Quantum subdiffusion with two- and three-body interactions

We study the dynamics of a few-quantum-particle cloud in the presence of two- and three-body interactions in weakly disordered one-dimensional lattices. The interaction is dramatically enhancing the Anderson localization length ξ ₁ of noninteracting particles. We launch compact wave packets and show that few-body interactions lead to transient subdiffusion of wave packets, m ₂ ~ t ^α , α< 1, on length scales beyond ξ ₁. The subdiffusion exponent is independent of the number of particles. Two-body interactions yield α ≈ 0.5 for two and three particles, while three-body interactions decrease it to α ≈ 0.2. The tails of expanding wave packets exhibit exponential localization with a slowly decreasing exponent. We relate our results to subdiffusion in nonlinear random lattices, and to results on restricted diffusion in high-dimensional spaces like e.g. on comb lattices.     

Maximum coefficient of light extinction in a nonabsorbing dispersive medium

The maximum value of the light extinction coefficient μ, which can be observed in a dispersive medium with a relative refractive index n of the scattering particles, is studied within the framework of a quasi-crystalline approximation for nonabsorbing dispersive media consisting of monodisperse spherical scatterers. A change in the diffraction parameter x of the scattering particles and their volume concentration c _v is accompanied by nonmonotonic variations of the extinction coefficient, and the function μ(x, c _v ) exhibits several maxima. The dimensions and concentrations of particles are determined, for which the extinction coefficient reaches the absolute maximum μ^max. The μ^max value exhibits a monotonic growth with increasing relative refractive index n of the scattering particles. The conditions of validity of the Ioffe-Regel criterion of radiation localization have been studied. It is established that the localization in nonabsorbing dispersive media can be observed only for n ? 2.7. The intervals of x and c _v in which the criterion of radiation localization is satisfied in dispersive media consisting of particles with n = 3.0 and 3.5 are determined.     

Investigation of <Emphasis Type="Italic">pn</Emphasis> correlations in <Superscript>4</Superscript>He<Emphasis Type="Italic">p</Emphasis> interactions at a momentum of 5 GeV/<Emphasis Type="Italic">c</Emphasis>

Proton-neutron correlations in ⁴Hep interactions are studied in an exclusive experiment by using a 2-m bubble chamber exposed to a 5-GeV/c beam of α particles (the kinetic energy of the protons in the nucleus rest frame is T _p = 620 MeV). Data on the production of pn pairs in 4π geometry for three channels, where it is possible to reconstruct the neutron momentum unambiguously, are used to determine the pn correlation function in ⁴Hep interactions. The experimental results are compared with the predictions of a modified Lednicky-Lyuboshitz model. The value obtained for the root-mean-square radius of the pn-emission region is R _pn = 2.1 ± 0.3 fm. The dependence of the correlation function on the modulus of the total momentum of the emitted nucleon pair and on the direction of the momentum transfer is studied. An indication that the emission of a pn pair proceeds predominantly through the production of a virtual deuteron is obtained.     

Censored Glauber Dynamics for the Mean Field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss Model. It is well known that at high temperature (β<1) the mixing time is Θ(nlog?n), whereas at low temperature (β>1) it is exp?(Θ(n)). Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed β>1, the mixing-time of this model is Θ(nlog?n), analogous to the high-temperature regime of the original dynamics. Furthermore, they showed cutoff for the original dynamics for fixed β<1. The question whether the censored dynamics also exhibits cutoff remained unsettled.In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Curie-Weiss model. Namely, we found a scaling window of order \(1/\sqrt{n}\) around the critical temperature β _c =1, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging.In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if β=1+δ for some δ>0 with δ ² n→∞, then the mixing-time has order (n/δ)log?(δ ² n). The cutoff constant is (1/2+[2(ζ² β/δ?1)]^?1), where ζ is the unique positive root of g(x)=tanh?(β x)?x, and the cutoff window has order n/δ.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Individual-collective crossover driven by particle size in dense assemblies of superparamagnetic nanoparticles

Prussian blue analogues (PBA) ferromagnetic nanoparticles Cs ^I _x Ni ^II [Cr ^III (CN)₆ ] _z ·3(H₂O) embedded in CTA⁺ (cetyltrimethylammonium) matrix have been investigated by magnetometry and magnetic small-angle neutron scattering (SANS). Choosing particle sizes (diameter D = 4.8 and 8.6 nm) well below the single-domain radius and comparable volume fraction of particle, we show that the expected superparamagnetic regime for weakly anisotropic isolated magnetic particles is drastically affected due to the interplay of surface/volume anisotropies and dipolar interactions. For the smallest particles (D = 4.8 nm), magnetocrystalline anisotropy is enhanced by surface spins and drives the system into a regime of ferromagnetically correlated clusters characterized by a temperature-dependent magnetic correlation length L _mag which is experimentally accessible using magnetic SANS. For D = 8.6 nm particles, a superparamagnetic regime is recovered in a wide temperature range. We propose a model of interacting single-domain particles with axial anisotropy that accounts quantitatively for the observed behaviors in both magnetic regimes.     

Die Anlagerung von radioaktiven Atomen und Ionen an Aerosolteilchen

The attachment of radioactive atoms and ions to spherical aerosol particles has been studied theoretically. For uncharged atoms the deposition is considered to be solely governed by thermal diffusion. With calculations based on the “limiting-sphere”-method ofArendt-Kallman it is found, that the attached activity is proportional toΦ ² for aerosol particle diametersΦ smaller than 0.1 μm, and proportional toΦ forΦ greater than 1 μm. For charged ions the diffusion process is modified by the influence of electrostatic forces between the diffusing ions and the aerosol particles. In the frequently occurring case of a symmetrically bipolar charged aerosol this influence can be expressed by a functionG _p(Φ), which depends on the diameterΦ and the effective numberp of elementary charges on the aerosol particle. For an aerosol particle diameterΦ greater than 0.1 μm the attached activity is proportional toΦ ^1.1, and forΦ smaller than 0.01 μm it is proportional toΦ ^1.55. The effects of neglecting various terms in the calculation are considered. The distribution of natural radioactivity on atmospheric aerosols has been calculated for various particle size distributions according toJunge. The calculation shows that about 90% of the total natural activity should be attached to particles smaller thanΦ=0.5 μm, and about 35% to particles smaller thanΦ=0.1 μm. The time T_1/2, in which the concentration of the radioactive particles decreases to half the initial value, depends on the concentration of the aerosol particles and on their size distribution. For 10⁴ aerosol particles per cm³ and the size distributions mentioned,T _1/2 varies between 15 and 30 seconds for radioactive ions. For radioactive atomsT _1/2 is greater than it is for ions in the range of aerosol particle diameters belowΦ=0.25 μm, and smaller ifΦ greater than 0.25 μm.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Electroproduction of <Emphasis Type="Italic">J/ψ</Emphasis> mesons within the semihard QCD approach and the color-singlet model

The deep-inelastic production of J/ψ mesons in electron-proton interactions at the HERA collider is considered within the semihard (k_T-factorization) QCD approach and within the color-singlet model. The dependence of the Q², p _T ² , z, y* and W distributions of J/ψ mesons on various sets of unintegrated gluon distributions and the dependence of the spin parameter α on p _T ² and Q² are investigated. The results of the calculations are compared with the latest experimental data obtained by the H1 and ZEUS Collaborations at the HERA collider. It is shown that experimental investigations of the polarization properties of J/ψ mesons over the kinematical region Q²<1 GeV² may provide an additional test of the statement that the dynamics of gluon distributions is governed by the Balitsky-Fadin-Kuraev-Lipatov equations.     

Interference analysis of the pion-production volume for hadron-hadron and nucleus-nucleus collisions at primary momenta in the range 3.8–5.2 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

By the method of interference correlations, it was directly proven for the first time that the pion-production volume in neutron-proton (np) interactions at primary momenta in the range 3.8–5.2 GeV/c is not constant. It was shown that the interference patterns for np and MgMg interactions are identical. It was established that the rate of expansion of the pion-production volume does not depend on the type of interacting particles (from np and e ⁺ e ^? to PbPb collisions) or on their primary energy (from 3.4 to 200 GeV). It was found that the determination of dimensions is possible only for individual approximately stationary volume elements in their rest frame. A change in the kinematical properties of the subensemble under analysis leads to changes both in the size of the respective element and in its shape.     

Evaluation of the Integrated Cross Sections of Reactions of Exclusive Pion and Kaon Electroproduction off Protons in the Resonance Region at Photon Virtualities from 5 to 12 GeV<Superscript>2</Superscript>

The integrated cross sections of the ep → eπ⁺n, ep → eπ⁰p, ep → eK⁺Λ, and ep → eK⁺Σ⁰ reactions are evaluated in the energy range of nucleon resonance excitation at photon virtualities Q² from 5 to 12 GeV². These exclusive channels will be explored at photon virtualities Q² > 5 GeV² for the first time in future experiments with the CLAS12 detector. The cross-section evaluation is based on the extrapolation of exclusive contributions to the inclusive structure functions F₁ and F₂ from a region of Q² < 5 GeV², in which the experimental data are available, to the region of higher Q². This evaluation of cross sections is of particular importance in the development of the program of experiments with the CLAS12 detector for studying the structure of the ground and excited nucleon states, which may reveal the dynamics of strong interactions in the nonperturbative regime.     

Formation of cumulative nuclei of <Superscript>4</Superscript>He in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

The formation of cumulative nuclei of ⁴He in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon was investigated for the first time under conditions of 4π acceptance. The slope parameter of the invariant cross sections for the formation of cumulative nuclei of ⁴He was determined, and new data on the correlations between the yield of these cumulative nuclei and the yield of charged particles and fragments in ¹⁶Op interactions were obtained.     

Proton-proton interaction with high multiplicity at energy of 70 GeV (proposal)

The goal of the proposed experiment is to investigate the collective behavior of particles in the process of multiple hadron production in pp interaction pp → n _π π + 2N at the beam energy E_lab = 70 GeV. The domain of high multiplicity n _π = 30–40, or z = n/\(\bar n\) = 4–6, will be studied. Near the threshold of reaction n _π → 69, z → z_th = 8.2, all particles acquire small relative momentum Δq < 1/R, where R is the dimension of the particle production region. As a consequence of multiboson interference, a number of collective effects may show up: (a) a drastic increase in the partial cross section σ(n) of production of n identical particles is expected, compared with commonly accepted extrapolation; (b) the formation of jets consisting of identical particles may occur as a result of the multiboson Bose-Einstein correlation (BEC) effect; (c) a large fluctuation of charged n(π⁺,π^?) and neutral n(π⁰) components and onset of centauros or chiral condensate effects are anticipated; (d) an increase in the rate of direct γ as a result of the bremsstrahlung in the partonic cascade and annihilation of π⁺π^? → nγ in dense and cold pionic gas or condensate is expected. In the domain of high multiplicity z ≥ 5, a major part of the c.m. energy \(\sqrt s = 11.6\) GeV is materialized, leading to a high-density thermalized hadronic system. Under this condition, a phase transition to cold quark-gluon plasma (QGP) may occur. The search for QGP signatures like large intermittency in the phase-space particle distribution and an enhanced rate of direct photons will be performed. The experimental setup is designed for detection of rare high-multiplicity events. The experiment is to be carried out at the extracted proton beam of the IHEP U-70 accelerator. The required beam intensity is ～10⁷ s^?1. Under the assumption that the partial cross section σ(n _π = 35) = 10-1 nb, the anticipated counting rate is 10-1 events/h. The multiboson BEC enhancement may drastically increase the counting rate.     

Energy spectra of secondary particles in γ families and their sensitivity to the spectrum of primary cosmic rays

Spectra of secondary particles (γ-rays) in γ-families detected in the X-ray chambers in the Pamirs (H = 600 g cm^?2) have been analyzed. These γ-ray spectra show a bend at the energy E* _γ ≈ (ΣE _γ )^min, where (ΣE _γ )^min is the lowest total energy of γ-rays in the families above which γ-families were selected. The bend is not related to the knee in the spectrum of primary particles; it is due to the use of the ΣE _γ selection criterion. The E _γ spectrum slope is sensitive to the spectrum of the primary cosmic rays in the region E _γ ≥ (ΣE _γ )^min.     

Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X^±Y^±Z^? consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X^±Y^±Z^? with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X^±X^±Z^?. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X^±X^±Z^?, which are stable at any particle masses, asymmetric trions X^±X^±Z^? possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t⁺d⁺p^? and t⁺d⁺d^? combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.     

Rare meson decay in supersymmetric theory with nonconservation of <Emphasis Type="Italic">R</Emphasis>-parity

The decay of mesons K ⁺ → π ^? l ⁺ l′⁺ and D ⁺ → K ^? l ⁺ l′⁺ (l, l′ = e, μ) involving a change of lepton number ΔL = 2 is considered in a supersymmetric extension of the standard model in which R-parity is not conserved due to trilinear Yukawa interactions. The obtained estimates for the probabilities of these decays are significantly lower than the direct experimental upper limits.     

Properties of proton clusters in inelastic CC interactions accompanied by the production of Λ and <Emphasis Type="Italic">K</Emphasis><Superscript>0</Superscript> particles at <Emphasis Type="Italic">p</Emphasis> = 4.2 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

Within a new relativistically invariant approach, the properties of proton clusters that are formed together with Λ and K⁰ particles in inelastic CC interactions at p=4.2 GeV/c per nucleon are investigated in the space of relative 4-velocities. The observed proton clusters are shown to be characterized by high values of the mean kinetic energy of the protons in the cluster rest frame: 〈T _p 〉=100±2 MeV.     

A study of fractional Schrödinger equation composed of Jumarie fractional derivative

In this paper we have derived the fractional-order Schrödinger equation composed of Jumarie fractional derivative. The solution of this fractional-order Schrödinger equation is obtained in terms of Mittag–Leffler function with complex arguments, and fractional trigonometric functions. A few important properties of the fractional Schrödinger equation are then described for the case of particles in one-dimensional infinite potential well. One of the motivations for using fractional calculus in physical systems is that the space and time variables, which we often deal with, exhibit coarse-grained phenomena. This means infinitesimal quantities cannot be arbitrarily taken to zero – rather they are non-zero with a minimum spread. This type of non-zero spread arises in the microscopic to mesoscopic levels of system dynamics, which means that, if we denote x as the point in space and t as the point in time, then limit of the differentials dx (and dt) cannot be taken as zero. To take the concept of coarse graining into account, use the infinitesimal quantities as (Δx) ^α (and (Δt) ^α ) with 0 < α < 1; called as ‘fractional differentials’. For arbitrarily small Δx and Δt (tending towards zero), these ‘fractional’ differentials are greater than Δx (and Δt), i.e. (Δx) ^α > Δx and (Δt) ^α > Δt. This way of defining the fractional differentials helps us to use fractional derivatives in the study of dynamic systems.