Bose-Einstein Condensate Dark Matter That Involves Composites

By improving the Bose-Einstein condensate model of dark matter through the repulsive three-particle interaction to better reproduce observables such as rotation curves, both different thermodynamic phases and few-particle correlations are revealed. Using the numerically found solutions of the Gross-Pitaevskii equation for averaging the products of local densities and for calculating thermodynamic functions at zero temperature, it is shown that the few-particle correlations imply a first-order phase transition and are reduced to the product of single-particle averages with a simultaneous increase in pressure, density, and quantum fluctuations. Under given conditions, dark matter exhibits rather the properties of an ideal gas with an effective temperature determined by quantum fluctuations. Characteristics of oscillations between bound and unbound states of three particles are estimated within a simple random walk approach to qualitatively models the instability of particle complexes. On the other hand, the density-dependent conditions for the formation of composites are analyzed using chemical kinetics without specifying the bonds formed. The obtain results can be extended to the models of multicomponent dark matter consisting of composites formed by particles with a large scattering length.Comment: 18 pages, 5 figure

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

Warm turbulence in the Boltzmann equation

We study the single-particle distributions of three-dimensional hard sphere gas described by the Boltzmann equation. We focus on the steady homogeneous isotropic solutions in thermodynamically open conditions, i.e. in the presence of forcing and dissipation. We observe nonequilibrium steady state solution characterized by a warm turbulence, that is an energy and particle cascade superimposed on the Maxwell-Boltzmann distribution. We use a dimensional analysis approach to relate the thermodynamic quantities of the steady state with the characteristics of the forcing and dissipation terms. In particular, we present an analytical prediction for the temperature of the system which we show to be dependent only on the forcing and dissipative scales. Numerical simulations of the Boltzmann equation support our analytical predictions.Comment: 4 pages, 5 figure

Gravity wave turbulence in a laboratory flume

We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size 12×6  m. For a wide range of amplitudes the wave energy spectrum was found to scale as Eω∼ω-ν in a frequency range of up to one decade. However, ν appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates