Related papers: Normal and superfluid fractions of inhomogeneous n…
The superfluid fraction $f$ of a quantum fluid is defined in terms of the response of the system to a weak and constant drag. Notably, Leggett long ago derived two simple expressions providing a rigorous upper bound and a heuristic lower…
In this paper we discuss, within the Gross--Pitaevskii framework, superfluidity, soliton nucleation, and instabilities in a non-equilibrium polariton fluid injected by a spatially localized and continuous-wave coherent pump and flowing…
We answer to 72 frequently asked questions about theories of multifractional spacetimes. Apart from reviewing and reorganizing what we already know about such theories, we discuss the physical meaning and consequences of the very recent…
Traditionally applied within equilibrium states, the charge-vortex dualities are expanded to address the complex dynamics of superfluids and ideal fluids under non-static conditions. We have constructed explicit mappings of finite…
We point out that two different definitions of the superfluid density - through statistical response to static gauge phase and through dynamic response to altering gauge phase - yield, generally speaking, different quantities in $d<3$. The…
We review some rigorous results on the equilibrium and non-equilibrium properties of superfluids and superconductors.
Supersolids are theoretically predicted quantum states that break the continuous rotational and translational symmetries of liquids while preserving superfluid transport properties. Over the last decade, much progress has been made in…
A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational…
Even when ideal solids are insulating, their states with crystallographic defects may have superfluid properties. It became clear recently that edge dislocations in $^4$He featuring a combination of microscopic quantum roughness and…
Turbulent fluid dynamics typically involves excitations on many different length scales. Classical incompressible fluids can be cleanly represented in Fourier space enabling spectral analysis of energy cascades and other turbulence…
This paper represents the full version of a paper published earlier in Physica A [246 (1997), 275]. The present paper includes argumentation, proofs and details omitted in the shortened version. The papers are a further development of the…
We study the semiflow $\mathcal{S}(t)$ defined by a semilinear parabolic equation with a singular square potential $V(x)=\frac{\mu}{|x|^2}$. It is known that the Hardy-Poincar\'{e} inequality and its improved versions, have a prominent role…
We investigate the superfluid fraction of crystalline stationary states within the framework of mean-field Gross-Pitaevskii theory. Our primary focus is on a two-dimensional system with a non-local soft-core interaction, where the…
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
We present the mechanics of a model of supersolid in the frame of the Gross-Pitaevskii equation at $T=0K$ that do not require defects nor vacancies. A set of coupled nonlinear partial differential equations plus boundary conditions is…
A new picture of both integer and fractional incompressible quantum Hall fluids as fluids carrying a electric quadrupole is introduced. This clarifies their geometric properties, provides a generic expression for Hall viscosity, and allows…
We simulate the Gross-Pitaevskii equation to model the development of turbulence in a quantum fluid confined by a cuboid box potential, and forced by shaking along one axis. We observe the development of isotropic turbulence from…
Finite-temperature quantum turbulence is often described in terms of two immiscible fluids that can flow with a non-zero mean relative velocity. Such out-of-equilibrium state is known as counterflow superfluid turbulence. We report here the…
A microscopic statistical model of a quantum solid is developed, where inside a crystalline lattice there can exist regions of disorder, such as dislocation networks or grain boundaries. The cores of these regions of disorder are allowed…
Vortex structures in dilute quantum fluids are studied using the Gross-Pitaevskii equation. The velocity and momentum of multiply quantized vortex rings are determined and their core structures analysed. For flow past a spherical object, we…