arXiv:1201.6363 · Physical Review A

Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

Manas Kulkarni, Austen Lamacraft

Published Aug 8, 2013• 76 citations

Abstract

We study the finite-temperature dynamical structure factor $S(k,\ensuremath{\omega})$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\ensuremath{\omega})$ has a width $\ensuremath{\propto}$${|k|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.

DOI: 10.1103/physreva.88.021603

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Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

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arXiv:1201.6363 · Physical Review A

Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

Manas Kulkarni, Austen Lamacraft

Published Aug 8, 2013• 76 citations

arXiv HTML PDF

Abstract

We study the finite-temperature dynamical structure factor

S(k,\ensuremath{\omega})

of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in

S(k,\ensuremath{\omega})

has a width

\ensuremath{\propto}$${|k|}^{3/2}

at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.

DOI: 10.1103/physreva.88.021603

Related papers

Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

Austen Lamacraft, Manas Kulkarni

Bulletin of the American Physical SocietyMar 4, 20141 citation

Stochastic Gross-Pitaevskii theory for a spin-1 Bose gas: Application to superfluidity in two dimensions

Andrew P. C. Underwood, P. B. Blakie

This paper develops and implements the stochastic projected Gross-Pitaevskii equation for spin-1 Bose gases, addressing key considerations for numerical simulations. As an application of the theory we explore equilibrium phases in a two-dimensional spin-1 gas, where quasi-long-range order emerges via a Berezinskii-Kosterlitz-Thouless transition. Our analysis includes the definition of superfluid densities for both mass and spin degrees of freedom in a manner suitable for implementation within a stochastic projected Gross-Pitaevskii equation simulation. We present a finite-temperature phase diagram for the ferromagnetic spin-1 Bose gas and identify three distinct superfluid phases: two exhibiting conventional Berezinskii-Kosterlitz-Thouless-like behavior and an additional phase that simultaneously supports independent mass and spin superflows. As temperature increases, the stability region of this additional phase shrinks. We provide a characterization of the phase transitions through consideration of the spin-component densities and the unbinding of multiple types of vortices. This work provides a foundation for further studies of nonequilibrium and finite-temperature phenomena in spinor Bose gases.This paper develops and implements the stochastic projected Gross-Pitaevskii equation for spin-1 Bose gases, addressing key considerations for numerical simulations. As an application of the theory we explore equilibrium phases in a two-dimensional spin-1 gas, where quasi-long-range order emerges via a Berezinskii-Kosterlitz-Thouless transition. Our analysis includes the definition of superfluid densities for both mass and spin degrees of freedom in a manner suitable for implementation within a stochastic projected Gross-Pitaevskii equation simulation. We present a finite-temperature phase diagram for the ferromagnetic spin-1 Bose gas and identify three distinct superfluid phases: two exhibiting conventional Berezinskii-Kosterlitz-Thouless-like behavior and an additional phase that simultaneously supports independent mass and spin superflows. As temperature increases, the stability region of this additional phase shrinks. We provide a characterization of the phase transitions through consideration of the spin-component densities and the unbinding of multiple types of vortices. This work provides a foundation for further studies of nonequilibrium and finite-temperature phenomena in spinor Bose gases.

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Dynamical structure factor of one-dimensional Bose gases: Experimental signatures of beyond-Luttinger-liquid physics

Nicole Fabbri, Miłosz Panfil, David Clément +4 more

Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a $^{87}\mathrm{Rb}$ condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at $T>0$ . Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.Interactions are known to have dramatic effects on bosonic gases in one dimension (1D). Not only does the ground state transform from a condensate like state to an effective Fermi sea, but new fundamental excitations, which do not have any higher-dimensional equivalents, are predicted to appear. In this work, we trace these elusive excitations via their effects on the dynamical structure factor of 1D strongly interacting Bose gases at low temperature. An array of 1D Bose gases is obtained by loading a $^{87}\mathrm{Rb}$ condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at $T>0$. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.

arXiv:1406.2176Physical Review AApr 13, 2015142 citations

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Kai Ji, V. N. Gladilin, Michiel Wouters

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A Renormalization-Group Study of Interacting Bose–Einstein Condensates: II. Anomalous Dimension η for $d \lesssim 4$ at Finite TemperaturesA Renormalization-Group Study of Interacting Bose–Einstein Condensates: II. Anomalous Dimension η for $d \lesssim 4$ at Finite Temperatures

Takafumi Kita

We study the anomalous dimension $η$ of homogeneous interacting single-component Bose-Einstein condensates at finite temperatures for $d\lesssim 4$ dimensions. This $η$ is defined in terms of the one-particle density matrix $ρ({\bf r})\equiv \langle \hatψ^\dagger({\bf r}_1)\hatψ({\bf r}_1+{\bf r})\rangle$ through its asymptotic behavior $ρ({\bf r})\rightarrow N_{\bf 0}/V+C r^{-d+2-η}$ for $r\rightarrow \infty$ , where $N_{\bf 0}/V$ is the condensate density and $C$ is a constant. It is shown that the anomalous dimension is given by $η=0.181ε^2$ to the leading order in $ε\equiv d-4$ . The change of the prefactor $0.181$ from the value $0.02$ at the transition point of the ${\rm O}(2)$ symmetric $ϕ^4$ model is attributed to the emergence of three-point vertices and the anomalous Green's function when $N_{\bf 0}$ acquires a finite value.We study the anomalous dimension $η$ of homogeneous interacting single-component Bose-Einstein condensates at finite temperatures for $d\lesssim 4$ dimensions. This $η$ is defined in terms of the one-particle density matrix $ρ({\bf r})\equiv \langle \hatψ^\dagger({\bf r}_1)\hatψ({\bf r}_1+{\bf r})\rangle$ through its asymptotic behavior $ρ({\bf r})\rightarrow N_{\bf 0}/V+C r^{-d+2-η}$ for $r\rightarrow \infty$, where $N_{\bf 0}/V$ is the condensate density and $C$ is a constant. It is shown that the anomalous dimension is given by $η=0.181ε^2$ to the leading order in $ε\equiv d-4$. The change of the prefactor $0.181$ from the value $0.02$ at the transition point of the ${\rm O}(2)$ symmetric $ϕ^4$ model is attributed to the emergence of three-point vertices and the anomalous Green's function when $N_{\bf 0}$ acquires a finite value.

arXiv:1909.11787Journal of the Physical Society of JapanSep 25, 20193 citations

Nonlinear Fluctuating Hydrodynamics for Kardar-Parisi-Zhang Scaling in Isotropic Spin Chains

Jacopo De Nardis, Sarang Gopalakrishnan, Romain Vasseur

Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.Finite temperature spin transport in integrable isotropic spin chains is known to be superdiffusive, with dynamical spin correlations that are conjectured to fall into the Kardar-Parisi-Zhang (KPZ) universality class. However, integrable spin chains have time-reversal and parity symmetries that are absent from the KPZ (Kardar-Parisi-Zhang) or stochastic Burgers equation, which force higher-order spin fluctuations to deviate from standard KPZ predictions. We put forward a nonlinear fluctuating hydrodynamic theory consisting of two coupled stochastic modes: the local spin magnetization and its effective velocity. Our theory fully explains the emergence of anomalous spin dynamics in isotropic chains: it predicts KPZ scaling for the spin structure factor but with a symmetric, quasi-Gaussian, distribution of spin fluctuations. We substantiate our results using matrix-product states calculations.

arXiv:2212.03696Physical Review LettersNov 9, 202339 citations

We study the finite-temperature dynamical structure factor

S(k,\ensuremath{\omega})

of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in

S(k,\ensuremath{\omega})

has a width

\ensuremath{\propto}$${|k|}^{3/2}

^{87}\mathrm{Rb}

condensate in a two-dimensional lattice potential. The dynamical structure factor of the system is probed by energy deposition through low-momentum Bragg excitations. The experimental signals are compared to recent theoretical predictions for the dynamical structure factor of the Lieb-Liniger model at

T>0

. Our results demonstrate that the main contribution to the spectral widths stems from the dynamics of the interaction-induced excitations in the gas, which cannot be described by the Luttinger liquid theory.

A Renormalization-Group Study of Interacting Bose–Einstein Condensates: II. Anomalous Dimension η for

d \lesssim 4

at Finite Temperatures

We study the anomalous dimension

η

of homogeneous interacting single-component Bose-Einstein condensates at finite temperatures for

d\lesssim 4

dimensions. This

η

is defined in terms of the one-particle density matrix

ρ({\bf r})\equiv \langle \hatψ^\dagger({\bf r}_1)\hatψ({\bf r}_1+{\bf r})\rangle

through its asymptotic behavior

ρ({\bf r})\rightarrow N_{\bf 0}/V+C r^{-d+2-η}

for

r\rightarrow \infty

, where

N_{\bf 0}/V

is the condensate density and

C

is a constant. It is shown that the anomalous dimension is given by

η=0.181ε^2

to the leading order in

ε\equiv d-4

. The change of the prefactor

0.181

from the value

0.02

at the transition point of the

{\rm O}(2)

symmetric

ϕ^4

model is attributed to the emergence of three-point vertices and the anomalous Green's function when

N_{\bf 0}

acquires a finite value.