Resonant nonlinear interactions between atmospheric waves in the polar summer mesopause region

Data obtained from the mobile SOUSY VHF radar at And(ya/Norway in summer 1987 have been used to study the nonlinear interactions between planetary waves, tides and gravity waves in the polar mesosphere, and the instability of background atmosphere above the mesopause. It is observed that 35-h planetary wave, diurnal, semidiurnal and terdiurnal tides are the prominent perturbations in the Lomb-Scargle spectra of the zonal wind component. By inspecting the frequency combinations, several triads are identified. By bispectral analysis it is shown that most bispectral peaks stand for quadratic coupling between tidal harmonics or between tide and planetary or gravity wave, and the height dependence of bispectral peaks reflects the variation of wave-wave interactions. Above the mesopause, the occurrence heights of the maximum L-S power spectral peaks corresponding to the prominent wave components tend to increase with their frequencies. This may result from the process in which two low frequency waves interact to generate a high frequency wave. Intensities of the planetary wave and tides increase gradually, arrive at their maxima, and then decay quickly in turn with increasing height. This kind of scene correlates with a "chain" of wave-wave resonant interactions that shifts with height from lower frequency segment to higher frequency segment. By instability analysis, it is observed that above the mesopause, the Richardson number becomes smaller and smaller with height, implying that the turbulent motion grows stronger and stronger and accordingly the background atmosphere more and more instable. It is suggested that the wave-wave sum resonant interaction and the wave dissipation due to instability are two dominant dynamical processes that occur in the mesopause region. The former invokes the energy transfer from lower frequency waves to higher frequency waves. The latter results in the heating of the atmosphere and accelerating of the background flow.     

Relationships between power-law long-range interactions and fractional mechanics

We investigate the relationships between models of power-law long-range interactions and mechanics based on fractional derivatives. We present the fractional Lagrangian density which gives the Euler–Lagrange equation that serves as the equation of motion for fractional-power-law long-range interactions. We derive this equation by the fractional variational method. In addition, we derive a Noether-like current from the fractional Lagrangian density.     

Fermion-mediated long-range interactions between bosons stored in an optical lattice

We describe a new method for creating spin-dependent long-range interactions between atomic ultra-cold neutral bosons—specifically ⁸⁷Rb—in an optical lattice. In this proposal, the bosonic system is immersed in a spin-polarized degenerate Fermi gas (almost perfectly non-interacting), here ⁶Li. We first show that the bosons acquire a long-range interaction analogous to Ruderman–Kittel–Kasuya–Yosida interaction in solids. The resulting fermion-mediated Bose–Bose interaction, which can depend on the bosons’ spin state, is tunable using inter-species Feshbach resonance. When the bosons are subject to a suitable optical lattice, 3-body loss processes are greatly suppressed. We conclude by showing that these interactions can lead to a supersolid phase for single-spin Bose system, and also to a fully tunable transverse field Ising model for a two-component Bose system.     

Critical exponents for long-range interactions

Long-range components of the interaction in statistical mechanical systems may affect the critical behavior, raising the system's effective dimension. Presented here are explicit implications to this effect of a collection of rigorous results on the critical exponents in ferromagnetic models with one-component Ising (and more genrally Griffiths=Simon class) spin variables. In particular, it is established that even in dimensions d<4 if a ferromagnetic Ising spin model has a reflection-positive pair interaction with a sufficiently slow decay, e.g. as J _x=1/|x| ^d+ with 0<d/2, then the exponents , , and ₄ exist and take their mean-field values. This proves rigorously an early renormalization-group prediction of Fisher, Ma and Nickel. In the converse direction: when the decay is by a similar power law with >-2, then the long-range part of the interaction has no effect on the existent critical exponent bounds, which coincide then with those obtained for short-range models.Also in the Physics Department. Research supported in part by the National Science Foundation Grant PHY 86-05164.     

Bounds on long-range hadronic interactions

Bounds on long-range nucleon-nucleon interactions are obtained from the analysis of gravitational experiments, molecular spectroscopy and low and intermediate energy nuclear phenomena. Previously existing results are improved, and rather general types of potentials are considered: potentials behaving as 1/Rⁿ and potentials corresponding to the exchange of scalar and pseudo-scalar particles.     

Topological defects with long-range interactions

We investigate a modified sine-Gordon equation which possesses soliton solutions with long-range interaction. We introduce a generalized version of the Ginzburg-Landau equation which supports long-range topological defects in D = 1 and D > 1. The interaction force between the defects decays so slowly that it is possible to enter the non-extensivity regime. These results can be applied to non-equilibrium systems, pattern formation and growth models.     

Spin glasses with long-range interactions

A spin-glass model with a general form of long-range interactions is introduced. The replica method and the renormalization group theory are used and the results are explained from the viewpoint of frustration effects compared with the non- random case. The so-called mean field approximation is shown to be invalid for 3-d RKKY interaction systems.     

Boundary between long-range and short-range critical behavior in systems with algebraic interactions

We investigate phase transitions of two-dimensional Ising models with power-law interactions, using an efficient Monte Carlo algorithm. For slow decay, the transition is of the mean-field type; for fast decay, it belongs to the short-range Ising universality class. We focus on the intermediate range, where the critical exponents depend continuously on the power law. We find that the boundary with short-range critical behavior occurs for interactions depending on distance r as r(-15/4). This answers a long-standing controversy between mutually conflicting renormalization-group analyses.     

Quantum long-range interactions in general relativity

We consider one-loop effects in general relativity that result in quantum long-range corrections to the Newton law, as well as to the gravitational spin-dependent and velocity-dependent interactions. Some contributions to these effects can be interpreted as quantum corrections to the Schwarzschild and Kerr metrics.     

Predissociation by rotation and long-range interactions

A formula of Bernstein for the limiting curve of dissociation is generalized to the case where the interaction potential in the dispersion region is represented by the [1, 0] Padé approximant to the multipole expansion of the energy. The determination of the asymptotic properties of the potential from pre-dissociation data is discussed. Recent data of Herzberg for the state B' ¹σ _u ⁺ of H₂ indicate that the Padé approximant gives a consistent representation of the potential. The classical example of pre-dissociation by rotation (HgH) is studied and for the state X ²σ⁺ a value of C ₆ similar to Bernstein is obtained. In addition C ₈ is estimated to be 89 a.u.     

Limits on possible long-range strong interactions

Limits on the strength of possible long-range (van der Waals) strong interaction forces having the form V ∝ r^?N for 2 ?N?7 are established from an analysis of exotic atom data.     

Existence of phase transitions for long-range interactions

Using a theorem about tangent functionals to convex functions, we obtain existence results for phase transitions. In a “large” Banach space of interactions very pathological behavior is found. In spaces of more “reasonable” interactions we obtain co-existing phases which differ in the expectation of a given observable, as well as broken translation invariance due to long-range order. As an example we consider the isotropic Heisenberg model.     

Many-body theory of synchronization by long-range interactions

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ? = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory. For α > d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2).     

Rigid rod adsorption including long-range dispersion interactions

The Caillé-Ågren analysis of rigid rod adsorption is extended by applying the van Kampen theory of condensation to include long-range dispersion interactions between the adsorbed rods. We discuss in greater detail the characteristics of the phase transition predicted by Caillé and Ågren between states having an isotropic and anisotropic distribution of rods adsorbed parallel to the surface. The maximum density range over which the anisotropic adsorbed phase is stable is determined as a function of the length-to-breadth ratio x of the rigid rods and the strength of the anisotropic dispersion energy. Critical surface adhesion and anisotropic dispersion energies necessary for anisotropic adsorption are also obtained as a function of x. In agreement with Caillé and Ågren the isotropic-anisotropic transition for rigid rod adsorption with attractive forces present is found to be second order. We also discuss the spreading pressure-density or area per molecule isotherms obtained for adsorbed rods having various values of x and surface adhesion and dispersion energies. Whenever feasible we compare our results with the spreading pressure isotherms obtained for monolayers of lyotropic molecules on either aqueous or mercury subphases and obtain qualitative agreement. In particular, the critical density and pressure associated with the two dimensional adsorbed gas-liquid condensation for rigid rods with x = 10 gives reasonable agreement with the critical constants observed by Hawkins and Benedek and Kim and Cannell for the corresponding condensation of pentadecanoic acid monolayers on neutral and acidified aqueous subphases. This agreement suggests that considerable dimerization of the pentadecanoic acid molecules may occur on aqueous surfaces.     

Cluster expansion for fluids with long-range interactions

We apply Kac's method of functional integration to a spatially non-uniform fluid with short and long-range interactions. The system with short-range interactions is treated as a reference system to which the long-range pair interaction is added as a perturbation. All equilibrium distribution functions of the reference system are assumed known. We show by diagram analysis that by a suitable choice of the density profile of the reference system the thermodynamic potential can be expressed in terms of a cluster expansion containing only irreducible diagrams. For a spatially uniform fluid in the thermodynamic limit our results reduce to those obtained by Siegert et al.     

Entropy of classical systems with long-range interactions

We discuss the form of the entropy for classical Hamiltonian systems with long-range interaction using the Vlasov equation which describes the dynamics of a N particle in the limit N-->infinity. The stationary states of the Hamiltonian system are subject to infinite conserved quantities due to the Vlasov dynamics. We show that the stationary states correspond to an extremum of the Boltzmann-Gibbs entropy, and their stability is obtained from the condition that this extremum is a maximum. As a consequence, the entropy is a function of an infinite set of Lagrange multipliers that depend on the initial condition. We also discuss in this context the meaning of ensemble inequivalence and the temperature.     

Quantitative analysis of long-range interactions between adsorbed dipolar molecules on Cu(111)

Highly dispersed superstructures of a dipolar iridium complex are formed on a Cu(111) surface. We show that the dilute superstructures with density-controlled intermolecular separations are stabilized by the strong and long-range repulsive intermolecular interactions. The repulsive intermolecular interactions are quantitatively evaluated by using low-temperature scanning tunneling microscopy, which are characterized by the surface-enhanced dipole-dipole interactions.     

Random cascading models and the link between long-range and short-range interactions in multiparticle production

A general recursive relation for the total multiplicity distribution is derived from a random cascading model with intermittency. The conditions for the existence of a fixed point solution are formulated. An explicit example of such a solution, corresponding to the negative binomial multiplicity distribution is presented. The intimate connection between random cascading models and models of disordered systems is explained and explored. Long-distance properties of the interaction are related to the spectrum of states describing the interaction at short range.