242 research outputs found
Multiple bound states in scissor-shaped waveguides
We study bound states of the two-dimensional Helmholtz equations with
Dirichlet boundary conditions in an open geometry given by two straight leads
of the same width which cross at an angle . Such a four-terminal
junction with a tunable can realized experimentally if a right-angle
structure is filled by a ferrite. It is known that for there is
one proper bound state and one eigenvalue embedded in the continuum. We show
that the number of eigenvalues becomes larger with increasing asymmetry and the
bound-state energies are increasing as functions of in the interval
. Moreover, states which are sufficiently strongly bent exist in
pairs with a small energy difference and opposite parities. Finally, we discuss
how with increasing the bound states transform into the quasi-bound
states with a complex wave vector.Comment: 6 pages, 6 figure
Spin rotation for ballistic electron transmission induced by spin-orbit interaction
We study spin dependent electron transmission through one- and
two-dimensional curved waveguides and quantum dots with account of spin-orbit
interaction. We prove that for a transmission through arbitrary structure there
is no spin polarization provided that electron transmits in isolated energy
subband and only two leads are attached to the structure. In particular there
is no spin polarization in the one-dimensional wire for which spin dependent
solution is found analytically. The solution demonstrates spin evolution as
dependent on a length of wire. Numerical solution for transmission of electrons
through the two-dimensional curved waveguides coincides with the solution for
the one-dimensional wire if the energy of electron is within the first energy
subband. In the vicinity of edges of the energy subbands there are sharp
anomalies of spin flipping.Comment: 9 oages, 7 figure
Hall-like effect induced by spin-orbit interaction
The effect of spin-orbit interaction on electron transport properties of a
cross-junction structure is studied. It is shown that it results in spin
polarization of left and right outgoing electron waves. Consequently, incoming
electron wave of a proper polarization induces voltage drop perpendicularly to
the direct current flow between source and drain of the considered
four-terminal cross-structure. The resulting Hall-like resistance is estimated
to be of the order of 10^-3 - 10^-2 h/e^2 for technologically available
structures. The effect becomes more pronounced in the vicinity of resonances
where Hall-like resistance changes its sign as function of the Fermi energy.Comment: 4 pages (RevTeX), 4 figures, will appear in Phys. Rev. Let
Two-component model of a spin-polarized transport
Effect of the spin-involved interaction of electrons with impurity atoms or
defects to the transport properties of a two-dimensional electron gas is
described by using a simplifying two-component model. Components representing
spin-up and spin-down states are supposed to be coupled at a discrete set of
points within a conduction channel. The used limit of the short-range
interaction allows to solve the relevant scattering problem exactly. By varying
the model parameters different transport regimes of two-terminal devices with
ferromagnetic contacts can be described. In a quasi-ballistic regime the
resulting difference between conductances for the parallel and antiparallel
orientation of the contact magnetization changes its sign as a function of the
length of the conduction channel if appropriate model parameters are chosen.
The effect is in agreement with recent experimental observations.Comment: 4 RevTeX pages with 4 figure
The brachistochrone problem in open quantum systems
Recently, the quantum brachistochrone problem is discussed in the literature
by using non-Hermitian Hamilton operators of different type. Here, it is
demonstrated that the passage time is tunable in realistic open quantum systems
due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton
operator. As an example, the numerical results obtained by Bulgakov et al. for
the transmission through microwave cavities of different shape are analyzed
from the point of view of the brachistochrone problem. The passage time is
shortened in the crossover from the weak-coupling to the strong-coupling regime
where the resonance states overlap and many branch points (exceptional points)
in the complex plane exist. The effect can {\it not} be described in the
framework of standard quantum mechanics with Hermitian Hamilton operator and
consideration of matrix poles.Comment: 18 page
Bound states in the continuum in open Aharonov-Bohm rings
Using formalism of effective Hamiltonian we consider bound states in
continuum (BIC). They are those eigen states of non-hermitian effective
Hamiltonian which have real eigen values. It is shown that BICs are orthogonal
to open channels of the leads, i.e. disconnected from the continuum. As a
result BICs can be superposed to transport solution with arbitrary coefficient
and exist in propagation band. The one-dimensional Aharonov-Bohm rings that are
opened by attaching single-channel leads to them allow exact consideration of
BICs. BICs occur at discrete values of energy and magnetic flux however it's
realization strongly depend on a way to the BIC's point.Comment: 5 pgaes, 4 figure
Observation of Caustics in the Trajectories of Cold Atoms in a Linear Magnetic Potential
We have studied the spatial and temporal dynamics of a cold atom cloud in the
conservative force field of a ferromagnetic guide, after laser cooling has been
switched off suddenly. We observe outgoing 'waves' that correspond to caustics
of individual trajectories of trapped atoms. This provides detailed information
on the magnetic field, the energy distribution and the spin states.Comment: 21 pages, incl. 12 figure
Projective Hilbert space structures at exceptional points
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study
projective Hilbert space structures in the vicinity of exceptional points
(EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are
Puiseux-expanded in terms of the root vectors at the EP. It is shown that the
apparent contradiction between the two incompatible normalization conditions
with finite and singular behavior in the EP-limit can be resolved by
projectively extending the original Hilbert space. The complementary
normalization conditions correspond then to two different affine charts of this
enlarged projective Hilbert space. Geometric phase and phase jump behavior are
analyzed and the usefulness of the phase rigidity as measure for the distance
to EP configurations is demonstrated. Finally, EP-related aspects of
PT-symmetrically extended Quantum Mechanics are discussed and a conjecture
concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte
Two-electron bound states in continuum in quantum dots
Bound state in continuum (BIC) might appear in open quantum dots for
variation of the dot's shape. By means of the equations of motion of Green
functions we investigate effect of strong intradot Coulomb interactions on that
phenomenon in the framework of impurity Anderson model. Equation that imaginary
part of poles of the Green function equals to zero gives condition for BICs. As
a result we show that Coulomb interactions replicate the single-electron BICs
into two-electron ones.Comment: To be published in JETP Letter
Weak localization in ferromagnets with spin-orbit interaction
Weak localization corrections to conductivity of ferromagnetic systems are
studied theoretically in the case when spin-orbit interaction plays a
significant role. Two cases are analyzed in detail: (i) the case when the
spin-orbit interaction is due to scattering from impurities, and (ii) the case
when the spin-orbit interaction results from reduced dimensionality of the
system and is of the Bychkov-Rashba type. Results of the analysis show that the
localization corrections to conductivity of ferromagnetic metals lead to a
negative magnetoresistance -- also in the presence of the spin-orbit
scattering. Positive magnetoresistance due to weak antilocalization, typical of
nonmagnetic systems, does not occur in ferromagnetic systems. In the case of
two-dimensional ferromagnets, the quantum corrections depend on the
magnetization orientation with respect to the plane of the system.Comment: 14 pages with 10 figures, corrected and extended version, Sec.7 adde
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