29 research outputs found
Solution of the wave equation in a tridiagonal representation space
We use variable transformation from the real line to finite or semi-infinite
spaces where we expand the regular solution of the 1D time-independent
Schrodinger equation in terms of square integrable bases. We also require that
the basis support an infinite tridiagonal matrix representation of the wave
operator. By this requirement, we deduce a class of solvable potentials along
with their corresponding bound states and stationary wavefunctions expressed as
infinite series in terms of these bases. This approach allows for simultaneous
treatment of the discrete (bound states) as well as the continuous (scattering
states) spectrum on the same footing. The problem translates into finding
solutions of the resulting three-term recursion relation for the expansion
coefficients of the wavefunction. These are written in terms of orthogonal
polynomials, some of which are modified versions of known polynomials. The
examples given, which are not exhaustive, illustrate the power of this approach
in dealing with 1D quantum problems.Comment: 13 page
The Dirac-Coulomb Problem: a mathematical revisit
We obtain a symmetric tridiagonal matrix representation of the Dirac-Coulomb
operator in a suitable complete square integrable basis. Orthogonal polynomials
techniques along with Darboux method are used to obtain the bound states energy
spectrum, the relativistic scattering amplitudes and phase shifts from the
asymptotic behavior of the polynomial solutions associated with the resulting
three-term recursion relation.Comment: 8 page
Dynamical mass generation via space compactification in graphene
Fermions in a graphene sheet behave like massless particles. We show that by
folding the sheet into a tube they acquire non-zero effective mass as they move
along the tube axis. That is, changing the space topology of graphene from 2D
to 1D (space compactification) changes the 2D massless problem into an
effective massive 1D problem. The size of the resulting mass spectrum depends
on the quantized azimuthal frequency and its line spacing is proportional to
the inverse of the tube diameter.Comment: 8 pages, 2 figure
Supersymmetric Jaynes-Cummings model and its exact solutions
The super-algebraic structure of a generalized version of the Jaynes-Cummings
model is investigated. We find that a Z2 graded extension of the so(2,1) Lie
algebra is the underlying symmetry of this model. It is isomorphic to the
four-dimensional super-algebra u(1/1) with two odd and two even elements.
Differential matrix operators are taken as realization of the elements of the
superalgebra to which the model Hamiltonian belongs. Several examples with
various choices of superpotentials are presented. The energy spectrum and
corresponding wavefunctions are obtained analytically.Comment: 12 pages, no figure
Microscale CFD Simulations of a Wind Energy Test Site in the Swabian Alps with Mesoscale Based Inflow Data
The current study describes analyses of the WINSENT wind energy test site located in complex terrain in Southern Germany by highly resolved numerical simulations. The resolved atmospheric turbulence is simulated with Delayed Detached Eddy Simulations by the flow solver FLOWer without consideration of the research wind turbines.
The mean inflow and wind direction of the analysed time period is provided by precursor simulations of project partners. The simulation model chain consists of three codes with different time scales and resolutions. The model chain provides a data transfer from mesoscale WRF simulations to OpenFOAM. As a next step OpenFOAM provides inflow data in the valley of the terrain site for the present FLOWer simulations, the code with the highest resolution in space and time. The mean velocity field provided by OpenFOAM is superimposed with fluctuations that are based on measurements to obtain the small turbulent scales within the FLOWer simulations, which the previous tools of the model chain can not resolve. Comparisons with the two already installed met masts clarify that the current FLOWer simulations provide an adequate agreement with measured data. The results are verified with the application of a second simulation, in which a homogeneous velocity profile is superimposed with turbulence. Thus, comparisons with measured data showed that the benefit of using the inflow data of this model chain is especially evident near the ground
Transport Properties through Double Barrier Structure in Graphene
The mode-dependent transmission of relativistic ballistic massless Dirac
fermion through a graphene based double barrier structure is being investigated
for various barrier parameters. We compare our results with already published
work and point out the relevance of these findings to a systematic study of the
transport properties in double barrier structures. An interesting situation
arises when we set the potential in the leads to zero, then our 2D problem
reduces effectively to a 1D massive Dirac equation with an effective mass
proportional to the quantized wave number along the transverse direction.
Furthermore we have shown that the minimal conductivity and maximal Fano factor
remain insensitive to the ratio between the two potentials V_2/V_1=\alpha.Comment: 18 pages, 12 figures, clarifications and reference added, misprints
corrected. Version to appear in JLT
Nonmonotonous Magnetic Field Dependence and Scaling of the Thermal Conductivity for Superconductors with Nodes of the Order Parameter
We show that there is a new mechanism for nonmonotonous behavior of magnetic
field dependence of the electronic thermal conductivity of clean
superconductors with nodes of the order parameter on the Fermi surface. In
particular, for unitary scatterers the nonmonotony of relaxation time takes
place. Contribution from the intervortex space turns out to be essential for
this effect even at low temperatures. Our results are in a qualitative
agreement with recent experimental data for superconducting UPt_3. For
E_{2u}-type of pairing we find approximately the scaling of the thermal
conductivity in clean limit with a single parameter x=T/T_c\sqrt{B_{c2}/B} at
low fields and low temperatures, as well as weak low-temperature dependence of
the anisotropy ratio K_{zz}/K_{yy} in zero field. For E_{1g}-type of pairing
deviations from the scaling are more noticeable and the anisotropy ratio is
essentially temperature dependent.Comment: 37 pages, 8 Postscript figures, REVTE