Surface Microparticles in Liquid Helium. Quantum Archimedes’ Principle

Deviations from Archimedes’ principle for spherical molecular hydrogen particles with the radius R₀ at the surface of ⁴He liquid helium have been investigated. The classical Archimedes’ principle holds if R₀ is larger than the helium capillary length L_cap ? 500 μm. In this case, the elevation of a particle above the liquid is h₊ ~ R₀. At 30 μm < R₀ < 500 μm, the buoyancy is suppressed by the surface tension and h₊ ~ R³₀/L²_cap. At R₀ < 30 μm, the particle is situated beneath the surface of the liquid. In this case, the buoyancy competes with the Casimir force, which repels the particle from the surface deep into the liquid. The distance of the particle to the surface is h_- ~ R^5/3_c/R^2/3₀ if R₀ > R_c. Here, \({R_c} \cong {\left( {\frac{{\hbar c}}{{\rho g}}} \right)^{1/5}} \approx 1\), where ? is Planck’s constant, c is the speed of light, g is the acceleration due to gravity, and ρ is the mass density of helium. For very small particles (R₀ < R_c), the distance h_ to the surface of the liquid is independent of their size, h_ = R_c.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

Thermopower of <Emphasis Type="Italic">R</Emphasis>B<Subscript>12</Subscript> dodecaborides (<Emphasis Type="Italic">R</Emphasis> = Ho,Er, Tm,Lu)

Detailed measurements of the Seebeck coefficient S(T) in a broad range of temperatures (T = 2–300 K) have been performed for the first time for RB₁₂ dodecaborides (R = Ho, Er, Tm, Lu) in paramagnetic (diamagnetic for LuB₁₂) and antiferromagnetic states. At intermediate temperatures (10–300 K), the thermopower is determined by the interaction of carriers with phonon modes, which are related to the oscillations of rare-earth atoms in the framework of atomic clusters B₁₂. A comparative analysis of the parameters determining photon drag the thermopower related to the phonon drag and the results of galvanomagnetic measurements shows evidence for a significant effect of spin fluctuations on the behavior of charge transport characteristics in RB₁₂ compounds with strong electron correlations.     

Dissimilarity between metallic-like transport in the dielectric spin density wave and field-induced spin density wave states in (TMTSF)<Subscript>2</Subscript>PF<Subscript>6</Subscript>

We report similarities and differences of the transport features in the spin density wave (SDW) and in the field-induced SDW (FISDW) phases of the quasi-one-dimensional compound (TMTSF)₂PF₆. As temperature decreases below ≈2 K, the resistance in both phases exhibits a maximum and a subsequent strong drop. However, the characteristic temperature of the R(T) maximum and its scaling behavior in different magnetic fields B are evidence that the nonmonotonic R(T) dependences have different origin in SDW and FISDW regions of the phase diagram. We also found that the borderline T₀(B, P) which divides the FISDW region of the P-B-T phase diagram into the hysteresis and nonhysteresis domains terminates in the N=1 subphase; the borderline thus has no extension to the SDW N=0 phase.     

Long-Lived Quantum Vortex Knots

The dynamics of the simplest torus quantum vortex knots in a superfluid at zero temperature has been simulated with a regularized Biot–Savart law (the torus radii R₀ and r₀ for the initial vortex configuration are much larger than the width of the vortex core ). The evolution times of knots until their significant deformation have been calculated with a small step in the parameter B₀ = r₀/R₀ for different values of the parameter Λ = log(R₀/ξ). It has been found that regions of quasi-stability appear at Λ ? 3 in the range B₀ ? 0.2, which correspond to long knot lifetimes and very large traveling distances up to several hundred R₀. This result is new and quite surprising because previously it was believed that the maximum lifetime of torus knots until reconnection does not exceed several typical periods. The opening of quasi-stable “windows” at increasing Λ is due to narrowing of main parametric resonances of the dynamic system in the parameter B₀.     

Equilibrium and stability of the charged particles’ fluxes drifting crosswise to the strong magnetic field at the expense of the Hall charge separation

The current equilibrium is investigated, where the generation of the Hall electric field on the magnetic Debye radius r _B = B ₀/(4πen _e) is considered by the drifting of the relativistic electrons crosswise to the strong magnetic field. In this case, the electron propagation is possible at the distance d that is essentially larger than the electron radius of the backward reflection in the magnetic field r ₀ ? m _e v _z c/(eB ₀). The instability of the joint drift motion of ions and electrons is investigated for the frequency oscillation w much higher than the ion cyclotron frequency w _Bi and by 4π n _i m _i c ² ? B ₀ ² and (k · B ₀) = 0. It is shown that the resonance effects by the ion beam’s plasma frequency w ? kv ₀ = w _pi leads to the generation of the nonpotential perturbations with the characteristic increment Imw ～ 10^?1 ÷ 10^{? 2} w _pi. Estimates show that the instability, associated with the propagation of the high-energy ion beam through the strong magnetic field, can essentially be like the edge-localized mode in tokamaks.     

Tokamak DEMO-FNS: Concept of magnet system and vacuum chamber

The level of knowledge accumulated to date in the physics and technologies of controlled thermonuclear fusion (CTF) makes it possible to begin designing fusion—fission hybrid systems that would involve a fusion neutron source (FNS) and which would admit employment for the production of fissile materials and for the transmutation of spent nuclear fuel. Modern Russian strategies for CTF development plan the construction to 2023 of tokamak-based demonstration hybrid FNS for implementing steady-state plasma burning, testing hybrid blankets, and evolving nuclear technologies. Work on designing the DEMO-FNS facility is still in its infancy. The Efremov Institute began designing its magnet system and vacuum chamber, while the Kurchatov Institute developed plasma-physics design aspects and determined basic parameters of the facility. The major radius of the plasma in the DEMO-FNS facility is R = 2.75 m, while its minor radius is a = 1 m; the plasma elongation is k ₉₅ = 2. The fusion power is P _FUS = 40 MW. The toroidal magnetic field on the plasma-filament axis is B _t0 = 5 T. The plasma current is I _p = 5 MA. The application of superconductors in the magnet system permits drastically reducing the power consumed by its magnets but requires arranging a thick radiation shield between the plasma and magnet system. The central solenoid, toroidal-field coils, and poloidal-field coils are manufactured from, respectively, Nb₃Sn, NbTi and Nb₃Sn, and NbTi. The vacuum chamber is a double-wall vessel. The space between the walls manufactured from 316L austenitic steel is filled with an iron—water radiation shield (70% of stainless steel and 30% of water).     

Description of small-angle neutron scattering data for nickel–chromium–aluminum alloy within quantum mechanics and classic polydisperse sphere model

The modified Yukawa potential is used to fit the nucleus model parameters to the data on small-angle neutron scattering on nickel—chromium—aluminum alloy for the product of the transferred momentum Q and the effective nucleus radius R, satisfying the condition QR ≤ ?. The analytical polydisperse sphere model is used to calculate the neutron scattering intensity and to determine the most probable macroscopic sphere radius R ₀ at QR ₀ ≥ 3?.     

Maximizing Complementary Quantities by Projective Measurements

In this work, we study the so-called quantitative complementarity quantities. We focus in the following physical situation: two qubits (q _A and q _B ) are initially in a maximally entangled state. One of them (q _B ) interacts with a N-qubit system (R). After the interaction, projective measurements are performed on each of the qubits of R, in a basis that is chosen after independent optimization procedures: maximization of the visibility, the concurrence, and the predictability. For a specific maximization procedure, we study in detail how each of the complementary quantities behave, conditioned on the intensity of the coupling between q _B and the N qubits. We show that, if the coupling is sufficiently “strong,” independent of the maximization procedure, the concurrence tends to decay quickly. Interestingly enough, the behavior of the concurrence in this model is similar to the entanglement dynamics of a two qubit system subjected to a thermal reservoir, despite that we consider finite N. However, the visibility shows a different behavior: its maximization is more efficient for stronger coupling constants. Moreover, we investigate how the distinguishability, or the information stored in different parts of the system, is distributed for different couplings.     

Effect of point defect concentration in NaCl and LiF crystals on the saturation field of the magnetoplastic effect

The effect is studied of the calcium impurity concentration in NaCl crystals and of preliminary x-ray irradiation of NaCl and LiF crystals on the magnetic saturation field B₀ characterizing the transition from the conventional proportionality of the dislocation mean path length l to the magnetic induction B squared(l∝B²) to saturation (l=const). B₀ is shown to increase with the calcium concentration in NaCl crystals and with the dose of x-ray irradiation of NaCl and LiF. This finding indicates that the dislocation breakaway from local defects in weak magnetic fields is controlled by the mechanism of longitudinal spin relaxation in a system of radical pairs that form due to interaction between dislocation cores and paramagnetic centers.     

Calculation of magnetic field in the region of the superconducting winding of window frame dipole for particle accelerators

The necessity of simulations in design of superconducting dipole magnets is due to the following circumstances. First, the critical current as a function of the magnetic field I _c(B) for the multicore superconducting cable which drops strongly requires the knowledge of the value of maximum magnetic field “felt” by its coils for estimation of the working current of the magnet. Second, for choosing the optimal number of coils of the winding (1 or 2) and the working current of the magnet, the ratio of B _max for the inner and outer layers of the dipole magnet winding should be known. Since usually the length of the dipole magnet exceeds many times its transverse size, in this work all calculations of B(x, y) are performed in the transverse plane crossing the center of the magnet. The field at the central point is chosen to be B(0, 0) = 2 T (this is the characteristic working value close to the maximum value in the dipole magnet of this type). In this work, the results of calculation of B(x, y) for single-and double-layered windings with 8 and 16 coils from circular hollow cable are presented.     

Phase Diagram of a Generalized ABC Model on the Interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site i=1,…,N is occupied by a particle of type α=A,B,C, with the average density of each particle species N _α /N=r _α fixed. These particles interact via a mean field nonreflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N→∞, i/N→x∈[0,1] has a unique density profile ρ _α (x) except for some special values of the r _α for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature \(T_{c}=3\sqrt{r_{A} r_{B} r_{C}}/2\pi\).     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

Screening of strongly charged macroparticles in liquid electrolyte solutions

A modified Poisson-Boltzmann model has been proposed which makes it possible to describe the screening of strongly charged macroparticles in liquid electrolyte Z: Z solutions in the case when parameter B= ZeQ₀/εRT?1(Q₀ is the surface electric charge, T is the temperature, ε is the solution permittivity, and Z is the valence of ions) provided that the solution is dilute: κR ≡ (8πZ²e²n_i0/εT)^1/2R?1 (n_i0 is the equilibrium number density of ions). It is assumed that the charge Q₀ of a macroparticle appears as a result of adsorption of ions of a certain polarity on its surface. Quantitative criteria of division of dissolved ions into capable and incapable of adsorption are formulated. For aqueous solutions, the adsorption mechanism always leads to values of B ? 1. It is shown that the charge inversion effect predicted by other authors on the basis of different models must be observed for such solutions for all Z ≥ 1. The effect of Brownian movement of macroparticles on their screening is considered. It is shown that viscous forces emerging during such movement lead to peripheral destruction (“washing out”) of the screening ionic shell of macroparticles and, as a result, to violation of their electroneutrality. This results in the emergence of two types of oppositely charged compound particles with small radii close to R and with radii much larger than R, the charge polarity of the latter being opposite to the polarity of Q₀. It is found that both types of ions of compound particles obey the “law of distribution” of the mean energy of their electric field, expressed by formula (29). The problem of ionic screening of gas bubbles accompanied by the formation of bubstons (bubbles stabilized by ions) is considered separately. It is shown that the bubston radius R in pure water and in aqueous solutions of electrolytes is equal to 14 nm irrespective of the ion number density n_i0. The value of n_i0 determines the number density n _b of bubstons themselves, which are formed spontaneously under equilibrium conditions.     

Hyperfine nuclear interaction at copper lattice sites of high-temperature superconductors studied by <Superscript>61</Superscript>Cu(<Superscript>61</Superscript>Ni) Mössbauer emission spectroscopy

Mössbauer emission spectroscopy on the ⁶¹Cu(⁶¹Ni) isotope has been used to determine the quadrupole coupling constant C(Ni) and magnetic induction B(Ni) for the ⁶¹Ni²⁺ probe at copper sites in Cu₂O, CuO, La_{2 ?x}Ba_xCuO₄, Nd_2?xCe_xCuO₄, RBa₂Cu₃O₆, and RBa₂Cu₃O₇ (R=Y, Nd, Gd, Yb). The compounds containing divalent copper were found to exhibit linear C(Ni) vs. C(Cu) and B(Ni) vs. B(Cu) relations [C(Cu) and B(Cu) are the quadrupole coupling constant and magnetic induction for the ⁶³Cu probe, respectively, found by NMR], which is interpreted as an argument for the copper being in divalent state. The deviation of the data points corresponding to the Cu(1) sites in RBa₂Cu₃O₆ and RBa₂Cu₃O₇ from the C(Ni) vs. C(Cu) straight line may be due either to the copper valence being other than 2+ (in the RBa₂Cu₃O₆ compounds) or to the principal axes of the total and valence electric field gradient being differently oriented (in the RBa₂Cu₃O₇ compounds).     

The Langevin formula for describing the magnetization curve of a magnetic liquid

It has been shown that, at the initial stage of the magnetization curve, the magnetic susceptibility of magnetic liquid determined as χ = Mμ₀/B (M is the magnetization, B is the magnetic induction in a sample) obeys the Curie law, and the magnetic susceptibility determined as χ = M/H (H is the magnetic field intensity in a sample) obeys the Curie–Weiss law. Since the Curie law is a particular case of the Langevin dependence, it is assumed that an experimental magnetization curve is described by the Langevin formula with a Langevin parameter ξ = PB/kT, where P is the magnetic moment of a particle and T is the temperature. Experimental verification has shown that, at parameter ξ, the mean relative deviation between the values of M measured and calculated by the Langevin formula is 5%. This deviation can be accounted for by the influence of dispersion of the magnetic moments of nanoparticles.