20,968 research outputs found
Spherically confined isotropic harmonic oscillator
The generalized pseudospectral Legendre method is used to carry out accurate
calculations of eigenvalues of the spherically confined isotropic harmonic
oscillator with impenetrable boundaries. The energy of the confined state is
found to be equal to that of the unconfined state when the radius of
confinement is suitably chosen as the location of the radial nodes in the
unconfined state. This incidental degeneracy condition is numerically shown to
be valid in general. Further, the full set of pairs of confined states defined
by the quantum numbers [(n+1, \ell) ; (n, \ell+2)], n = 1,2,.., and with the
radius of confinement {(2 \ell +3)/2}^{1/2} a.u., which represents the single
node in the unconfined (1, \ell) state, is found to display a constant energy
level separation exactly given by twice the oscillator frequency. The results
of similar numerical studies on the confined Davidson oscillator with
impenetrable boundary as well as the confined isotropic harmonic oscillator
with finite potential barrier are also reported .The significance of the
numerical results are discussed.Comment: 28 pages, 4 figure
Phase transitions in Ising model on a Euclidean network
A one dimensional network on which there are long range bonds at lattice
distances with the probability has been taken
under consideration. We investigate the critical behavior of the Ising model on
such a network where spins interact with these extra neighbours apart from
their nearest neighbours for . It is observed that there is
a finite temperature phase transition in the entire range. For , finite size scaling behaviour of various quantities are consistent with
mean field exponents while for , the exponents depend on
. The results are discussed in the context of earlier observations on
the topology of the underlying network.Comment: 7 pages, revtex4, 7 figures; to appear in Physical Review E, minor
changes mad
Magnetotransport of Dirac Fermions on the surface of a topological insulator
We study the properties of Dirac fermions on the surface of a topological
insulator in the presence of crossed electric and magnetic fields. We provide
an exact solution to this problem and demonstrate that, in contrast to their
counterparts in graphene, these Dirac fermions allow relative tuning of the
orbital and Zeeman effects of an applied magnetic field by a crossed electric
field along the surface. We also elaborate and extend our earlier results on
normal metal-magnetic film-normal metal (NMN) and normal metal-barrier-magnetic
film (NBM) junctions of topological insulators [Phys. Rev. Lett. {\bf 104},
046403 (2010)]. For NMN junctions, we show that for Dirac fermions with Fermi
velocity , the transport can be controlled using the exchange field
of a ferromagnetic film over a region of width . The
conductance of such a junction changes from oscillatory to a monotonically
decreasing function of beyond a critical which leads to the
possible realization of magnetic switches using these junctions. For NBM
junctions with a potential barrier of width and potential , we find
that beyond a critical , the criteria of conductance maxima
changes from to for
integer . Finally, we compute the subgap tunneling conductance of a normal
metal-magnetic film-superconductor (NMS) junctions on the surface of a
topological insulator and show that the position of the peaks of the zero-bias
tunneling conductance can be tuned using the magnetization of the ferromagnetic
film. We point out that these phenomena have no analogs in either conventional
two-dimensional materials or Dirac electrons in graphene and suggest
experiments to test our theory.Comment: 11 pages, 12 figures; v
Tuning the conductance of Dirac fermions on the surface of a topological insulator
We study the transport properties of the Dirac fermions with Fermi velocity
on the surface of a topological insulator across a ferromagnetic strip
providing an exchange field over a region of width . We show
that the conductance of such a junction changes from oscillatory to a
monotonically decreasing function of beyond a critical . This
leads to the possible realization of a magnetic switch using these junctions.
We also study the conductance of these Dirac fermions across a potential
barrier of width and potential in the presence of such a
ferromagnetic strip and show that beyond a critical , the
criteria of conductance maxima changes from
to for integer . We point out that these novel phenomena
have no analogs in graphene and suggest experiments which can probe them.Comment: v1 4 pages 5 fig
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