Quantum fluids in nanoporous media—Effects of the confinement and fractal geometry

Abstract

The complex behavior of such quantum fluids like liquid 4 He and liquid 3 He in nanoporous media is determined by spatial quantization because of geometrical confinement as well as by significant contribution from the surface atoms. In the present report we will review the procedure, results and discuss the issues for fractionalized nonextensive hydrodynamical approach to describe the properties of quantum fluids inside nanopores and propose consideration of strong correlated quantum liquid by means of fractionalized Schrödinger equation. The zero-point energy of atoms of two stable isotopes of helium -4 He and 3 He -is high enough to prevent their solidification even at extremely low temperatures without application of external pressure. So they belong to the class of quantum fluids with strong correlations between atoms but their behavior is quite different at low temperatures. The first one represents a Bose-system and shows superfluid transition at 2.17 K while atoms of 3 He are governed by Fermi-statistics and superfluid transition can be observed only at much lower temperatures (about 1 mK) when the pairing of two atoms occurs. But even at liquid helium temperatures (1.5-4.2 K) the effects of quantum statistics for 3 He atoms become pronounceable especially in nanoscale confinement (nanoporous media, thin adsorbed layers on solid substrates) [1][2][3] and in the presence of nanoscale disorder induced for example by silica aerogel strands [4]. In recent years the problem of correct description of quantum fluids in the confined geometry at nanoscale length has emerged [5][6][7][8]. It has been recognized that the quantum fluids at these circumstances can be considered as a new state of quantum matter due to close values between characteristic lengths for these quantum liquids and the size of geometrical confinement and significant contri- *Corresponding author (email: dtayursk@gmail.com) bution from the surface atoms. So one has to apply new physics to describe such systems with taking into account their complex nature. For example, last two years the attempts to develop the fractionalized two-fluid hydrodynamics for nanoporous media with fractal dimensions have been made [9,10]. The actuality of such new hydrodynamics becomes very clear because of numerous studies of quantum liquids inside nanoporous media [11,12] as well as because of last developments in chemical synthesis of aerogels with different network of strands (from fibrous to globular one [13]). One of the interesting obtained results is that density waves (the first sound) and temperature waves (the second sound) become strongly coupled even in the absence of viscosity, so it is purely geometric effect of fractal space of nanopores [9,10]. In this paper we will review the procedure, results and discuss the issues for this approach. Theoretical models for bulk superfluid helium-4There are several approaches to describe the behavior of bulk superfluid helium-4. For example, two-fluid model [14,15],

Preventing critical collapse of higher-order solitons by tailoring unconventional optical diffraction and nonlinearities

“…FSE is currently attracting a great deal of attention in different branches of physics, including condensed-matter physics [46][47][48] and quantum physics [49][50][51] . Importantly, a new hallmark of FSE development published in 2015 by Longhi 52 found that a fractional quantum harmonic oscillator can be realized based on transverse laser beam dynamics in aspherical optical cavities, pushing the studies of fractional physical system into optics.…”