"Depletion" of Superfluid Density: Universal Low-temperature Thermodynamics of Superfluids
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911637204631552 |
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| author | Berger, Viktor Prokof'ev, Nikolay Svistunov, Boris |
| author_facet | Berger, Viktor Prokof'ev, Nikolay Svistunov, Boris |
| contents | In a Galilean superfluid, the depletion of superfluid density with rising temperature can be attributed to thermally excited non-interacting phonons. For systems without Galilean symmetry, it has been shown [1] that ``phonon wind" is no longer responsible for the depletion of superfluid density. In this work, we develop the theory of superfluid density at low temperature ($T$) and provide detailed derivations of all results announced in [1]. Using Popov's hydrodynamic action, we show that the theory of low-temperature depletion in a $d$-dimensional quantum superfluid maps onto the problem of finite-size ($L$) corrections in a $(d+1)$-dimensional anisotropic (pseudo-)classical-field system with U(1)-symmetric complex-valued action. In addition to generalizing Landau's (canonical) formula, we develop the grand canonical theory, which in a broader context reveals a universal scaling, $T^{d+1}$ and $1/L^{d+1}$, for finite-$T$ and finite-$L$ effects of many thermodynamic quantities. We validate our theory with numeric simulations of interacting lattice bosons and the J-current model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22683 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | "Depletion" of Superfluid Density: Universal Low-temperature Thermodynamics of Superfluids Berger, Viktor Prokof'ev, Nikolay Svistunov, Boris Quantum Gases Statistical Mechanics In a Galilean superfluid, the depletion of superfluid density with rising temperature can be attributed to thermally excited non-interacting phonons. For systems without Galilean symmetry, it has been shown [1] that ``phonon wind" is no longer responsible for the depletion of superfluid density. In this work, we develop the theory of superfluid density at low temperature ($T$) and provide detailed derivations of all results announced in [1]. Using Popov's hydrodynamic action, we show that the theory of low-temperature depletion in a $d$-dimensional quantum superfluid maps onto the problem of finite-size ($L$) corrections in a $(d+1)$-dimensional anisotropic (pseudo-)classical-field system with U(1)-symmetric complex-valued action. In addition to generalizing Landau's (canonical) formula, we develop the grand canonical theory, which in a broader context reveals a universal scaling, $T^{d+1}$ and $1/L^{d+1}$, for finite-$T$ and finite-$L$ effects of many thermodynamic quantities. We validate our theory with numeric simulations of interacting lattice bosons and the J-current model. |
| title | "Depletion" of Superfluid Density: Universal Low-temperature Thermodynamics of Superfluids |
| topic | Quantum Gases Statistical Mechanics |
| url | https://arxiv.org/abs/2506.22683 |