The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones $^4$ He give the $λ$ -transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.The modern theory of Bose-Einstein condensation, superfluidity, and superconductivity is reviewed. The thermodynamic principle for superfluid flow and the equation of motion for condensed bosons are given. Computer simulations of Lennard-Jones $^4$He give the $λ$-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.

cond-mat.stat-mechCross-listedarXiv:2511.08953Nov 13, 20250 citations

Depletion of superfluid density: Universal low-temperature thermodynamics of superfluids

Viktor Berger, Nikolay V. Prokof'ev, Boris V. Svistunov

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.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.

arXiv:2506.22683Physical review. B./Physical review. BFeb 12, 20261 citation

Theory of Superfluidity

F.W. Cummings, James R. Johnston

Physical ReviewDec 5, 19671 citation

Aspects of a model of superfluidity

James R. Johnston, F.W. Cummings

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BJul 1, 19682 citations

^4

He give the

λ

-transition and the superfluid viscosity. The statistical mechanical theory of high-temperature superconductivity is presented. Critical comparison is made with older approaches, such as ground energy state condensation, irrotational superfluid flow, and the macroscopic wavefunction.

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.