The effect of soft modes on solitons in a linear lattice

Solitons are simulated in an anharmonic linear lattice that is susceptible to a soft mode instability. The soft mode characteristic is introduced in the system by the addition of a term (−Au _n ² ) in the potential between the neighbouring atoms and the evolution of the system is studied as the soft mode parameterA varies from zero to the square of the limiting optical frequency. It is shown that the displacement pattern of the system shows three regions. First there is a region in which the relative displacements of the atoms show large amplitude oscillations. This is followed successively by a domain in which the relative displacements of the atoms are negligible and then by the soliton itself. In the soft mode region, the displacements of the atoms preceding the soliton decrease drastically in a linear fashion first, parabolically next and later become steady. It further exhibits a kind of devil’s stair cases.     

Matter wave interferometry for measuring a molecular transition dipole moment

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ ₁) is less than that of the LOL (V ₀) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ ₁ > V ₀, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ ₁ < V ₀. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.     

Heat conductivity of a nonlinear β-FPU lattice

In this work, we propose a new approach to the computation of heat conductivity in nonlinear systems. The total heat conductivity process is decomposed into two parts: one part is an equilibrium process at the same temperature T of either end of the lattice, which does not transfer energy and the other is a nonequilibrium process at temperature ΔT of one end and a zero temperature of the opposite end of the lattice. This approach makes it possible to somewhat reduce the time of computation of heat conductivity at ΔT → 0. The threshold temperature T _thr is found to behave as T _thr ∼ N ⁻³, where N is the lattice length. The threshold temperature conventionally separates two mechanisms of heat conductivity: at T < T _thr, phonon heat conductivity is dominant; at T > T _thr, the contribution of soliton heat conductivity increases with increasing temperature. The problem of the computation of heat conductivity in the limit ΔT → 0 reduces to the heat conductivity of a harmonic lattice with time-dependent bond rigidities determined by an equilibrium process at temperature T. An exact expression for the temperature dependence of sound velocity in a lattice with a β-FPU potential at T < 10 is derived. A numerical experiment confirmed the existence of solitons and breathers that correspond to a modified Korteweg-de Vries (KdV) equation. The problem of the quantitative contribution of solitons and breathers to heat conductivity requires further study.     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.     

On the Point-Particle (Newtonian) Limit¶of the Non-Linear Hartree Equation

We consider the nonlinear Hartree equation describing the dynamics of weakly interacting non-relativistic Bosons. We show that a nonlinear M?ller wave operator describing the scattering of a soliton and a wave can be defined. We also consider the dynamics of a soliton in a slowly varying background potential W(ɛx). We prove that the soliton decomposes into a soliton plus a scattering wave (radiation) up to times of order ɛ⁻¹. To leading order, the center of the soliton follows the trajectory of a classical particle in the potential W(ɛx). Received: 30 June 2000 / Accepted: 25 June 2001     

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Concentration dependence of the lattice constant of disordered interstitial solid solutions

The lattice constant of the A-(C) interstitial solid solutions is calculated, and its dependence on the solution composition is determined for arbitrary concentration c_C of the C atoms and their arbitrary distribution over interstices of different types. For c _c ≪1, a linear dependence of the lattice constant on c_C is established, which is also observed experimentally. The influence of temperature redistribution of interstitial atoms over interstices of different types, leading to a specific nonlinear temperature dependence of the lattice constant, is investigated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–5, December, 2005.     

Constant-cutoff approach to Λ (1405) resonance in the bound-state soliton model

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB = 1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study strong and electromagnetic properties of the Λ(1405) hyperon in the bound-state approach to theSU(3)-soliton model for the hyperons, withSU(3)-symmetry breaking. We calculate the strong coupling constantg _Λ*NK; , the magnetic moment of Λ*, the mean square radii, and the radiative decay amplitudes. Finally we compare the present results with those obtained using other models and with the available empirical data. We show that there is a general qualitative agreement between our results and the results of other models and available empirical data, except for the Λ*πΣ coupling, which, as in the case of the complete Skyrme model, vanishes in the second-order approximation of the kaon fluctuations used in this work.     

The Existence and Stability of Noncommutative Scalar Solitons

 We establish existence and stability results for solitons in noncommutative scalar field theories in even space dimension 2d. In particular, for any finite rank spectral projection P of the number operator 𝒩 of the d-dimensional harmonic oscillator and sufficiently large noncommutativity parameter θ we prove the existence of a rotationally invariant soliton which depends smoothly on θ and converges to a multiple of P as θ→∞. In the two-dimensional case we prove that these solitons are stable at large θ, if P=P _N , where P _N projects onto the space spanned by the N+1 lowest eigenstates of 𝒩, and otherwise they are unstable. We also discuss the generalisation of the stability results to higher dimensions. In particular, we prove stability of the soliton corresponding to P=P ₀ for all θ in its domain of existence. Finally, for arbitrary d and small values of θ, we prove without assuming rotational invariance that there do not exist any solitons depending smoothly on θ. Received: 13 July 2001 / Accepted: 9 July 2002 Published online: 10 January 2003     

TG/DTA evidence of fluorine incorporation into YBa2Cu3O6⋅+δ

TG/DAT evidence to support incorporation of fluorine into superconducting orthorhombic lattice in YBa₂Cu₃O_6⋅+δ is presented. It is inferred that the F atom goes substitutionally in place of O atom in the lattice. Replacement of two oxygen atoms by four fluorine atoms did not alter theT _cof the product. By a similar replacement of two of its oxygens by fluorine atoms, the tetragonal modification of the oxide yields a product that remains non-superconducting down to 30 K.     

Low-frequency lattice dynamics in Ba1−x KxBiO3 oxides according to 39K NMR data

The spin-lattice relaxation times T ₁ in Ba_1−x K_xBiO₃ (x=0.3, 0.4, 0.5) were measured in the normal temperature range (20–300 K).A substantial contribution to the spin-lattice relaxation rate from dynamic local distortions of the crystal lattice near potassium atoms is found. The activation energy of this process increases with decreasing potassium concentration, and the frequency of lattice excitations decreases. The nature of the low-frequency lattice dynamics is discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 344–349 (10 September 1999)     

On the surface properties of a nanodiamond

The dependences of the specific surface energy, the surface tension, and the surface pressure on the size, the surface shape, and the temperature of a nanodiamond with a free surface have been investigated using the Mie-Lennard-Jones interatomic interaction potential. The nanocrystal has the form of a parallelepiped faceted by the (100) planes with a square base. The number of atoms N in the nanocrystal varies from 5 to ∞. The isothermal isomorphic dependences of the specific surface energy, its isochoric derivative with respect to the temperature, the surface tension, and the surface pressure on the nanodiamond size have been calculated at temperatures ranging from 20 to 4300 K. According to the results of the calculations, the surface energy under this conditions is positive, which indicates that the nanodiamond cannot be fragmented at temperatures up to 4300 K. The surface pressure for the nanodiamond P _sf (N) ∼ N ^−1/3 is considerably less than the Laplace pressure P _ls (N)^−1/3 ∼ N ^−1/3 for the same nanocrystal at the given values of the temperature, the density, and the number of atoms N. As the temperature increases from 20 to 4300 K, the lowering of the isotherm P _sf (N) is considerably more pronounced than that of the isotherm P _ls (N). At high temperatures, the isotherm P _sf (N) changes the shape of the size dependence and goes to the range of extension of small nanocrystals. It has been demonstrated that the lattice parameter of the nanodiamond can either decrease or increase with a decrease in the nanocrystal size. The most significant change in the lattice parameter of the nanodiamond is observed at temperatures below 1000 K.     

Simulation of diffusion instability of a mercury atomic distribution in the cadmium-mercury-tellurium alloy

The formation of inhomogeneities in Cd_xHg_1-x Te alloys upon post-growth cooling or upon low-temperature annealing is simulated numerically. The mechanism of the formation of inhomogeneities is based on the diffusion instability in a system involving mercury atoms located at lattice sites, interstitial mercury atoms, and cation vacancies. It is revealed that, upon prolonged annealing of the Cd_xHg_1-x Te alloys with a cadmium content x = 0.2 at a temperature of ∼200°C, the concentrations of mercury atoms at lattice sites, interstitial mercury atoms, and vacancies are characterized by an inhomogeneous nearly periodical distribution arising from a small fluctuation when the initial equilibrium concentration of interstitial mercury atoms exceeds a threshold value (∼3 × 10¹⁷ cm⁻³). The spatial and time scales of the concentration distribution are determined primarily by the equilibrium concentration of vacancies and do not depend on the type of fluctuation involved. The spatial period of the concentration distribution increases linearly from 0.01 to 3.00 μm as the equilibrium concentration of vacancies changes from 10¹⁹ to 10¹⁴ cm⁻³. At lower concentrations of vacancies, the periodic structure is formed for a considerably longer time.     

Effect of nonstoichiometry and ordering on the period of the basis structure of cubic titanium carbide

We have examined the influence of nonstoichiometry and order-disorder phase transformations on the basis period (of type B1) of the structure of titanium carbide TiC_y (0.5<y<1.0). We found that ordering of titanium carbide TiC_y with formation of superstructures of the type Ti Ti₂C and Ti₃C₂ leads to growth of the period of the basis crystal lattice in comparison with the disordered carbide. Taking the change in the lattice period into account, we discuss the question of the directions of the static displacements of atoms near a vacancy. Fiz. Tverd. Tela (St. Petersburg) 41, 1134–1141 (July 1999)     

Residual impurity effects on the magnetic ordering in α-Mn observed by hyperfine interaction

We report on the lattice location of indium in and the magnetic ordering of manganese in its α- and β-phases, as seen by perturbed angular correlation. Quadrupole interaction spectra show that indium prefers to replace Mn atoms of type I in α-Mn, but replaces type II atoms in the β-Mn structure. The interaction strength equalseQV _zz /h=3.6 (6) MHz in α-Mn and 172.3 (3) MHz with ν=0.13 (1) in β-Mn. No magnetic ordering down to 4.2 K was observed in β-Mn, while belowT _N =95 K in the α-Mn phase, a magnetic hyperfine interaction appears indicating two distinct magnetic probe environments. The hyperfine field, when measured atT=4.2 K, equals for 70% of the probes 6.33 (1) T, while the remaining fraction senses a 3.10 (4) T field. The magnitudes of the hyperfine fields are essentially unaffected by a variety of conditions in the sample preparation. The ordering temperature, on the contrary, turns out to be rather sensitive to residual impurities especially any oxygen contamination.     

Electronic structure and half-metallic property of Si<Subscript>3</Subscript>CaC<Subscript>4</Subscript>

The electronic structures and magnetic properties of Si₃CaC₄ in zinc-blende phase has been studied by employing the first-principles method based on density functional theory (DFT). The calculations predict stable ferromagnetic ground state in Si₃CaC₄, resulting from calcium substitution for silicon. The calculated total magnetic moment is 2.00 μ _B per supercell, which mainly arises from the Ca and neighboring C atoms. Band structures and density of states studies show half-metallic (HM) ferromagnetic property for Si₃CaC₄. The ferromagnetic coupling is generally observed between the Ca and C atoms. The ferromagnetism of Si₃CaC₄ can be explained by the hole-mediated double exchange mechanism. The sensitivity of half-metallicity of Si₃CaC₄ as a function of lattice constant is also discussed, and the half-metallicity can be kept in a wider lattice constant range.     

Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations

We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV) and the NQC equation. This allows us to present rational solutions for the whole Adler-Bobenko-Suris (ABS) list except Q4. The known Miura transformation for soliton solutions between the NQC equation and Q3_δ and the known degenerations for solitons from Q3_δ to Q2, Q1_δ, H3_δ, H2 and H1 in the ABS list are used. We show that the Miura transformation and degenerations are valid as well for rational solutions which are usually considered as “long-wave-limit” of solitons. All the rational solutions can be expressed in terms of {z _j} which are linear functions of (n, m).     

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects (superconducting granules, superfluid helium in a porous medium, traps with Bose-condensed atoms, etc.) is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number n ₀ of the sites in the system (the “number of Cooper pairs” per granule, the number of atoms in a trap, etc.) leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on n ₀. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in n ₀ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum path-integral Monte Carlo calculations. Zh. éksp. Teor. Fiz. 114, 591–604 (August 1998)     

Mechanism of three-dimensional polymerization of fullerite C60 at high pressures

A series of polycrystalline phases corresponding to different stages of three-dimensional polymerization and destruction of C₆₀ molecules has been synthesized by heating fullerite C₆₀ under a pressure P=12.5 GPa. The structure of the phases can be identified as fcc, and the lattice period decreases with increasing heating temperature. A model of three-dimensional polymerization in which the lattice parameter is a continuous function of the fraction of covalently bonded molecules is proposed. The model makes it possible to estimate the number of atoms in the sp ³ state. The hardness of the polymerized fcc phases is studied on the basis of percolation of rigidity. It is shown experimentally that the period a≈13.8 Å is the threshold for the formation of a three-dimensionally rigid C₆₀ polymer. It is found that the thermal stability of the strongly and weakly polymerized phases is qualitatively different. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 755–759 (10 December 1996)     

Mixing of neutral atoms and lepton number oscillations

We discuss oscillations of two neutral atoms which proceed with the violation of lepton number. One of the neutral atoms is stable, the other one represents a quasistationary state subjected to electromagnetic deexcitation. The system of neutral atoms exhibits oscillations similar to those of the system of neutral kaons and neutron-antineutron oscillations in the nuclear medium. The underlying mechanism is a transition of two protons and two bound electrons to two neutrons p + p + e _b ⁻ + e _b ⁻ ↔ n + n. A signature of the oscillations might be an electromagnetic deexcitation of the involved unstable nucleus and atomic shell with the electron holes. A resonant enhancement of the neutrinoless double electron capture takes place when the atomic masses tend to be degenerate. Qualitative estimates show that in searches for lepton number violation oscillations of atoms might be a possible alternative to the conventional mechanism of the neutrinoless double β decay process with emission of two electrons. The article is published in the original.