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arXiv:2608.11129

Moment of Inertia of an Interacting Bose Gas

Aleksandar Gecić, Victor E. Ambruş, Kenji Fukushima

Published Aug 11, 2026• 0 citations
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Abstract

The response of many-body quantum systems to rotation can be characterized by the moment of inertia. For a classical gas, the moment of inertia can be expressed as the integral of the enthalpy density multiplied by the squared radial distance from the rotation axis. In quantum field theory, the finite rotation in the grand canonical ensemble demands the causality bound. This constraint imposes technical challenges in treating transverse momenta discretized with the Bessel function zeros. However, we define the moment of inertia in the limit of zero angular velocity, in which the causality constraint is irrelevant and ordinary quantum field theoretical techniques can be applied. We evaluate the moment of inertia in the $ϕ^4$ theory and find that, surprisingly, the interacting effects including the ring-diagram resummation are consistent with the classical expectation and the moment of inertia density remains proportional to the enthalpy density.

DOI
10.48550/arxiv.2608.11129

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The superfluid fraction of an atomic cloud can be defined using the cloud's response to a rotation of the external potential, i.e. the moment of inertia. In this paper we derive analytical results for the moment of inertia of a small number of non-interacting Bosons using the canonical ensemble. The required symmetrized averages are obtained via a representation of the partition function by permutation cycles. Our results are useful to discriminate purely quantum statistical effects from interaction effects in studies of superfluidity and phase transitions in finite samples.
We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ( T ), angular velocity ( Ω ), and the coupling constant ( α ). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain T or α . Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high T and for large α . Published by the American Physical Society 2024
An equilibrium superfluid is defined as a substance whose moment of inertia in thermal equilibrium is less than the classical value. The ideal Bose-Einstein gas below its transition temperature is shown to be an equilibrium superfluid. However, a more detailed analysis of the relation between angular momentum and angular velocity shows that experiments carried out with practical angular momenta and velocities would give an abnormally large apparent moment of inertia in thermal equilibrium, i.e., the gas would appear to be an "infrafluid." Nevertheless, a weakly interacting Bose-Einstein gas can be used as a model of a superfluid, if the superfluid state is assumed to be metastable rather than the thermodynamic equilibrium state.
In this paper, a developed Hartree-Fock semiclassical approximation is used to calculate the temperature and interaction dependence of the moment of inertia of a rotating condensate Boson gas. A fully classical and quantum mechanical treatment for the moment of inertia are given in terms of the normalized temperature. We found that the moment of inertia is considerably affected by the interaction. The present analysis, shows that the superfluid effects in the moment of inertia of a condensate Boson gas can be observed at temperatures $T > .25 T_0 $ and not dramatically smaller than T0T_0T0​.
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