Table of contents

The quantum chromodynamics (QCD) approach to the problem of multiplicity distributions in high-energy particle collisions is described. The solutions of QCD equations for generating functions of the multiplicity distributions in gluon and quark jets are presented both for fixed and for running coupling constants. Characteristics have been found which are very sensitive to distributions shapes. The predictions are compared with experimental data. Evolution of the multiplicity distributions with decreasing phase space windows is considered and discussed in relation to the notions of intermittency and fractality. Some other QCD effects are briefly described.

The theory of Brownian motion as described by nonlinear Langevin equations and the corresponding Fokker–Planck equations is discussed. The general problems of the theory of nonlinear Brownian motion considered are: Brownian motion in a medium with nonlinear friction; the critical analysis of three forms of the relevant Langevin and Fokker–Planck equations (Ito's form, Stratonovich's form, and the kinetic form); the Smoluchowski equations and master equations for different cases; two methods of transition from master equation to Fokker–Planck equation; master equations for one-step processes; traditional and nontraditional definition of transition probabilities; evolution of free energy and entropy in Brownian motion; Lyapunov functionals. The following particular examples are considered: Brownian motion in self-oscillatory systems; H-theorem for the van der Pol oscillator; S-theorem; oscillator with inertial nonlinearity; bifurcation of energy of the limiting cycle; oscillator with multistable stationary states; oscillators in discrete time; bifurcations of energy of the limiting cycle and the period of oscillations; criterion of instability upon transition to discrete time, based on the H-theorem; Brownian motion of quantum atoms oscillators in the equilibrium electromagnetic field; Brownian motion in chemically reacting systems; partially ionised plasmas; the Malthus–Verhulst process.

One of his articles written with a co-author Gamov called 'My half-article'. Here his 'half-biography' is presented. It covers the first very important part of his life, starting from his youth in Odessa, his student years in Petrograd–Leningrad and several of his visits to Germany, Denmark, and England in connection with his scientific work. Special attention is devoted to his first scientific researches (1926–1928) at the Leningrad State University and to his relations with fellow students—M P Bronstein, D D Ivanenko, and L D Landau. His research into α-decay—its genesis and subsequent fate—is analysed. This article is in many respects based on new archive material.

In the years 1934–1968, when he worked in the USA, Gamow developed the Big Bang theory and suggested an idea deciphering the genetic code. These were his main scientific achievements in the period in question. He also tackled the problem of nuclear sources of stellar energy. From 1948 he participated in the construction of the American hydrogen bomb. He wrote over twenty science and popular science books.

The letters exchanged between Peter Kapitza and George Gamow are published here for the first time. The correspondence throws light on the active support accorded by Kapitza to his Russian colleagues and on his work as the coeditor of a prestigious series of physics monographs published by Clarendon Press, Oxford. Gamow comes over in his letters, relating to one of the most interesting periods of his creative activity (1929 – 1934), in full blaze of his personality.

In a paper published in 1953, i.e., more than a decade before the observational discovery of the cosmic microwave background radiation, George Gamow predicted theoretically the temperature of this radiation. He estimated it to be 7 K, which is very close to the subsequently measured value of about 3 K. Gamow found the present temperature of the background radiation on the basis of general formulas of cosmological dynamics. This prediction was in no way related to primordial nucleosynthesis.This circumstance has and is still causing misunderstanding in those cases in which the authors have raised doubts about Gamow's results, although an actual error has never been demonstrated. A detailed analysis makes it possible to understand how Gamow's calculation is possible. The problem lies in the fact that Gamow makes a certain additional implicit assumption which allows him to dispense with information on nucleosynthesis. This assumption is discussed in the context of the state of cosmology in the period from the fifties to the seventies, and of the current status of this branch of science.