Jakub Kopyciński, Maciej Łebek, Maciej Marciniak, Rafał Ołdziejewski, Wojciech Górecki, Krzysztof Pawłowski
SciPost Phys. 12, 023 (2022) ·
published 14 January 2022
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Describing properties of a strongly interacting quantum many-body system
poses a serious challenge both for theory and experiment. In this work, we
study excitations of one-dimensional repulsive Bose gas for arbitrary
interaction strength using a hydrodynamic approach. We use linearization to
study particle (type-I) excitations and numerical minimization to study hole
(type-II) excitations. We observe a good agreement between our approach and
exact solutions of the Lieb-Liniger model for the particle modes and
discrepancies for the hole modes. Therefore, the hydrodynamical equations find
to be useful for long-wave structures like phonons and of a limited range of
applicability for short-wave ones like narrow solitons. We discuss potential
further applications of the method.
SciPost Phys. Core 4, 016 (2021) ·
published 7 June 2021
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We analyze the thermodynamic Casimir effect in strongly anizotropic systems
from the vectorial $N\to\infty$ class in a slab geometry. Employing the
imperfect (mean-field) Bose gas as a representative example, we demonstrate the
key role of spatial dimensionality $d$ in determining the character of the
effective fluctuation-mediated interaction between the confining walls. For a
particular, physically conceivable choice of anisotropic dispersion and
periodic boundary conditions, we show that the Casimir force at criticality as
well as within the low-temperature phase is repulsive for dimensionality $d\in
(\frac{5}{2},4)\cup (6,8)\cup (10,12)\cup\dots$ and attractive for $d\in
(4,6)\cup (8,10)\cup \dots$. We argue, that for $d\in\{4,6,8\dots\}$ the
Casimir interaction entirely vanishes in the scaling limit. We discuss
implications of our results for systems characterized by $1/N>0$ and possible
realizations in the context of quantum phase transitions.
Mr Łebek: "Dear Referee, we would like..."
in Submissions | report on Thermodynamic Casimir forces in strongly anisotropic systems within the $N\to \infty$ class