Helium films from two to three dimensions

Recent studies of helium films adsorbed on uniform solid surfaces reveal a rich variety of distinctive regimes. Monolayer films display several phases approximating two dimensional gases, liquids and solids as well as substrate ordered structures. Detailed theoretical models are achieving considerable quantitative success in describing and predicting properties of most of the phases. An important subset of the current studies involves the evolution from two dimensional to bulk behavior, including the onset of superfluidity.     

The depletion potential in one, two and three dimensions

We study the behavior of the depletion potential in binary mixtures of hard particles in one, two, and three dimensions within the framework of a general theory for depletion potential using density functional theory. By doing so we extend earlier studies of the depletion potential in three dimensions to the cases ofd = 1 and 2 about which little is known, despite their importance for experiments. We also verify scaling relations between depletion potentials in sphere-sphere and wall-sphere geometries ind = 3 and in disk-disk and wall-disk geometries ind = 2, which originate from geometrical considerations.     

Supersymmetric quantum mechanics in one,two and three dimensions

We discuss a few supersymmetric quantum mechanical models in one, two and three dimensions. In the case of one particle in both two and three dimensions we present some examples where supersymmetry is unbroken and the ground state is many-fold degenerate. Further, we consider the supersymmetric generalization of the nearest neighbour XY model and show that supersymmetry remains unbroken in this case.     

Evolution of fermion pairing from three to two dimensions

We follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.     

Crossover from one to three dimensions for a gas of hard-core bosons

We develop a variational theory of the crossover from the one-dimensional (1D) regime to the 3D regime for ultracold Bose gases in thin waveguides. Within the 1D regime we map out the parameter space for fermionization, which may span the full 1D regime for suitable transverse confinement.     

Self-assembling of gold nanoparticles in one, two, and three dimensions

In the present work, we report the growth of ordered arrays of gold nanoparticles passivated with n-alkylthiol molecules using crystallization in toluene vapor. We kept constant the average particle size and the length of the passivating molecule (1-dodecanethiol). The temperature and time of growth were varied. We show that in the initial stages of the growth, nano-chains of particles are produced. These nano-chains aggregate to form two-dimensional arrays. In the initial stages the nano-chains form a two-dimensional square lattice which then relaxes to a close-packed structure. In latter stages of growth a three-dimensional supercrystal is produced. It is found that the packing of nanoparticles corresponds to an average FCC lattice. However, large variations on the local parameters of the lattice are observed. Near the edges of the supercrystal the anomalous packing reported by Zanchet et al. [20] and Fink et al. [21] was observed. The energy of the observed structures is analyzed using molecular dynamics simulation. It is concluded that using the vapor growth method, it is possible to produce controlled ordered structures from one to three dimensions. Received: 24 February 2000 / Accepted: 28 March 2000 / Published online: 13 July 2000     

Infrared behaviour of metallic systems in one, two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.     

Infrared behaviour of metallic systems in one,two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.     

Diffusion-influenced fluorescence quenching dynamics in one to three dimensions

The fluorescence decay curves obtained from diffusion-influenced quenching in various spatial dimensions are discussed. The two-dimensional quenching has, because of intractable fitting functions, previously been dealt with only in the completely diffusion-controlled case (corresponding to the Smoluchowski boundary condition). In this paper, an approximation for the two-dimensional (2D)-quenching behavior with the Collins-Kimball boundary condition is presented. The nonlinear least-squares method has been used to analyze simulated decay data. The consequences the choice of an incorrect model has on the final results as well as the possibility to discriminate between different dimensionalities are investigated. Also, some inherent properties of the fitting functions are studied.     

The ferromagnetism of ultrathin films; from two to three dimensions

We review the properties of ultrathin ferromagnetic films, with attention to simple physical arguments that outline their principal properties. A ferromagnetic monolayer clearly provides an illustration of two dimensional magnetism. It is argued that the crossover to three dimensional behavior occurs when only a few monolayers are present, both in the low temperature spin wave regime, and near the transition temperature. We discuss anisotropy and its role in inducing long range order in ultrathin films, and spin reorientation transitions.     

Melting in two dimensions—the current status

The current status of the controversy relating to melting in two dimensions is surveyed. To begin with, a review is given of the seminal work of Kosterlitz and Thouless. This is followed by a discussion of the modifications introduced by Nelson and Halperin. The search for the continuous transitions and the intermediate hexatic phase predicted by these theories is then described, covering both the laboratory as well as simulation experiments. Alternate viewpoints to thekt theory aired recently in the literature are also briefly examined. The paper concludes with an outlook for the future. Jawaharlal Nehru Fellow     

Extrema statistics of Wiener-Einstein processes in one,two, and three dimensions

The maxima and first-passage-time statistics of Wiener-Einstein processes are evaluated analytically in one, two, and three dimensions. We show that the mean square maximum displacement has the same time dependence as the mean square displacement, i.e., it grows linearly with time. The ratio of the mean square maximum to the mean square displacement is shown to decrease with increasing dimensionality. We also calculate the mean first passage time for the process to attain a given absolute displacement and find that it grows as the square of the displacementand is independent of the dimensionality of the process. In addition, we evaluate the dispersion of maxima and of first passage times and discuss their dependence on dimensionality.Supported in part by the National Science Foundation under Grant CHE 75-20624.     

Melting transition of a network model in two dimensions

The freezing transition of a network model for tensionless membranes confined to two dimensions is investigated by Monte Carlo simulations and scaling arguments. In this model, a freezing transition is induced by reducing the tether length. Translational and bond-orientational order parameters and elastic constants are determined as a function of the tether length. A finite-size scaling analysis is used to show that the crystal melts via successive dislocation and disclination unbinding transitions, in qualitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. The hexatic phase is found to be stable over only a very small interval of tether lengths. Received 4 June 1999 and Revised in final form 1 September 1999     

The spin glass correlation length and the crossover from three to two dimensions

The identification of a time and temperature dependent spin glass correlation length, ξ(t,T), has consequences for samples of finite size. Previous experiments on layered samples show a suppression of the freezing temperature with decreasing sample thickness. The correlation length exceeding the finite sample thickness can explain these results. This novel analysis lends further credence to the correlation length paradigm of understanding spin glasses.