A. Yu. Cherny

Scattering from surface fractals in terms of composing mass fractals

We argue that a finite iteration of any surface fractal can be composed of mass-fractal iterations of the same fractal dimension. Within this assertion, the scattering amplitude of surface fractal is shown to be a sum of the amplitudes of composing mass fractals. Various approximations for the scattering intensity of surface fractal are considered. It is shown that small-angle scattering (SAS) from a surface fractal can be explained in terms of power-law distribution of sizes of objects composing the fractal (internal polydispersity), provided the distance between objects is much larger than their size for each composing mass fractal. The power-law decay of the scattering intensity

Short-range particle correlations in a dilute Bose gas

I(q) \propto q^{D_{\mathrm{s}}-6}

The influence of an order-disorder type structural phase transition on the isotope effect

, where

Structure of organosilicon dendrimers of higher generations

2 < D_{\mathrm{s}} < 3

An adiabatic transport of Bose–Einstein condensates in double-well traps

is the surface fractal dimension of the system, is realized as a non-coherent sum of scattering amplitudes of three-dimensional objects composing the fractal and obeying a power-law distribution

Dilute Bose gas: short-range particle correlations and ultraviolet divergence

d N(r) \propto r^{-\tau} dr

Bound states in gauge theories as the Poincaré group representations

, with

Small-angle scattering from the deterministic fractal systems1

D_{\mathrm{s}}=\tau-1

DILUTE BOSE GAS REVISED

. The distribution is continuous for random fractals and discrete for deterministic fractals. We suggest a model of surface deterministic fractal, the surface Cantor-like fractal, which is a sum of three-dimensional Cantor dusts at various iterations, and study its scattering properties. The present analysis allows us to extract additional information from SAS data, such us the edges of the fractal region, the fractal iteration number and the scaling factor.

BOUND PAIR STATES BEYOND THE CONDENSATE FOR FERMI SYSTEMS BELOW TC : THE PSEUDOGAP AS A NECESSARY CONDITION

The thermodynamics of a homogeneous dilute Bose gas with an arbitrarily strong repulsion between particles is investigated on the basis of the exact relation connecting the pair correlation function with the in-medium pair wave functions and occupation numbers. It is shown that the effective-interaction scheme, which is reduced to the Bogoliubov model with the effective pairwise potential, is not acceptable for investigating the short-range particle correlations in a dilute strongly interacting Bose gas. In contrast to this scheme, our model is thermodynamically consistent and free of the ultraviolet divergences due to accurate treatment of the short-range boson correlations. An equation for the in-medium scattering amplitude is derived that makes it possible to find the in-medium renormalization for the pair wave functions at short boson separations. Low-density expansions for the main thermodynamic quantities are reinvestigated on the basis of this equation. In addition, the expansions are found for the interaction and kinetic energies per particle. It is demonstrated that for a many-boson system of hard spheres the interaction energy is equal to zero for any boson density. The exact relationship between the chemical potential and in-medium pair wave functions is also established.