Dynamic and static density-density correlations in the one-dimensional Bose gas: Exact results and approximations

Cherny, Alexander Yu.; Brand, Joachim

doi:10.1103/physreva.79.043607

Cited by 34 publications

(48 citation statements)

References 40 publications

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“…Our approach is particularly suitable to describe the umklapp region of momenta q in the vicinity of 2k F , where k F is the Fermi wavevector of the mapped Fermi gas. In this region, a Random Phase Approximation perturbative approach [39][40][41][42] is not applicable and predicts a non regular behavior for the dynamic structure factor. Although the dynamic structure factor is amenable to Bethe Ansatz calculations [43,44], to date the strongly interacting regime has not been covered by this technique at finite temperature.…”

Section: Introductionmentioning

confidence: 99%

Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

2015

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We study the effect of thermal and quantum fluctuations on the dynamical response of a onedimensional strongly-interacting Bose gas in a tight atomic waveguide. We combine the Luttinger liquid theory at arbitrary interactions and the exact Bose-Fermi mapping in the Tonks-Girardeauimpenetrable-boson limit to obtain the dynamic structure factor of the strongly-interacting fluid at finite temperature. Then, we determine the drag force felt by a potential barrier moving along the fluid in the experimentally realistic situation of finite barrier width and temperature.

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Section: Introductionmentioning

confidence: 99%

Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

2015

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“…[122,127]). In particular, the DE predictions for these structure factors have smaller magnitudes at small momenta k k F than the corresponding CE structure factors.…”

Section: B Second-order Correlationsmentioning

confidence: 99%

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

et al. 2015

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We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The system is initially prepared in its noninteracting ground state and the interaction strength is then abruptly switched to a positive value, corresponding to repulsive interactions between the bosons. We calculate equal-time correlation functions of the nonequilibrium Bose field for small systems of up to five particles via symbolic evaluation of coordinate Bethe-ansatz expressions for operator matrix elements between Lieb-Liniger eigenstates. We characterize the relaxation of the system by comparing the time-evolving correlation functions following the quench to the equilibrium correlations predicted by the diagonal ensemble and relate the behavior of these correlations to that of the quantum fidelity between the many-body wave function and the initial state of the system. Our results for the asymptotic scaling of local second-order correlations with increasing interaction strength agree with the predictions of recent generalized thermodynamic Bethe-ansatz calculations. By contrast, third-order correlations obtained within our approach exhibit a markedly different power-law dependence on the interaction strength as the Tonks-Girardeau limit of infinitely strong interactions is approached.

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“…(6), we can compute various correlation functions, from which we can gain more insights into the properties of polarons and molecules. We focus on the one-body correlation function [44,45] and the density-density correlation function [46,48].…”

Section: Correlationsmentioning

confidence: 99%

Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas

Mao

Guan

2016

Phys. Rev. A

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Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clear distinction between the polaron and molecule is conceived by the probability distribution, single particle reduced density matrix and density-density correlations, which are calculated directly from the Bethe ansatz wave function. Such a polaron-molecule crossover presents a universal nature of an impurity immersed into a fermionic medium with an attraction in one dimension.

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Dynamic and static density-density correlations in the one-dimensional Bose gas: Exact results and approximations

Cited by 34 publications

References 40 publications

Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

Dynamic structure factor and drag force in a one-dimensional strongly interacting Bose gas at finite temperature

Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis

Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas

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