Condensate oscillations in a Penrose tiling lattice

We study the dynamics of a Bose-Einstein condensate subject to a particular Penrose tiling lattice. In such a lattice, the potential energy at each site depends on the neighbour sites, accordingly to the model introduced by Sutherland [16]. The Bose-Einstein wavepacket, initially at rest at the lattice symmetry center, is released. We observe a very complex time-evolution that strongly depends on the symmetry center (two choices are possible), on the potential energy landscape dispersion, and on the interaction strength. The condensate-width oscillates at different frequencies and we can identify large-frequency reshaping oscillations and low-frequency rescaling oscillations. We discuss in which conditions these oscillations are spatially bounded, denoting a self-trapping dynamics.     

Electronic spectrum of the three-dimensional Penrose lattice

The electronic spectrum of the three-dimensional Penrose lattice with “central” decoration by atoms is investigated using the tight binding model with nearest-neighbor interaction. Inverse participation ratios, higher moments of density probabilities, and fractal dimensions of the system are determined. The WFs are critical (they have a power-law dependence on the distance) at all energies in the band and are multifractal measures leading to the entire spectrum of the exponents. The results show that the system is in the critical state of the metal-insulator transition. On critical WFs, the cubic root temperature dependence of the conductivity is obtained.     

Ising spin orders and magnetic interactions analyzed in phason space in a 2-dimensional Penrose lattice

Simulated annealing calculations were performed on a Penrose lattice with the aim of clarifying the relation between the interaction connections and the magnetic orders in the phason space. Alternating signs were assumed in the magnetic interactions up to the second shortest distances between spins. Two different types of long-range antiferromagnetic orders were found for two cases with reversed sign of the interactions. The two types of order were most adequately interpreted as the orders of subdivisions in the occupation domain in the phason space. Reasonable interpretations of the mechanism of the subdivisions are given on the basis of the physical interactions projected to the phason space.     

Penrose tiling fractality in coordination Cayley’s tree graphs representation

We offer the mathematical apparatus for mapping lattice and cellular systems into the generalized coordination Cayley’s tree graphs. These Cayley’s trees have a random branchiness property and an intralayer interbush local intersection. Classical Bethe-Cayley tree graphs don’t have these properties. Bush type simplicial decomposition on Cayley’s tree graphs is introduced, on which the enumerating polynomials or enumerating distributions are built. Within the entropy methodology three types of fractal characteristics are introduced, which characterize quasi-crystalline pentagonal Penrose tiling. The quantitative estimate for the frontal-radial fractal percolation on a Cayley’s tree graph of a Penrose tiling leading to the overdimensioned effect is calculated.     

The magnetic properties of the two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field

The two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field is studied by means of the double-time Green's function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed.     

Electronic and optical properties of a nanoring in the presence of external magnetic field

Optical properties of a nanoring with Winternitz–Smorodinsky confinement potential in the presence of an external magnetic field have been studied theoretically. Our results demonstrate that energy, oscillator strength and the linear, nonlinear and total absorption are strongly affected by size of the nanoring. Also, we found that magnetic field has little influence on energy difference, oscillator strength and optical absorption of the nanoring.     

Electronic correlation effects on the properties of an half-filled octahedron cluster in a magnetic field

The present study focuses on electronic correlation effects on magnetic energy, the spin-spin correlation function of an octahedron cluster in the (3↑, 3 ↓) electronic configuration threaded by a magnetic field. Some other spin configurations are also discussed and various field directions are considered. An accurate diagonalisation technique has been used to solve the Hubbard Hamiltonian. A result is analysed on a linear energy stabilisation at low magnetic flux. Moreover, two types of antiferromagnetic transition versus the flux occurring for a correlation term larger than a critical one have been observed, i.e. the likelihood of a charge excitation before the antiferromagnetic transition. Finally, a comparison between the results obtained from the exact diagonalisation and the Gutzwiller method has been carried out, leading to a suggested modification of the Gutzwiller approach in order to improve it. Received 23 June 1999 and Received in final form 28 July 2000     

Unconventional superfluidity of superconductivity on Penrose lattice

Using the attractive Hubbard model as an example, we theoretically investigate the gap function, superfluid density, and superconductivity(SC) transition temperature on the semiperiodic Penrose lattice. First, we clarify that the gap function, density of states, and superfluid density positively correlate to the extended degree of single-particle states around the Fermi energy. Second,we confirm that the paramagnetic component of the superfluid density does not decay to zero in the thermodynamic...     

Two-particle correlations on a 1D lattice in a constant magnetic field

The problem of two particles interacting through the Hubbard potential on a 1D finite lattice in a constant uniform magnetic field is solved. Exact wave functions are determined, and an equation for the energy spectrum is constructed and analyzed. The possibility of a field-induced singlet-triplet transition is demonstrated.     

Tight binding electrons on a disordered square lattice in a magnetic field

A semiclassical WKB treatment of the density of states spectrum of tight-binding electrons moving in a disordered two dimensional lattice in the presence of a transverse magnetic field is presented. The disorder is accounted for in the coherent potential approximation and analytical results are derived. For both ordered and disordered systems the line position of magnetic subbands as well as the cluster lineshape of the density of states agree quite well with exact numerical results.     

Electronic conductance of a multi-channel point contact in a magnetic field

We present the numerical results of the electronic conductanceG of a quantum wire with a multichannel point contact structure in a perpendicular external magnetic fieldH at zero temperature, based on the rigorous quantum mechanics of a two-dimensional noninteracting electron gas. Computational results show the approximate quantization of the electronic conductance. WheH is weak,Ginteger multiples of 2e ²/h; and whenH is trong, Ginteger multiples of 2ne ²/h, wheren is the number of channels in the point contact structure of the quantum wire. Quantum leaps take place whenH±2m ^* E _F /[e(2j+1)], wherej is either zero or a positive integer small enough for the external magnetic fieldH to be strong, andm ^* is the effective mass of an electron in the device. To our knowledge, no report on this quantization of electronic conductance has been published. Oscillations are manifest in theGH curves for comparatively narrow channels because of the quantum size effect.     

Electronic structure of disclinated graphene in a uniform magnetic field

The electronic structure in the vicinity of the 1-heptagonal and 1-pentagonal defects in the carbon graphene plane is investigated for the case of hyperboloidal geometry. Using a continuum gauge field-theory model, the local density of states around the Fermi energy is calculated for both cases. In this model, the disclination is represented by a SO(2) gauge vortex and the corresponding metrics follows from the elasticity properties of the graphene membrane. To enhance the interval of energies, a self-consistent perturbation scheme is used. The Landau states are investigated and compared with the predicted values. A discussion on the influence of the Zeeman effect is included.