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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2603.09856 |
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| _version_ | 1866914383090679808 |
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| author | Lee, Eunwoo |
| author_facet | Lee, Eunwoo |
| contents | We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$, where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$, with $μ$ the particle-number chemical potential and $T$ the temperature.
We then study the large-angular-momentum limit $Ω_a\toω$. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$, but with a less universal residue depending separately on $μ/T$ and $ω/T$. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09856 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equilibrium Partition Function of Non-Relativistic CFTs in Harmonic Trap Lee, Eunwoo High Energy Physics - Theory Quantum Gases We investigate the equilibrium partition function of non-relativistic conformal field theories in harmonic quantization. We first analyze the hydrodynamic regime and show that, at leading order, the partition function exhibits a universal structure determined by the equation of state: the logarithm of the partition function develops simple poles in $ω^2-Ω_a^2$, where $ω$ is the harmonic trapping frequency and $Ω_a$ are angular velocities acting as chemical potentials for angular momentum. The corresponding residue is determined by a single-variable function of $μ/T$, with $μ$ the particle-number chemical potential and $T$ the temperature. We then study the large-angular-momentum limit $Ω_a\toω$. In this regime centrifugal effects nearly cancel the trapping potential, and the logarithm of the partition function again exhibits simple poles in $ω^2-Ω_a^2$, but with a less universal residue depending separately on $μ/T$ and $ω/T$. As explicit examples we analyze superfluid systems realizable in cold-atom experiments, in particular fermions at unitarity confined in a harmonic trap. |
| title | Equilibrium Partition Function of Non-Relativistic CFTs in Harmonic Trap |
| topic | High Energy Physics - Theory Quantum Gases |
| url | https://arxiv.org/abs/2603.09856 |