The density of a one-dimensional Bose gas far from an impurity - Archive ouverte HAL
Article Dans Une Revue Physical Review B Année : 2023

The density of a one-dimensional Bose gas far from an impurity

Résumé

We consider an impurity in a one-dimensional weakly-interacting Bose gas and analytically calculate the density profile of the Bose gas. Within the mean-field approximation, by increasing the distance from the impurity, the Bose gas density saturates exponentially fast to its mean thermodynamic-limit value at distances beyond the healing length. The effect of quantum fluctuations drastically changes this behavior, leading to a power law decay of the density deviation from the mean density. At distances longer than the healing length and shorter than a new length scale proportional to the impurity coupling strength, the power-law exponent is $2$, while at longest distances the corresponding exponent becomes $3$. The latter crossover does not exist in two special cases. The first one is realized for infinitely strongly coupled impurity; then the density deviation always decays with the exponent $2$. The second special case occurs when the new length scale is smaller than the healing length, i.e., at weak impurity coupling; then the density deviation always decays with the exponent $3$. The obtained results are exact in the impurity coupling strength and account for the leading order in the interaction between the particles of the Bose gas.

Dates et versions

hal-04204648 , version 1 (12-09-2023)

Identifiants

Citer

Aleksandra Petković, Zoran Ristivojevic. The density of a one-dimensional Bose gas far from an impurity. Physical Review B, 2023, 108 (17), pp.174510. ⟨10.1103/PhysRevB.108.174510⟩. ⟨hal-04204648⟩
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