On the stability of the three classes of Newtonian three-body planar periodic orbits

Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.In this paper,these reported orbits are checked stringently by means of a reliable numerical approach(namely the"Clean Numerical Simulation",CNS),which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification.It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time,and are thus most possibly unstable at least.It is suggested to carefully check whether or not these seven unstable orbits are the so-called"computational periodicity"mentioned by Lorenz in 2006.This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.     

Metal-insulator transition in Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>S crystals

Results of an experimental study of MnS, FeS, and Fe _x Mn_1?x S single crystals are presented. The phase composition, the lattice parameters, and the state of paramagnetic ions in Fe _x Mn_1?x S have been determined by x-ray diffraction analysis and Mössbauer spectroscopy. A sequence of transitions have been found in iron manganese sulfide with x = 0.29 at temperatures T ₁ ≈ 25–50 K, T ₂ ≈ 125 K, and T ₃ ≈ 190 K with a change in kinetic properties and the formation of a metallic state at low temperatures T ≈ 2 K. The possibility of a Mott-Hubbard transition in Fe _x Mn_1?x S sulfides with variation of the composition and the temperature is discussed.     

Calorimetry of (1 − <Emphasis Type="Italic">x</Emphasis>)BaTiO<Subscript>3</Subscript>-<Emphasis Type="Italic">x</Emphasis>Ba(Mg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>)O<Subscript>3</Subscript> solid solutions

Phase transitions in ceramic samples of (1 ? x)BaTiO₃-xBa(Mg_1/3Nb_2/3)O₃ solid solutions were studied by differential scanning calorimetry for x = 0, 0.01, 0.02, and 0.03 in the temperature ranges 255–290 K and 310–410 K. The experimental data obtained were used to derive the thermodynamic parameters of the phase transitions occurring at T _c ≈ 400?300 K and T ₁ ≈ 290?300 K and construct the concentration phase diagram.     

Temperature dependence of the surface upper critical field of superconducting alloys

The temperature dependence of the surface upper critical field,H _c3, nearT _c is calculated for arbitrary values of the mean free pathl by taking into account the fourthorder term of the generalized Ginzburg-Landau theory. For finitel the boundary condition is modified such that the normal derivative of the energy gap at the surface becomes positive. The slope of the curveH _c3/H _c2 versust=T/T _c att=1 is found to decrease monotoneously from zero to ?1.040 as one goes from the “dirty” to the “clean” limit.     

Optical and dielectric studies of phase transitions in single crystals of NaNbO<Subscript>3</Subscript>-Gd<Subscript>1/3</Subscript>NbO<Subscript>3</Subscript> solid solutions

The temperature dependences of the permittivity ? and the false-color image patterns obtained by the rotating polarizer method for single crystals of (1 ? x)NaNbO_3?x Gd_1/3NbO₃ (x = 0.003, 0.090) solid solutions with different degrees of diffuseness of the phase transition are investigated. A multifractal analysis of the false-color images has revealed anomalies in the temperature dependences of the parameter ?_∞ of the multifractal spectrum. For a sample with a sharp phase transition (x ≈ 0.003), the temperature of this anomaly is in good agreement with the temperature of the jumps in the permittivity ?(T) and birefringence. For an NNG crystal with x ≈ 0.09, which exhibits a diffuse maximum of ?(T), the temperatures of the anomalies of ?_∞(T) differ in the central and peripheral regions, which correlates with the distribution of Gd over the crystal.     

High-temperature dynamic behavior in bulk liquid water: A molecular dynamics simulation study using the OPC and TIP4P-Ew potentials

Classical molecular dynamics simulations were performed to study the high-temperature (above 300 K) dynamic behavior of bulk water, specifically the behavior of the diffusion coefficient, hydrogen bond, and nearest-neighbor lifetimes. Two water potentials were compared: the recently proposed “globally optimal” point charge (OPC) model and the well-known TIP4P-Ew model. By considering the Arrhenius plots of the computed inverse diffusion coefficient and rotational relaxation constants, a crossover from Vogel–Fulcher–Tammann behavior to a linear trend with increasing temperature was detected at T* ≈ 309 and T* ≈ 285 K for the OPC and TIP4P-Ew models, respectively. Experimentally, the crossover point was previously observed at T* ± 315–5 K. We also verified that for the coefficient of thermal expansion α _P (T, P), the isobaric α _P (T) curves cross at about the same T* as in the experiment. The lifetimes of water hydrogen bonds and of the nearest neighbors were evaluated and were found to cross near T*, where the lifetimes are about 1 ps. For T < T*, hydrogen bonds persist longer than nearest neighbors, suggesting that the hydrogen bonding network dominates the water structure at T < T*, whereas for T > T*, water behaves more like a simple liquid. The fact that T* falls within the biologically relevant temperature range is a strong motivation for further analysis of the phenomenon and its possible consequences for biomolecular systems.     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Self-similar magnetic structures and magnetic flux “Giant” creep

The penetration of a magnetic flux into a type-II high-T _c superconductor occupying the half-space x > 0 is considered. At the superconductor surface, the magnetic field amplitude increases in accordance with the law b(0, t) = b ₀(1 + t)^m (in dimensionless coordinates), where m > 0. The velocity of penetration of vortices is determined in the regime of thermally activated magnetic flux flow: v = v ₀exp?ub;?(U _0/T )(1-b?b/?x)?ub;, where U ₀ is the effective pinning energy and T is the thermal energy of excited vortex filaments (or their bundles). magnetic flux “Giant” creep (for which U ₀/T? 1) is considered. The model Navier-Stokes equation is derived with nonlinear “viscosity” v ∝ U ₀/T and convection velocity v _f ∝ (1 ? U ₀/T). It is shown that motion of vortices is of the diffusion type for j → 0 (j is the current density). For finite current densities 0 < j < j _c, magnetic flux convection takes place, leading to an increase in the amplitude and depth of penetration of the magnetic field into the superconductor. It is shown that the solution to the model equation is finite at each instant (i.e., the magnetic flux penetrates to a finite depth). The penetration depth x _eff ^A (t) ∝ (1 + t)^{(1 + m/2)/2} of the magnetic field in the superconductor and the velocity of the wavefront, which increases linearly in exponent m, exponentially in temperature T, and decreases upon an increase in the effective pinning barrier, are determined. A distinguishing feature of the solutions is their self-similarity; i.e., dissipative magnetic structures emerging in the case of giant creep are invariant to transformations b(x, t) = β^m b(t/β, x/β^{(1 + m/2)/2}), where β > 0.     

Transformation of dielectric properties and appearance of relaxation behavior in Pb<Subscript>5</Subscript>(Ge<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>x</Subscript>)<Subscript>3</Subscript>O<Subscript>11</Subscript> crystals

The special features of the dielectric properties and conduction of ferroelectric crystals of Pb₅(Ge_1?xSi_x)₃O₁₁ (0 ≤ x ≤ 0.67) solid solutions were studied. Permittivity anomalies close to the temperatures T₁ ≈ 260 K and T₂ ≈ 130 K, the appearance of relaxator behavior at x > 0.35, and critical behavior of the concentration dependences of dielectric and pyroelectric characteristics at x₁ = 0.35 and x₂ = 0.60 were observed and studied. These phenomena were found to be related to the dynamics of charge localization on defects with activation energies of U_a1 ≈ 0.6 eV and U_a2 ≈ 0.23 eV. Relaxator behavior appears when the Curie point lies in the temperature region of thermal charge localization. The concentration dependence features at x₁ and x₂ are explained by the coincidence of the Curie point and the centers of the temperature regions of charge localization on the U_a1 and U_a2 defect levels, respectively.     

Surface and volume phase states of Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript>x</Subscript>BO<Subscript>3</Subscript> crystals in the vicinity of the Néel point

The behavior of the magnetic system of a surface layer of macroscopic Fe_1?xGa_xBO₃ crystal (x=0, 0.3) in the vicinity of the Néel temperature T_N was studied. The studies were made by a method involving simultaneous gamma, x-ray, and electron Mössbauer spectroscopy that made it possible to obtain information simultaneously from surface layers and from the bulk of a macroscopic crystal. It was found that the temperature T_N(L) at which a thin layer at a depth L from the surface switches to a disordered state is lower than T_N for the bulk and is lower the closer this layer is to the surface. In the vicinity of T_N, a nonuniform state is observed in which the bulk of the crystal is magnetically ordered and the surface layer is disordered. The transition temperature T_N(L) decreases from T_N to its surface value within a surface layer of a “critical” thickness.     

Heat capacity anomaly in the vicinity of the tricritical and upper critical points

The anomalous behavior of the isochoric heat capacity of a mixture of methane, pentane and heptane is studied experimentally in the vicinity of the liquid-vapor critical point in the cases when (a) the critical temperature T _c approaches the tricritical point T _TCP and (b) the critical temperature approaches the upper critical end point T _U . It is shown that in all cases, the singular part of the heat capacity of the mixture has the form C_sing=A¦τ¦^?α, where τ=(T ? T _c )/T _c and α≈0.11. When T _c →T _U , amplitude A of the heat capacity anomaly is found to be approximately constant. At the same time, the amplitude of the anomaly tends to zero in the vicinity of the tricritical point: A∝¦τ_c¦^ε, where τ_c=(T _c ? T _TCP )/T _TCP and ε=1.6?1.7. The inevitable vanishing of this mode of the heat capacity anomaly leads to a negative value of the critical index \(\tilde \alpha\) characterizing the heat capacity anomaly at the tricritical point, while the tricritical point theory and the isomorphism hypothesis predict \(\tilde \alpha = 0.5\).     

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.     

(Pr–Ca) Manganites That Display Multiferroic Properties: High-Temperature Magnetic,Resistive, and Dielectric Measurements

Complex magnetic, resistive, and dielectric studies of Pr_1–xCa_xMnO₃ (х = 0.15–0.30) manganites reveal multiferroic properties at T?T_C in these solid solutions. States with local magnetization in the form of ferromagnetic clusters (nucleation temperature T* ≈ 700 K) and high dielectric constants coexist in the temperature window T_C ≤ T ≤ T*. There is a correlation between the temperature dependences of specific resistance and specific magnetization.     

Intercluster conduction in lightly doped La<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>MnO<Subscript>3</Subscript> manganites in the paramagnetic temperature range

The magnetotransport and magnetic properties of La _{1 ? x} Ca _x MnO₃ polycrystalline samples (x = 0–0.3) annealed under vacuum and in the oxygen environment are investigated in the temperature range from 77 to 400 K. The magnetic studies of lightly doped manganites reveal persistence of short-range magnetic order up to a temperature T* ≈ 300 K, which is about 2–3 times higher than their Curie temperature T _C. The temperature dependence of the electrical resistivity measured from T* down to nearly T ≈ T _C is fitted by the relation logρ ～ T ^?1/2, which is characteristic of granular metals with electrons tunneling among nanoclusters of magnetic metals embedded in a dielectric host. The magnetoresistance of polycrystalline samples annealed in the oxygen environment has been observed to increase. The electrical, magnetic, and magnetotransport properties of the manganites can be accounted for by the formation of magnetic nanoclusters below T*, tunneling (or hopping) of carriers among the nanoclusters, variation in the magnetic cluster size, and tunneling barrier thickness with variations in temperature and magnetic field strength, as well as by the effect of annealing in different media on the cluster properties.     

Thermodynamics of a Magnetic Transition in MnS<Subscript>2</Subscript> at High Pressures

The behavior of the specific heat of MnS₂ at high pressures has been studied. A significant increase in the transition temperature T_N to an antiferromagnetic state with the pressure from 48.2 K at atmospheric pressure to 76 K at a pressure of 5.3 GPa has been revealed. The initial pressure derivative is dT _N /dP = 4.83 K/GPa. It has been found that the parameter α = d(logT _N )/d(logV ) = ?6.6 ± 0.1 is significantly different from the value α = ?10/3 ≈ ?3.3 (Bloch relation), which is typical of numerous antiferromagnetic insulators—transition- metal oxides and fluorides. The volume jump at the magnetic transition point has been estimated. The necessity of direct dilatometric measurements of the volume has been justified.     

High-order harmonic generation by atoms in a two-color laser field: Phase control of recombination radiation spectrum and duration

The feasibility of phase control over above-threshold tunnel ionization and subsequent recombination emission in two-frequency laser fields is studied. It is shown that, in such fields, we can control the instants of ionization t₀ (within optical cycle T) and recombination t _k . The conditions that minimize the characteristic times δt₀?T and δt _k ?T, within which effective ionization and recombination occur, were found. Phase control allows recombination radiation to be generated with the selection of a narrow spectral range, while additional high-frequency “background illumination” sets up high harmonic “amplification” conditions. It was shown that special two-frequency pumping with elliptically polarized radiation can generate coherent electromagnetic pulses of attosecond width. The width of the pulses decreases as the intensity of pumping increases and can reach subattosecond values. Experimental generation of such pulses may lead to a breakthrough in the development of new methods for femto-and attosecond diagnostics of fast processes.     

Zero differential resistance of a two-dimensional electron gas in a one-dimensional periodic potential at high filling factors

The nonlinear magnetotransport of a two-dimensional (2D) electron gas in one-dimensional lateral superlattices based on a selectively doped GaAs/AlAs heterostructure is studied. The one-dimensional potential modulation of the 2D electron gas is performed by means of a series of metallic strips formed on the surface of a heterostructure with the use of electron beam lithography and a lift-off process. The dependence of the differential resistance r_xx on the magnetic field B < 1.5T in superlattices with the period a = 400 nm at a temperature of T = 4.2 K is investigated. It is found that electronic states with r_xx ≈ 0 appear in one-dimensional lateral superlattices in crossed electric and magnetic fields. It is shown that states with r_xx ≈ 0 in 2D electronic systems with one-dimensional periodic modulation arise at the minima of commensurability oscillations of the magnetoresistance.     

Knight shift in superconducting oxides BaPb<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Bi<Subscript>x</Subscript>O<Subscript>3</Subscript> (<Emphasis Type="Italic">x</Emphasis> < 0.35)

The Knight shift ²⁰⁷K_s for the ²⁰⁷Pb nuclei in the metal phase of the oxides BaPb_1?xBi_xO₃ (x < 0.35) has been analyzed as a function of the concentration. The shift, which is proportional to the density of states near the Fermi energy: ²⁰⁷K_s ～ N(E_F), reaches a maximum for an oxide with the maximum superconducting transition temperature T_c(x ≈ 0.25) = 12 K. A significant increase in the width of the shift distribution with the Bi concentration testifies to the formation of a nonuniform state of the electronic system in the conduction band of superconducting oxides, which is accompanied by an increase in short-wavelength contributions to the spin susceptibility. To detect the ²⁰⁷Pb NMR spectra in superconducting oxides with x > 0.2, the ¹⁷O-²⁰⁷Pb spin-echo double-resonance method is used, which provides successful detection of the ²⁰⁷Pb NMR signal with an anomalously high rate of spin-spin relaxation T ₂ ^?1 > 500 ms^?1. Thus, fundamental restrictions arising in investigations of rapidly relaxing ²⁰⁷Pb nuclei, which are “unobservable” in superconducting oxides BaPb_1?xBi_xO₃ when they are studied by traditional single-resonance methods of pulse NMR spectroscopy, have been overcome.