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Spectral properties of periodic one-dimensional array of nanorings in a magnetic field are investigated. Two types of the superlattice are considered. In the first one, rings are connected by short one-dimensional wires while in the second…
We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line…
Born-Infeld non-linear electrodynamics arises naturally as a field theory description of the dynamics of strings and branes. Most analyses of this theory have been limited to studying it as a classical field theory. We quantize this theory…
The 2-- to 1--dimensional crossover of the localisation length of electrons confined to a disordered quantum wire of finite width $L_y$ is studied in a model of electrons moving in the potential of uncorrelated impurities. An analytical…
We present a versatile design of freely suspended quantum point contacts with particular large one-dimensional subband quantization energies of up to 10meV. The nanoscale bridges embedding a two-dimensional electron system are fabricated…
The distribution of voltage in sub-micron cellular domains remains poorly understood. In neurons, the voltage results from the difference in ionic concentrations which are continuously maintained by pumps and exchangers. However, it not…
In this report we summarize a recent progress in exploration of correlated two-dimensional electron states in partially filled high Landau levels. At a mean-field Hartree-Fock level they can be described as charge-density waves, either…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
A low order diagrammatic study of the dimension dependent Su-Schrieffer-Heeger model Hamiltonian in the weak electron-phonon coupling regime is presented. Exact computation of both the charge carrier effective mass and the electron spectral…
According to the introduction of a minimal length to quantum field theory which is directly related to a generalized uncertainty principle the implementation of the gauge principle becomes much more intricated. It has been shown in another…
We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum…
The ground state and the excitation spectrum of strongly correlated electrons in quantum dots are investigated. An analytical solution is constructed by exact diagonalization of the Hamiltonian in terms of the $N$-particle eigenmodes.
For the one-dimensional, extended Peierls--Hubbard model we calculate analytically the ground-state energy and the single-particle gap to second order in the Coulomb interaction for a given lattice dimerization. The comparison with…
We investigate a one--dimensional wire of interacting electrons connected to one--dimensional noninteracting leads in the absence and in the presence of a backscattering potential. The ballistic wire separates the charge and spin parts of…
We present a detailed analysis of the nature of electronic eigenfunctions in one-dimensional quasi-periodic chains based on a clustering idea recently introduced by us [Sil et al., Phys. Rev. {\bf B 48}, 4192 (1993) ], within the framework…
We study the effect of electron-electron interaction on a two dimensional (2D) disordered lattice. For the case of two electrons the analytical estimates are presented showing a transition from localized to delocalized states in a way…
In this work, we discuss the resonance states of a quantum particle in a periodic potential plus a static force. Originally this problem was formulated for a crystal electron subject to a static electric field and it is nowadays known as…
We formulate a non-relativistic quantum field theory to model interactions between quantized electromagnetic fields and localized charge-current distributions. The electronic degrees of freedom are encoded in microscopic polarization and…
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law…
The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and…