15,654 research outputs found
Phonon emission and arrival times of electrons from a single-electron source
In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy
Entanglement Entropy of Two Spheres
We study the entanglement entropy S_{AB} of a massless free scalar field on
two spheres A and B whose radii are R_1 and R_2, respectively, and the distance
between the centers of them is r. The state of the massless free scalar field
is the vacuum state. We obtain the result that the mutual information
S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and
proportional to the product of the areas of the two spheres when r>>R_1,R_2,
where S_A and S_B are the entanglement entropy on the inside region of A and B,
respectively. We discuss possible connections of this result with the physics
of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in
section V, a typo in eq.(25) corrected, published versio
Field-driven topological glass transition in a model flux line lattice
We show that the flux line lattice in a model layered HTSC becomes unstable
above a critical magnetic field with respect to a plastic deformation via
penetration of pairs of point-like disclination defects. The instability is
characterized by the competition between the elastic and the pinning energies
and is essentially assisted by softening of the lattice induced by a
dimensional crossover of the fluctuations as field increases. We confirm
through a computer simulation that this indeed may lead to a phase transition
from crystalline order at low fields to a topologically disordered phase at
higher fields. We propose that this mechanism provides a model of the low
temperature field--driven disordering transition observed in neutron
diffraction experiments on single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from
[email protected]
Electromagnetic and gravitational responses and anomalies in topological insulators and superconductors
One of the defining properties of the conventional three-dimensional
("-", or "spin-orbit"-) topological insulator is its
characteristic magnetoelectric effect, as described by axion electrodynamics.
In this paper, we discuss an analogue of such a magnetoelectric effect in the
thermal (or gravitational) and the magnetic dipole responses in all symmetry
classes which admit topologically non-trivial insulators or superconductors to
exist in three dimensions. In particular, for topological superconductors (or
superfluids) with time-reversal symmetry which lack SU(2) spin rotation
symmetry (e.g. due to spin-orbit interactions), such as the B phase of He,
the thermal response is the only probe which can detect the non-trivial
topological character through transport. We show that, for such topological
superconductors, applying a temperature gradient produces a thermal- (or mass-)
surface current perpendicular to the thermal gradient. Such charge, thermal, or
magnetic dipole responses provide a definition of topological insulators and
superconductors beyond the single-particle picture. Moreover we find, for a
significant part of the 'ten-fold' list of topological insulators found in
previous work in the absence of interactions, that in general dimensions the
effective field theory describing the space-time responses is governed by a
field theory anomaly. Since anomalies are known to be insensitive to whether
the underlying fermions are interacting or not, this shows that the
classification of these topological insulators is robust to adiabatic
deformations by interparticle interactions in general dimensionality. In
particular, this applies to symmetry classes DIII, CI, and AIII in three
spatial dimensions, and to symmetry classes D and C in two spatial dimensions.Comment: 16 pages, 2 figure
Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement
We develop a numerical approach for quantifying entanglement in mixed quantum
states by convex-roof entanglement measures, based on the optimal entanglement
witness operator and the minimax optimization method. Our approach is
applicable to general entanglement measures and states and is an efficient
alternative to the conventional approach based on the optimal pure-state
decomposition. Compared with the conventional one, it has two important merits:
(i) that the global optimality of the solution is quantitatively verifiable,
and (ii) that the optimization is considerably simplified by exploiting the
common symmetry of the target state and measure. To demonstrate the merits, we
quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of
three-qubit full-rank mixed states composed of the GHZ state, the W state, and
the white noise, the simplest mixtures of states with different genuine
multipartite entanglement, which have not been quantified before this work. We
discuss some general properties of the form of the optimal witness operator and
of the convex structure of mixed states, which are related to the symmetry and
the rank of states
Accuracy of Mesh Based Cosmological Hydrocodes: Tests and Corrections
We perform a variety of tests to determine the numerical resolution of the
cosmological TVD eulerian code developed by Ryu et al (1993). Tests include
512^3 and 256^3 simulations of a Pk=k^{-1} spectrum to check for
self-similarity and comparison of results with those from higher resolution SPH
and grid-based calculations (Frenk et al 1998). We conclude that in regions
where density gradients are not produced by shocks the code degrades resolution
with a Gaussian smoothing (radius) length of 1.7 cells. At shock caused
gradients (for which the code was designed) the smoothing length is 1.1 cells.
Finally, for \beta model fit clusters, we can approximately correct numerical
resolution by the transformation R^2_{core}\to R^2_{core}-(C\Delta l)^2, where
\Delta l is the cell size and C=1.1-1.7. When we use these corrections on our
previously published computations for the SCDM and \Lambda CDM models we find
luminosity weighted, zero redshift, X-ray cluster core radii of (210\pm 86,
280\pm 67)h^{-1}kpc, respectively, which are marginally consistent with
observed (Jones & Forman 1992) values of 50-200h^{-1}kpc. Using the corrected
core radii, the COBE normalized SCDM model predicts the number of bright
L_x>10^{43}erg/s clusters too high by a factor of \sim 20 and the \Lambda CDM
model is consistent with observations.Comment: ApJ in press (1999
Mutual information challenges entropy bounds
We consider some formulations of the entropy bounds at the semiclassical
level. The entropy S(V) localized in a region V is divergent in quantum field
theory (QFT). Instead of it we focus on the mutual information
I(V,W)=S(V)+S(W)-S(V\cup W) between two different non-intersecting sets V and
W. This is a low energy quantity, independent of the regularization scheme. In
addition, the mutual information is bounded above by twice the entropy
corresponding to the sets involved. Calculations of I(V,W) in QFT show that the
entropy in empty space cannot be renormalized to zero, and must be actually
very large. We find that this entropy due to the vacuum fluctuations violates
the FMW bound in Minkowski space. The mutual information also gives a precise,
cutoff independent meaning to the statement that the number of degrees of
freedom increases with the volume in QFT. If the holographic bound holds, this
points to the essential non locality of the physical cutoff. Violations of the
Bousso bound would require conformal theories and large distances. We speculate
that the presence of a small cosmological constant might prevent such a
violation.Comment: 10 pages, 2 figures, minor change
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