315 research outputs found
Mapping between Hamiltonians with attractive and repulsive potentials on a lattice
Through a simple and exact analytical derivation, we show that for a particle
on a lattice, there is a one-to-one correspondence between the spectra in the
presence of an attractive potential and its repulsive counterpart
. For a Hermitian potential, this result implies that the number of
localized states is the same in both, attractive and repulsive, cases although
these states occur above (below) the band-continnum for the repulsive
(attractive) case. For a \mP\mT-symmetric potential that is odd under parity,
our result implies that in the \mP\mT-unbroken phase, the energy eigenvalues
are symmetric around zero, and that the corresponding eigenfunctions are
closely related to each other.Comment: 6 pages, 1 figur
Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems
At small layer separations, the ground state of a nu=1 bilayer quantum Hall
system exhibits spontaneous interlayer phase coherence and has a
charged-excitation gap E_g. The evolution of this state with increasing layer
separation d has been a matter of controversy. In this letter we report on
small system exact diagonalization calculations which suggest that a single
phase transition, likely of first order, separates coherent incompressible (E_g
>0) states with strong interlayer correlations from incoherent compressible
states with weak interlayer correlations. We find a dependence of the phase
boundary on d and interlayer tunneling amplitude that is in very good agreement
with recent experiments.Comment: 4 pages, 4 figures included, version to appear in Phys. Rev. Let
Superfluidity of electron-hole pairs in randomly inhomogeneous bilayer systems
In bilayer systems electron-hole (e-h) pairs with spatially separated
components (i.e., with electrons in one layer and holes in the other) can be
condensed to a superfluid state when the temperature is lowered. This article
deals with the influence of randomly distributed inhomogeneities on the
superfluid properties of such bilayer systems in a strong perpendicular
magnetic field. Ionized impurities and roughenings of the conducting layers are
shown to decrease the superfluid current density of the e-h pairs. When the
interlayer distance is smaller than or close to the magnetic length, the
fluctuations of the interlayer distance considerably reduce the superfluid
transition temperature.Comment: 13 pages, 3 figure
Is there a d.c. Josephson Effect in Bilayer Quantum Hall Systems?
We argue on the basis of phenomenological and microscopic considerations that
there is no d.c. Josephson effect in ordered bilayer quantum Hall systems, even
at T=0. Instead the tunnel conductance is strongly enhanced, approaching a
finite value proportional to the square of the order parameter as the
interlayer tunneling amplitude vanishes.Comment: 5 pages, 2 figure
The elusive memristor: properties of basic electrical circuits
We present a tutorial on the properties of the new ideal circuit element, a
memristor. By definition, a memristor M relates the charge q and the magnetic
flux in a circuit, and complements a resistor R, a capacitor C, and an
inductor L as an ingredient of ideal electrical circuits. The properties of
these three elements and their circuits are a part of the standard curricula.
The existence of the memristor as the fourth ideal circuit element was
predicted in 1971 based on symmetry arguments, but was clearly experimentally
demonstrated just this year. We present the properties of a single memristor,
memristors in series and parallel, as well as ideal memristor-capacitor (MC),
memristor-inductor (ML), and memristor-capacitor-inductor (MCL) circuits. We
find that the memristor has hysteretic current-voltage characteristics. We show
that the ideal MC (ML) circuit undergoes non-exponential charge (current) decay
with two time-scales, and that by switching the polarity of the capacitor, an
ideal MCL circuit can be tuned from overdamped to underdamped. We present
simple models which show that these unusual properties are closely related to
the memristor's internal dynamics. This tutorial complements the pedagogy of
ideal circuit elements (R,C, and L) and the properties of their circuits.Comment: 22 pages, 12 figures, substantial text revisio
Dynamical Properties in the Bilayer Quantum Hall Ferromagnet
The spectral functions of the pseudospin correlation functions in the bilayer
quantum Hall system at \nu=1 are investigated numerically, where the pseudospin
describes the layer degrees of freedom. In the pseudospin-ferromagnetic phase,
the lowest-energy excitation branch is closely connected with the ground state
through the fluctuations of pseudospin S_y and S_z, and it plays a significant
role on the tunneling properties in this system. For the system with very small
tunneling amplitude and layer separation smaller than the critical one, the
system-size dependence of calculated spectral function A_{y z} suggests the
superfluidity on the tunneling current in the absence of impurities.Comment: 4 pages, 1 Postscript figur
Quantum catastrophes: a case study
The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty
domain D of physical values of parameters. This means that for these
parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it
ad hoc} choice of the inner product in the physical Hilbert space of quantum
bound states (i.e., via an {\it ad hoc} construction of the so called metric).
The name of quantum catastrophe is then assigned to the
N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave
domain D along such a path that at the boundary of D, an N-plet of bound state
energies degenerates and, subsequently, complexifies. At any fixed ,
this process is simulated via an N by N benchmark effective matrix Hamiltonian
H. Finally, it is being assigned such a closed-form metric which is made unique
via an N-extrapolation-friendliness requirement.Comment: 23 p
Recent advances on information transmission and storage assisted by noise
The interplay between nonlinear dynamic systems and noise has proved to be of
great relevance in several application areas. In this presentation, we focus on
the areas of information transmission and storage. We review some recent
results on information transmission through nonlinear channels assisted by
noise. We also present recent proposals of memory devices in which noise plays
an essential role. Finally, we discuss new results on the influence of noise in
memristors.Comment: To be published in "Theory and Applications of Nonlinear Dynamics:
Model and Design of Complex Systems", Proceedings of ICAND 2012 (Springer,
2014
- …