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

• URL: http://arxiv.org/abs/2308.15130v1
• Date: Tue, 29 Aug 2023 08:56:24 GMT
• Title: The density of a one-dimensional Bose gas far from an impurity
• Authors: Aleksandra Petkovic and Zoran Ristivojevic
• Abstract summary: We consider an impurity in a weakly-interacting Bose gas and calculate the density profile of the Bose gas. The effect of quantum fluctuations drastically changes this behavior, leading to a power law decay of the density deviation from the mean density. 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.
• Score: 55.2480439325792
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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