A Simple Theory of Condensation

A simple assumption of an emergence in gas of small atomic clusters consisting of $c$ particles each, leads to a phase separation (first order transition). It reveals itself by an emergence of ``forbidden'' density range starting at a certain temperature. Defining this latter value as the critical temperature predicts existence of an interval with anomalous heat capacity behaviour $c_p\propto\Delta T^{-1/c}$. The value $c=13$ suggested in literature yields the heat capacity exponent $\alpha=0.077$.Comment: 9 pages, 1 figur

On the Potential of the Excluded Volume and Auto-Correlation as Neuromorphometric Descriptors

This work investigates at what degree two neuromorphometric measurements, namely the autocorrelation and the excluded volume of a neuronal cell can influence the characterization and classification of such a type of cells. While the autocorrelation function presents good potential for quantifying the dendrite-dendrite connectivity of cells in mosaic tilings, the excluded volume, i.e. the amount of the surround space which is geometrically not accessible to an axon or dendrite, provides a complementary characterization of the cell connectivity. The potential of such approaches is illustrated with respect to real neuronal cells.Comment: 15 pages, 6 figure

Cyclotron effective mass of 2D electron layer at GaAs/AlGaAs heterojunction subject to in-plane magnetic fields

We have found that Fermi contours of a two-dimensional electron gas at \rmGaAs/Al_xGa_{1-x}As interface deviate from a standard circular shape under the combined influence of an approximately triangular confining potential and the strong in-plane magnetic field. The distortion of a Fermi contour manifests itself through an increase of the electron effective cyclotron mass which has been measured by the cyclotron resonance in the far-infrared transmission spectra and by the thermal damping of Shubnikov-de Haas oscillations in tilted magnetic fields with an in-plane component up to 5 T. The observed increase of the cyclotron effective mass reaches almost 5 \% of its zero field value which is in good agreement with results of a self-consistent calculation.Comment: 4 pages, Revtex, figures can be obtained on request from [email protected]; to appear in Phys. Rev. B (in press). No changes, the corrupted submission replace

Spin and Charge Luttinger-Liquid Parameters of the One-Dimensional Electron Gas

Low-energy properties of the homogeneous electron gas in one dimension are completely described by the group velocities of its charge (plasmon) and spin collective excitations. Because of the long range of the electron-electron interaction, the plasmon velocity is dominated by an electrostatic contribution and can be estimated accurately. In this Letter we report on Quantum Monte Carlo simulations which demonstrate that the spin velocity is substantially decreased by interactions in semiconductor quantum wire realizations of the one-dimensional electron liquid.Comment: 13 pages, figures include

Semi-classical spectrum of integrable systems in a magnetic field

The quantum dynamics of an electron in a uniform magnetic field is studied for geometries corresponding to integrable cases. We obtain the uniform asymptotic approximation of the WKB energies and wavefunctions for the semi-infinite plane and the disc. These analytical solutions are shown to be in excellent agreement with the numerical results obtained from the Schrodinger equations even for the lowest energy states. The classically exact notions of bulk and edge states are followed to their semi-classical limit, when the uniform approximation provides the connection between bulk and edge.Comment: 17 pages, Revtex, 6 figure

On fermionic tilde conjugation rules and thermal bosonization. Hot and cold thermofields

A generalization of Ojima tilde conjugation rules is suggested, which reveals the coherent state properties of thermal vacuum state and is useful for the thermofield bosonization. The notion of hot and cold thermofields is introduced to distinguish different thermofield representations giving the correct normal form of thermofield solution for finite temperature Thirring model with correct renormalization and anticommutation properties.Comment: 13 page

Quasiparticle Effective Mass for the Two- and Three-Dimensional Electron Gas

We calculate the quasiparticle effective mass for the electron gas in two and three dimensions in the metallic region. We employ the single particle scattering potential coming from the Sj\"{o}lander-Stott theory and enforce the Friedel sum rule by adjusting the effective electron mass in a scattering calculation. In 3D our effective mass is a monotonically decreasing function of $r_s$ throughout the whole metallic domain, as implied by the most recent numerical results. In 2D we obtain reasonable agreement with the experimental data, as well as with other calculations based on the Fermi liquid theory. We also present results of a variety of different treatments for the effective mass in 2D and 3D.Comment: 12 pages, 2 figure

Fractional Systems and Fractional Bogoliubov Hierarchy Equations

We consider the fractional generalizations of the phase volume, volume element and Poisson brackets. These generalizations lead us to the fractional analog of the phase space. We consider systems on this fractional phase space and fractional analogs of the Hamilton equations. The fractional generalization of the average value is suggested. The fractional analogs of the Bogoliubov hierarchy equations are derived from the fractional Liouville equation. We define the fractional reduced distribution functions. The fractional analog of the Vlasov equation and the Debye radius are considered.Comment: 12 page

Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

Correlation energy and spin polarization in the 2D electron gas

The ground state energy of the two--dimensional uniform electron gas has been calculated with fixed--node diffusion Monte Carlo, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits the density and polarization dependence of the simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first--order polarization transition occurs shortly before Wigner crystallization as the density is lowered.Comment: Minor typos corrected, see erratum: Phys. Rev. Lett. 91, 109902(E) (2003