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:2006.07766 · Physical Review Letters

High Temperature Virial Expansion to Universal Quench Dynamics

Mingyuan Sun, Peng Zhang, Hui Zhai

Published Sep 10, 2020• 12 citations
arXivHTMLPDF

Abstract

High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this Letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from noninteracting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for the low-momentum part with k<k^{*}, and increases for high-momentum part with k>k^{*}, where k^{*} is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of k^{*}λ that agrees perfectly with the experiment, with λ being the thermal de Broglie wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.

DOI
10.1103/physrevlett.125.110404

Related papers

High-temperature virial expansion of contour Green's functions

Baihua Gong

High-temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this paper we generalize this method to the study of nonequilibrium dynamics based on contour Green's functions and present the diagrammatic rules to calculate the virial expansion coefficients. As an application of our theory, we recover the dynamics of a Bose gas quenched from noninteracting to finite interaction and obtain analytically the long-time limit of the momentum distribution function of the gas, consistent with previous numerical results.

Physical Review A•Aug 19, 2022•1 citation

Quench dynamics of thermal Bose gases across wide and narrow Feshbach resonances

Xiaoyi Yang, Ren Zhang

Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near wide, narrow, and intermediate Feshbach resonances. Our results show that the shallow bound state near Feshbach resonances leads to oscillation of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$. Near the wide Feshbach resonance, the long-time momentum distribution ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$ oscillates when the scattering length ${a}_{s}$ is quenched to large but with finite positive values. The oscillation frequency is determined by the bound-state energy. When ${a}_{s}$ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, when the background scattering length ${a}_{\mathrm{bg}}$ is larger than de Broglie wave length $\ensuremath{\lambda}$, there is an oscillation, and the frequency is determined by the energy of the shallow bound state in the open channel. When ${a}_{\mathrm{bg}}<0$ or $0<{a}_{\mathrm{bg}}\ensuremath{\ll}\ensuremath{\lambda}$, there is no shallow bound state in the open channel, and hence no oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.

arXiv:2301.06028•Physical Review A•Jun 21, 2023•1 citation

Universal Dynamics of a Degenerate Bose Gas Quenched to Unitarity

Chao Gao, Mingyuan Sun, Peng Zhang +1 more

Motivated by an unexpected experimental observation from the Cambridge group, [Eigen et al., Nature 563, 221 (2018)], we study the evolution of the momentum distribution of a degenerate Bose gas quenched from the weakly interacting regime to the unitary regime. For the two-body problem, we establish a relation that connects the momentum distribution at a long time to a subleading term in the initial wave function. For the many-body problem, we employ the time-dependent Bogoliubov variational wave function and find that, in certain momentum regimes, the momentum distribution at long times displays the same exponential behavior found by the experiment. Moreover, we find that this behavior is universal and is independent of the short-range details of the interaction potential. Consistent with the relation found in the two-body problem, we also numerically show that this exponential form is hidden in the same subleading term of the Bogoliubov wave function in the initial stages. Conceptually, our results show that, for quench to the universal regime and coherent quantum dynamics afterward, the universal longtime behavior is hidden in the initial state.

arXiv:1812.06709•Physical Review Letters•Jan 30, 2020•20 citations

Quantum Thermalization Dynamics of Fermi Gases Quenched to the BEC‐BCS Crossover

Licheng Yi, Shuxian Yu, Meimei Wu +2 more

Understanding nonequilibrium dynamics of strongly interacting quantum systems represents one of the most challenging problems in many-body physics. Here, quantum thermalization dynamics are explored in real-time in an ultracold Fermi gas suddenly quenched to the BEC-BCS crossover. When quenched to unitarity, it is observed that the cloud size remains unchanged in the early evolution while the momentum distribution emerges two prethermal states with a lifetime difference of two orders of magnitude in the early and intermediate stage before very slowly evolving to the final stationary state. It is revealed that a crossover momentum, at which the momentum distribution remains nearly unchanged, is determined by the thermal wavelength at high temperatures and the Fermi momentum while at low temperatures. It is identified that the universal prethermal dynamics scaling where momentum distributions with different temperatures collapse onto one curve. When quenched to the BEC side, the thermalization rapidly relaxes into a prethermal state and exhibits the low energy oscillation related to the molecular bound states. This work provides benchmarks for the study of quantum thermalization in strongly interacting fermionic many-body systems.

Advanced Science•May 29, 2025•3 citations

Universal dynamic scaling and Contact dynamics in quenched quantum gases

Jia-Nan Cui, Zhengqiang Zhou, Mingyuan Sun

Recently universal dynamic scaling is observed in several systems, which exhibit a spatiotemporal self-similar scaling behavior, analogous to the spatial scaling near phase transition. The latter one arises from the emergent continuous scaling symmetry. Motivated by this, we investigate the possible relation between the scaling dynamics and the continuous scaling symmetry in this paper. We derive a theorem that the scaling invariance of the quenched Hamiltonian and the initial density matrix can lead to the universal dynamic scaling. It is further demonstrated both in a two-body system analytically and in a many-body system numerically. For the latter one, we calculate the dynamics of quantum gases quenched from the zero interaction to a finite interaction via the non-equilibrium high-temperature virial expansion. A dynamic scaling of the momentum distribution appears in certain momentum-time windows at unitarity as well as in the weak interacting limit. Remarkably, this universal scaling dynamics persists approximately with smaller scaling exponents even if the scaling symmetry is fairly broken. Our findings may offer a new perspective to interpret the related experiments. We also study the Contact dynamics in the BEC–BCS crossover. Surprisingly, the half-way time displays a maximum near unitarity while some damping oscillations occur on the BEC side due to the dimer state, which can be used to detect possible two-body bound states in experiments.

arXiv:2203.14245•Frontiers of Physics•Dec 11, 2023•1 citation

High-temperature limit of the resonant Fermi gas

Vudtiwat Ngampruetikorn, Meera M. Parish, Jesper Levinsen

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range ${R}^{*}$ in the interaction. In the limit where the thermal wavelength $\ensuremath{\lambda}\ensuremath{\ll}{R}^{*}$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\ensuremath{\lambda}/|a|\ensuremath{\gg}1$ and ${R}^{*}/\ensuremath{\lambda}\ensuremath{\gg}1$, we estimate the value of the fourth virial coefficient at unitarity for ${R}^{*}=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density, and entropy, as well as the spectral function at high temperatures.

arXiv:1410.7797•Physical Review A•Jan 8, 2015•30 citations
High temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this Letter we generalize the high temperature virial expansion approach to treat far-from-equilibrium quench dynamics. As an application of our framework, we study the dynamics of a Bose gas quenched from noninteracting to unitarity, and we compare our theoretical results with unexplained experimental results by the Cambridge group [Eigen et al., Nature 563, 221 (2018)]. We show that, during the quench dynamics, the momentum distribution decreases for the low-momentum part with k<k^{}, and increases for high-momentum part with k>k^{}, where k^{} is a characteristic momentum scale separating the low- and the high-momentum regimes. We determine the universal value of k^{}λ that agrees perfectly with the experiment, with λ being the thermal de Broglie wavelength. We also find a jump of the halfway relaxation time across k^{*}λ and the nonmonotonic behavior of energy distribution, both of which agree with the experiment. Finally, we address the issue whether the longtime steady state thermalizes or not, and we find that this state reaches a partial thermalization, namely, it thermalizes for the low-energy part with kλ≲1 but does not thermalize for the very high momentum tail with kλ≫1. Our framework can also be applied to quench dynamics in other systems.
High-temperature virial expansion is a powerful tool in equilibrium statistical mechanics. In this paper we generalize this method to the study of nonequilibrium dynamics based on contour Green's functions and present the diagrammatic rules to calculate the virial expansion coefficients. As an application of our theory, we recover the dynamics of a Bose gas quenched from noninteracting to finite interaction and obtain analytically the long-time limit of the momentum distribution function of the gas, consistent with previous numerical results.
Using high-temperature virial expansion, we study the quench dynamics of the thermal Bose gases near wide, narrow, and intermediate Feshbach resonances. Our results show that the shallow bound state near Feshbach resonances leads to oscillation of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$. Near the wide Feshbach resonance, the long-time momentum distribution ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{\mathbf{k}}$ oscillates when the scattering length as{a}_{s}as​ is quenched to large but with finite positive values. The oscillation frequency is determined by the bound-state energy. When as{a}_{s}as​ is quenched to infinity or negative value, the oscillation vanishes. Near the narrow Feshbach resonance, when the background scattering length abg{a}_{\mathrm{bg}}abg​ is larger than de Broglie wave length $\ensuremath{\lambda}$, there is an oscillation, and the frequency is determined by the energy of the shallow bound state in the open channel. When abg<0{a}_{\mathrm{bg}}<0abg​<0 or $0<{a}_{\mathrm{bg}}\ensuremath{\ll}\ensuremath{\lambda}$, there is no shallow bound state in the open channel, and hence no oscillation. We check our conclusion using some realistic systems, and the results are consistent with our conclusion.
Motivated by an unexpected experimental observation from the Cambridge group, [Eigen et al., Nature 563, 221 (2018)], we study the evolution of the momentum distribution of a degenerate Bose gas quenched from the weakly interacting regime to the unitary regime. For the two-body problem, we establish a relation that connects the momentum distribution at a long time to a subleading term in the initial wave function. For the many-body problem, we employ the time-dependent Bogoliubov variational wave function and find that, in certain momentum regimes, the momentum distribution at long times displays the same exponential behavior found by the experiment. Moreover, we find that this behavior is universal and is independent of the short-range details of the interaction potential. Consistent with the relation found in the two-body problem, we also numerically show that this exponential form is hidden in the same subleading term of the Bogoliubov wave function in the initial stages. Conceptually, our results show that, for quench to the universal regime and coherent quantum dynamics afterward, the universal longtime behavior is hidden in the initial state.
Understanding nonequilibrium dynamics of strongly interacting quantum systems represents one of the most challenging problems in many-body physics. Here, quantum thermalization dynamics are explored in real-time in an ultracold Fermi gas suddenly quenched to the BEC-BCS crossover. When quenched to unitarity, it is observed that the cloud size remains unchanged in the early evolution while the momentum distribution emerges two prethermal states with a lifetime difference of two orders of magnitude in the early and intermediate stage before very slowly evolving to the final stationary state. It is revealed that a crossover momentum, at which the momentum distribution remains nearly unchanged, is determined by the thermal wavelength at high temperatures and the Fermi momentum while at low temperatures. It is identified that the universal prethermal dynamics scaling where momentum distributions with different temperatures collapse onto one curve. When quenched to the BEC side, the thermalization rapidly relaxes into a prethermal state and exhibits the low energy oscillation related to the molecular bound states. This work provides benchmarks for the study of quantum thermalization in strongly interacting fermionic many-body systems.
Recently universal dynamic scaling is observed in several systems, which exhibit a spatiotemporal self-similar scaling behavior, analogous to the spatial scaling near phase transition. The latter one arises from the emergent continuous scaling symmetry. Motivated by this, we investigate the possible relation between the scaling dynamics and the continuous scaling symmetry in this paper. We derive a theorem that the scaling invariance of the quenched Hamiltonian and the initial density matrix can lead to the universal dynamic scaling. It is further demonstrated both in a two-body system analytically and in a many-body system numerically. For the latter one, we calculate the dynamics of quantum gases quenched from the zero interaction to a finite interaction via the non-equilibrium high-temperature virial expansion. A dynamic scaling of the momentum distribution appears in certain momentum-time windows at unitarity as well as in the weak interacting limit. Remarkably, this universal scaling dynamics persists approximately with smaller scaling exponents even if the scaling symmetry is fairly broken. Our findings may offer a new perspective to interpret the related experiments. We also study the Contact dynamics in the BEC–BCS crossover. Surprisingly, the half-way time displays a maximum near unitarity while some damping oscillations occur on the BEC side due to the dimer state, which can be used to detect possible two-body bound states in experiments.
We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range R∗{R}^{*}R∗ in the interaction. In the limit where the thermal wavelength $\ensuremath{\lambda}\ensuremath{\ll}{R}^{*}$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths aaa. By interpolating from the perturbative limits $\ensuremath{\lambda}/|a|\ensuremath{\gg}1$ and ${R}^{*}/\ensuremath{\lambda}\ensuremath{\gg}1$, we estimate the value of the fourth virial coefficient at unitarity for R∗=0{R}^{*}=0R∗=0 and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density, and entropy, as well as the spectral function at high temperatures.