Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n > 2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses. PACS Number: 05.20.-y, 02.30.Mv, 66.10.-x, 78.70.Nx, 05.60.Cd     

Discrete binning: correspondence limit consistent analysis of classical probabilities using faux angular momenta and multi-polar harmonic moments to give ‘quantum-like’ probabilities

This paper develops discrete binning (DB) for N_i slices for classical probability functions for an arbitrary number of classical continuous variables, x_i , where 0 ≤?x_i ≤?1 or ?1 ≤?x_i ≤?1. Faux angular momenta, j_i , are introduced where 2j_i +?1 =?N_i , and the discrete probabilities for the various |j_im_i ? are calculated with a generalisation of the theory of Anderson and Aquilanti. Discrete probabilities are calculated from Legendre moments of the classical intensities with Clebsch–Gordan moments. The m_i may represent vibrational quanta, rotational angular momenta, or discrete values of the impact parameter, scattering angles and other variables. DB directly yields probabilities for different m_i , but in the correspondence limit (large j_i ) the discrete probabilities correspond to classical probabilities, I({x _{m i} }), at known discrete values {x _{m i} }. DB probabilities sum to unity, but some may be negative. Since the Clebsch–Gordan coefficients appropriate for this work are actually Gram (discrete Chebyshev) polynomials, DB is equivalent to compression and/or smoothing of data using Gram polynomials. For large N_i , DB and histogram binning (HB) provide equivalent probabilities and statistical errors. However, smoothing can often reduce the statistical errors for DB probabilities. DB is related to Legendre moment binning (LMB), but DB guides the most consistent implementation of LMB. The rule of three is introduced to provide finer resolution for DB, HB, and LMB analysis. This also leads to fractional slice binning (FSB), which is equivalent to Gaussian binning. The paper presents one-, two-, and three-dimensional examples, and spectroscopic plots are very useful for summarising the results.     

Dynamics of cold atoms in a quadrupole magnetic trap with an orbiting potential

We study the dynamics of atoms confined to a quadrupole magnetic trap with an orbiting potential. For typical values of the experimental parameters of the trap, the rotating magnetic field is shown to produce high-frequency modulation of atomic momenta with an amplitude comparable to the widths of the momentum distributions for the lowest oscillation states of atoms in the time-averaged potential. We find the quantum-statistical momentum and position distributions of atoms and show that at temperatures much higher than the effective vibrational temperature of the atoms in the trap the quantum-statistical momentum and position distributions are Gaussian. We also establish that at temperatures comparable to the effective vibrational temperature of the atoms the quantum-statistical momentum distribution has an annular structure in the trap’s symmetry plane, which is due to the deep modulation of the atomic momenta caused by the rotating magnetic field. Zh. éksp. Teor. Fiz. 114, 23–36 (July 1998)     

Even and odd amplitudes of distributions of third particles in nuclear fission

The principal values for the even and odd components of the amplitudes of the angular distributions of α particles emitted as the third particles in true low-energy ternary fission of nuclei are calculated within the quantum theory of fission using natural approximations for the dependence of the potential scattering phases of the α particle on its orbital momenta and experimental angular distributions, unperturbed by the fissioning nucleus rotation, of these third α particles. Knowing the angular dependences of these components, we can estimate the angular dependences of the T-odd ROT and TRI asymmetry coefficients for the ternary fission of actinide nuclei induced by cold polarized neutrons.     

Gap discrete breathers in two-component three-dimensional and two-dimensional crystals with Morse interatomic potentials

The properties of gap discrete breathers in three-dimensional and two-dimensional crystals of the composition A ₃ B with interatomic bonds described by the Morse potential have been investigated by the molecular dynamics method for different ratios between the masses of components m _A /m _B . The transition to a thermal equilibrium from a state far from equilibrium has been studied for the two-dimensional crystal. In this case, a short-wavelength phonon vibrational mode is excited in the crystal. This mode appears to be modulationally unstable for not too small amplitudes. During the transition to the state characterized by a uniform energy distribution between all vibrational modes of the crystal, the energy is localized in the form of gap discrete breathers, which exist in time intervals that exceed their oscillation period by several orders of magnitude.     

Mutual Derivation Between Arbitrary Distribution Forms of Momenta and Momentum Components

International Journal of Theoretical Physics - The mutual derivation between arbitrary distribution forms of momenta and momentum components of particles produced in an isotropic emission source...     

Forbidden vibrational-rotational transitions and Herman-Wallis factors in fundamental IR bands of symmetric-top molecules

Within the theory of coupled schemes of ordering of vibrational-rotational interactions, the operator of the effective dipole moment of single-quantum vibrational transitions is represented in the form of an infinite series in vibrational (normal coordinates and conjugate momenta) or rotational variables (components of the total angular momentum). Mechanisms of activation of infrared-inactive totally symmetric vibrations in molecules of the D _2a , D _3h , C _3h , D _n (n ≥ 3), S ₄, T, T _a , and O symmetries and forbidden vibrational-rotational transitions in IR bands of active vibrations have been studied. The group-theoretic analysis of tensor parameters in higher-order effective dipole moments of single-quantum vibrational transitions in axially symmetric molecules has been performed. The strengths of allowed transitions and forbidden transitions in fundamental and hot IR bands of axially symmetric molecules are calculated with allowance for the Herman-Wallis factors. For effective dipole moments of multiquantum transitions in molecules, models are developed in the form of infinite series in rotational variables and in the form of Padé approximants.     

Volume effects in the theory of equilibrium and quasiequilibrium states of multicomponent solid solutions

A phenomenological theory of equilibrium and quasiequilibrium states of multicomponent solid solutions is constructed taking account of volume effects. Quasiequilibrium states are characterized by the fact that only some of the conditions for thermal dynamic equilibrium of the system are satisfied. The short-range parts of the interatomic interactions are taken into account by introducing the proper volumes of the atoms based on a generalized lattice model. The long-range parts of the potentials are taken into account in the effective-field approximation. The equations for the quasiequilibrium components in the solutions are introduced taking account of the nonuniformity in the distributions of the less mobile nonequilibrium components. The conditions for spinodal decomposition of a solid solution with an arbitrary number of components in the equilibrium and quasiequilibrium cases are obtained. An equation for equilibrium spinodal decomposition of a three-component microheterogeneous solid solution is found. Fiz. Tverd. Tela (St. Petersburg) 41, 1609–1613 (September 1999)     

Liouville and Fokker–Planck dynamics for classical plasmas and radiation

We consider a nonequilibrium statistical system formed by many classical non‐relativistic particles of opposite electric charges (plasma) and by the classical dynamical electromagnetic (EM) field. The charges interact with one another directly through instantaneous Coulomb potentials and with the dynamical degrees of freedom of the transverse EM field. The system may also be subject to external influences of: i) either static, but spatially inhomogeneous, electric and magnetic fields (case 1)), or ii) weak distributions of electric charges and currents (case 2)). The particles and the dynamical EM field are described, for any time t > 0, by the classical phase‐space probability distribution functional (CPSPDF) f and, at the initial time (t = 0), by the initial CPSPDF f_in. The CPSPDF f and f_in, multiplied by suitable Hermite polynomials (for particles and field) and integrated over all canonical momenta, yield new moments. The Liouville equation and f_in imply a new nonequilibrium linear infinite hierarchy for the moments. In case 1), f_in describes local equilibrium but global nonequilibrium, and we propose a long‐time approximation in the hierarchy, which introduces irreversibility and relaxation towards global thermal equilibrium. In case 2), the statistical system, having been at global thermal equilibrium, without external influences, for t ≤ 0, is subject to weak external charge‐current distributions: then, new hierarchies for moments and their long‐time behaviours are discussed in outline. As examples, approximate mean‐field (Vlasov) approximations are treated for both cases 1) and 2).     

Buffer-gas effect on the rotovibrational line intensity distribution: Analysis of possible mechanisms

Line intensities A_m () of the HF fundamental band (T=293 K) are found to decrease linearly with the buffer-gas (Xe) density (-16 Amagat). The obtained slopes of the A _m (d)/ A _m (0) vs. plots are maximum at | m | =1 () and rapidly drop with |m|. Many possible mechanisms are considered; the most effective one appears to be the HF-Xe bimer formation, with the equilibrium constant strongly depending on the rotational quantum number. The rigid-rotator approximation used gives the density derivatives considerably smaller than the measured ones. The disbalance may be lessened for vibrating rotators by allowance for the interband intensity transfer induced by the vibrational modulation of short-range forces. Received 17 January 2000     

Structural, electronic and vibrational properties of indium oxide clusters

Geometric, electronic and vibrational properties of the most stable and energetically favourable configurations of indium oxide clusters In_mO_n (1≤m, n≤4) are investigated using density functional theory. The lowest energy geometries prefer the planar arrangement of the constituent atoms with a trend to maximize the number of ionic In-O bonds. Due to the charge transfer from In to O atoms, the electrostatic repulsion occurs between the atoms with the same kind of charge. The minimization of electrostatic repulsion and the maximization of In-O bond number compete between each other and determine the location of the isometric total energy. The most stable linear In-O-In-O structure of In₂O₂ cluster is attributed to the reduced electrostatic repulsive energy at the expense of In-O bond number, while the lowest energy rhombus-like structure of In₂O₃ cluster reflects the maximized number of In-O bonds. Furthermore, the vibrational frequencies of the lowest energy clusters are calculated and compared with the available experimental results. The energy gap and the charge density distribution for clusters with varying oxygen/indium ratio are also discussed.     

Molecular dynamics simulation model of hydrogen recycling on carbon divertor for neutral transport analysis in large helical device

To perform the neutral-transport simulation with processes in which hydrogen molecules contribute to the reaction such as molecular assisted recombination, the parameters of emitted neutral particles at the wall such as the energy distributions and the form (atom or molecule) of emitted neutral particles are necessary as a boundary condition of the calculation. Therefore, in order to provide information of recycled hydrogen on the divertor to neutral-transport code, molecular dynamics simulation of a hydrogen atom injection into a carbon material is performed to obtain the distributions of emission angle and translational energy of emitted hydrogen atoms and molecules. The distributions of rotational and vibrational energies are also investigated in the case of molecular hydrogen emission. Moreover, the quantum rotational state J, and vibrational state v are estimated from the classical value obtained by the simulation.     

A new proof of the Stillinger-Lovett complete shielding condition

It is shown that any equilibrium state of classical charged particles with correlation having a spatial decay faster than 1/¦x¦^v+2 in dimensionv=2, 3 obeys the Stillinger-Lovett second moment condition. Under the same clustering hypothesis, arbitrary localized external charge distributions are completely shielded.     

An analysis of electron density fluctuations in air shower cores and the question of large transverse momenta

Electron density distributions in air shower cores recorded with the 32 m² neon hodoscope of the Kiel array have been analysed, looking for the existence of significant multicores which might result from large transverse momentum emission of high energy particles. The shower sizes are between 10⁴ and 5×10⁶ particles, corresponding to primary energies up to a few times 10⁷ GeV. Several spurious effects simulating multicores have been found, but there are no indications for the existence of large transverse momenta.     

Eigenvalue problem for arbitrary linear combinations of a boson annihilation and creation operator

The eigenvalue problem for arbitrary linear combinations kα + μα^? of a boson annihilation operator α and a boson creation operator α^? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α^? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α^? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter.     

Relativistic fermion in a spherically symmetric potential well of finite depth in a two-dimensional space

The problem of existence of bounded relativistic fermion states in a spherically symmetric well of finite depth in a two-dimensional space is investigated. The well depth critical for the appearance of standard states with energies E = m, 0, and –m is determined; moreover, cases with zero and nonzero fermion momenta are considered. Approximate analytical expressions for the critical depths of narrow and wide wells are derived which are in good agreement with the results of numerical calculations. Approximate energies of levels located on the boundaries of the upper and lower continuums and determined analytically are in good agreement with the results of numerical calculations.