Table of contents

The notion that electrons in high-T_c cuprates pair via antiferromagnetic spin fluctuations is discussed and the symmetry of the superconducting order parameter is analyzed. Three approaches to the problem, one phenomenological (with an experimental dynamic magnetic susceptibility) and two microscopic (involving, respectively, the Hubbard model and the tJ-model) are considered and it is shown that in each case strong-coupling theory leads to a d-wave order parameter with zeros at the Fermi surface. The review then proceeds to consider experimental techniques in which the d-symmetry of the order parameter may manifest itself. These include low-temperature thermodynamic measurements, measurements of the penetration depth and the upper critical field, Josephson junction experiments to obtain the phase of the superconducting order parameter, and various spectroscopic methods. The experimental data suggest that the order parameter in cuprates is -wave. Ginzburg–Landau theory for a superconductor with a d-wave order parameter is outlined and both an isolated vortex and a vortex lattice are investigated. Finally, some theoretical aspects of the effects of nonmagnetic impurities on a d-wave superconductor are considered.

Nonlinear, collective, soliton type excitations in zigzag molecular chains are analyzed. It is shown that the non-linear dynamics of a chain dramatically changes in passing from the one-dimensional linear chain to the more realistic planar zigzag model — due, in particular, to the geometry-dependent anharmonism that comes into the picture. The existence or otherwise of solitons is determined in this case by the interplay between the geometrical anharmonism and the physical anharmonism of the interstitial interaction, of opposite signs. The nonlinear dynamic analysis of the three most typical zigzag models (two-dimensional alpha-spiral, polyethylene transzigzag backbone, and the zigzag chain of hydrogen bonds) shows that the zigzag structure essentially limits the soliton dynamics to finite, relatively narrow, supersonic soliton velocity intervals and may also result in that several acoustic soliton types (such as extension and compression varieties) develop simultaneously in the chain. Accordingly, the inclusion of chain geometry is necessary if physical phenomena are to be described in terms of solitary waves.

In the mid-1950s, experimental studies of condensed matter at extremely high pressures (i.e., high energy densities) started to appear in the scientific literature, made possible by using strong shock waves to influence intensively the state of the substance being studied. Russian Federal Nuclear Centres in Sarov and Snezhinsk and their Academy of Sciences counterparts in Moscow, Chernogolovka, and Novosibirsk were instrumental in developing dynamic measurement techniques and forming this new line of investigation of extreme states of matter, based on application of shock waves in high-pressure physics.