4 He background and compute the energy of dimerization.

Journal de Physique IV (Proceedings)•May 1, 2000•0 citations

Scattering of 3He atoms from 4He surfaces

E. Krotscheck, Robert E. Zillich

We develop a first-principles, microscopic theory of impurity atom scattering from inhomogeneous quantum liquids such as adsorbed films, slabs, or clusters of ${}^{4}\mathrm{He}.$ The theory is built upon a quantitative, microscopic description of the ground state of both the host liquid as well as the impurity atom. Dynamic effects are treated by allowing all ground-state correlation functions to be time dependent. Our description includes both the elastic and inelastic coupling of impurity motion to the excitations of the host liquid. As a specific example, we study the scattering of ${}^{3}\mathrm{He}$ atoms from adsorbed ${}^{4}\mathrm{He}$ films. We examine the dependence of ``quantum reflection'' on the substrate, and the consequences of impurity bound states, resonances, and background excitations for scattering properties. A thorough analysis of the theoretical approach and the physical circumstances point towards the essential role played by inelastic processes which determine almost exclusively the reflection probabilities. The coupling to impurity resonances within the film leads to a visible dependence of the reflection coefficient on the direction of the impinging particle.

arXiv:cond-mat/9802229•Physical review. B, Condensed matter•Sep 1, 1998•13 citations

MANY-BOSON DYNAMIC CORRELATIONS

C. E. Campbell, E. Krotscheck

In this paper we present an overview of a systematic development of the linear equations of motion for a dynamically correlated wave function that moves beyond the previous theories that include time-dependent pair correlations at most. We argue that these time-dependent pair correlations are insufficient to describe important physical effects in the energy/momentum regime of the 4 He roton; minimally, time-dependent three-body correlations are necessary to capture the relevant physics. For simplicity we illustrate this on the problem of atomic impurities in 4 He .

International Journal of Modern Physics B•Oct 20, 2008•2 citations

A MICROSCOPIC LOOK AT LIQUID HELIUM: THE 3 He IMPURITY CASE

A. Polls, Adelchi Fabrocini

The description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one 3 He impurity in liquid 4 He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two- and three-particle correlation functions is needed to obtain a realistic ground state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excitation energies. The theory describes accurately the experimental spectrum along all the available momentum range. As empirically shown by the experiments, a marked deviation from the quadratic Landau-Pomeranchuck behavior is found and the momentum dependent effective mass of the impurity increases of ~50% at q~1.7 Å-1 with respect to its q=0 value. Although the main emphasis is given to the correlated basis function theory, we present also comparisons with other methods, as diffusion Monte Carlo, variational Monte Carlo with shadow wave functions and time dependent correlations.

arXiv:cond-mat/9911261•International Journal of Modern Physics B•May 10, 2001•0 citations

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

Richard Schmidt, Michael Knap, Dmitri A. Ivanov +3 more

In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.

arXiv:1702.08587•Reports on Progress in Physics•Jan 5, 2018•205 citations
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.
It has been suggested recently that 4He{}^{4}\mathrm{He}4He can be prepared and studied as a quasi-one-dimensional quantum fluid. In this paper we calculate the static and dynamic properties of one-dimensional 4He{}^{4}\mathrm{He}4He using variational methods based upon the Jastrow-Feenberg wave function and its extension to dynamic systems with time-dependent, correlated wave functions. We calculate the zero temperature equation of state and show that in one dimension 4He{}^{4}\mathrm{He}4He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 ${\mathrm{\AA{}}}^{\ensuremath{-}1}.$ We calculate the Feynman excitation spectrum and corrections that contain multiphonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a 3He{}^{3}\mathrm{He}3He impurity and calculate the zero concentration chemical potential as a function of 4He{}^{4}\mathrm{He}4He linear density. We also compute the 3He{}^{3}\mathrm{He}3He-3He{}^{3}\mathrm{He}3He effective interaction in the 4He{}^{4}\mathrm{He}4He background and compute the energy of dimerization.
It has been suggested recently that 4 He can be prepared and studied as a quasi one-dimensional quantum fluid. We calculate the static and dynamic properties of one-dimensional 4 He using variational methods based upon the Jastrow-Feenberg wavefunction and its extension to dynamic systems with time-dependent, correlated wavefunctions. The zero temperature equation of state shows that in one-dimension 4 He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 A -1 . We also calculate the excitation spectrum including corrections that contain multi-phonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a 3 He impurity and calculate the zero concentration chemical potential as a function of He linear density. We also compute the 3 He- 3 He effective interaction in the 4 He background and compute the energy of dimerization.
We develop a first-principles, microscopic theory of impurity atom scattering from inhomogeneous quantum liquids such as adsorbed films, slabs, or clusters of 4He.{}^{4}\mathrm{He}.4He. The theory is built upon a quantitative, microscopic description of the ground state of both the host liquid as well as the impurity atom. Dynamic effects are treated by allowing all ground-state correlation functions to be time dependent. Our description includes both the elastic and inelastic coupling of impurity motion to the excitations of the host liquid. As a specific example, we study the scattering of 3He{}^{3}\mathrm{He}3He atoms from adsorbed 4He{}^{4}\mathrm{He}4He films. We examine the dependence of ``quantum reflection'' on the substrate, and the consequences of impurity bound states, resonances, and background excitations for scattering properties. A thorough analysis of the theoretical approach and the physical circumstances point towards the essential role played by inelastic processes which determine almost exclusively the reflection probabilities. The coupling to impurity resonances within the film leads to a visible dependence of the reflection coefficient on the direction of the impinging particle.
In this paper we present an overview of a systematic development of the linear equations of motion for a dynamically correlated wave function that moves beyond the previous theories that include time-dependent pair correlations at most. We argue that these time-dependent pair correlations are insufficient to describe important physical effects in the energy/momentum regime of the 4 He roton; minimally, time-dependent three-body correlations are necessary to capture the relevant physics. For simplicity we illustrate this on the problem of atomic impurities in 4 He .
The description of the properties of liquid Helium is a challenge for any microscopic many-body theory. In this context, we study the ground state and the excitation spectrum of one 3 He impurity in liquid 4 He at T=0 with the aim of illustrating the power of the correlated basis function formalism in describing heavily correlated systems. The strong interatomic interaction and the large density require the theory to be pushed to a high degree of sophistication. A many-body correlation operator containing explicit two- and three-particle correlation functions is needed to obtain a realistic ground state wave function, whereas a perturbative expansion including up to two phonon correlated states must be enforced to study the impurity excitation energies. The theory describes accurately the experimental spectrum along all the available momentum range. As empirically shown by the experiments, a marked deviation from the quadratic Landau-Pomeranchuck behavior is found and the momentum dependent effective mass of the impurity increases of ~50% at q~1.7 Å-1 with respect to its q=0 value. Although the main emphasis is given to the correlated basis function theory, we present also comparisons with other methods, as diffusion Monte Carlo, variational Monte Carlo with shadow wave functions and time dependent correlations.
In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.