Ground-state Properties of One-dimensional Matter and The Zel'dovich effect in Rydberg Atoms

The following dissertation consists of three parts. The first two concern ground - state properties of one - dimensional matter, while the third describes an experimental realization of the Zel'dovich effect in Rydberg atoms. Motivated by emerging experimental possibilities to confine atoms and molecules in quasi - one -dimensional geometries, in Chapters 1 and 2 we analyze ground - state properties of strictly onedimensional molecular matter comprised of identical particles of mass m interacting by a Morse potential between nearest neighbors. We find that due to zero - point motion, the system first undergoes a discontinuous evaporation transition into a diatomic gas followed by a continuous dissociation transition into a monoatomic gas. In particular we find that spin - polarized isotopes of hydrogen and 3He are monoatomic gases, 4H6 is a diatomic gas, while molecular hydrogen and heavier substances are Luttinger liquids. We also investigate the effect of finite pressure on the properties of the liquid and monoatomic gas phases. In particular we estimate a pressure at which molecular hydrogen undergoes an inverse Peierls transition into a metallic state which is a one - dimensional analog of the transition predicted by Wigner and Huntington in 1935. In Chapter 2, we show that dissociar tion of the Luttinger liquid is a process initiated at the system edge. The latter becomes unstable against quantum fluctuations at a value of De Boer's number which is smaller than that of the bulk instability which parallels the classical phenomenon of surface melting. In 1959 Ya. B. Zel'dovich predicted that the bound - state spectrum of the non - relativistic Coulomb problem distorted at small distances by a short - range potential undergoes a peculiar reconstruction whenever this potential alone supports a low - energy scattering resonance. However documented experimental evidence of this effect has been lacking. In Chapter 3 we demonstrate that along the Periodic Table of elements the Zel'dovich effect manifests itself as a systematic periodic variation of the Rydberg spectra with a period proportional to the cubic root of the atomic number. This dependence, which is supported by analysis of experimental and numerical data, has its origin in the binding properties of the ionic core of the atom.

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