21,422 research outputs found
A characterization of positive linear maps and criteria of entanglement for quantum states
Let and be (finite or infinite dimensional) complex Hilbert spaces. A
characterization of positive completely bounded normal linear maps from
into is given, which particularly gives a
characterization of positive elementary operators including all positive linear
maps between matrix algebras. This characterization is then applied give a
representation of quantum channels (operations) between infinite-dimensional
systems. A necessary and sufficient criterion of separability is give which
shows that a state on is separable if and only if
for all positive finite rank elementary operators
. Examples of NCP and indecomposable positive linear maps are given and
are used to recognize some entangled states that cannot be recognized by the
PPT criterion and the realignment criterion.Comment: 20 page
The Dynamical Yang-Baxter Relation and the Minimal Representation of the Elliptic Quantum Group
In this paper, we give the general forms of the minimal matrix (the
elements of the -matrix are numbers) associated with the Boltzmann
weights of the interaction-round-a-face (IRF) model and the minimal
representation of the series elliptic quantum group given by Felder
and Varchenko. The explicit dependence of elements of -matrices on spectral
parameter are given. They are of five different forms (A(1-4) and B). The
algebra for the coefficients (which do not depend on ) are given. The
algebra of form A is proved to be trivial, while that of form B obey
Yang-Baxter equation (YBE). We also give the PBW base and the centers for the
algebra of form B.Comment: 23 page
Inhomogeneity driven by Higgs instability in gapless superconductor
The fluctuations of the Higgs and pseudo Nambu-Goldstone fields in the 2SC
phase with mismatched pairing are described in the nonlinear realization
framework of the gauged Nambu--Jona-Lasinio model. In the gapless 2SC phase,
not only Nambu-Goldstone currents can be spontaneously generated, but the Higgs
field also exhibits instablity. The Nambu-Goldstone currents generation
indicates the formation of the single plane wave LOFF state and breaks rotation
symmetry, while the Higgs instability favors spatial inhomogeneity and breaks
translation invariance. In this paper, we focus on the Higgs instability which
has not drawn much attention yet. The Higgs instability cannot be removed
without a long range force, thus it persists in the gapless superfluidity and
induces phase separation. In the case of g2SC state, the Higgs instability can
only be partially removed by the electric Coulomb energy. However, it is not
excluded that the Higgs instability might be completely removed in the charge
neutral gCFL phase by the color Coulomb energy.Comment: 21 pages, 5 figure
A new multiscale finite element method for high-contrast elliptic interface problems
We introduce a new multiscale finite element method which is
able to accurately capture solutions of elliptic interface problems with high
contrast coefficients by using only coarse quasiuniform meshes, and without
resolving the interfaces. A typical application would be the modelling of flow
in a porous medium containing a number of inclusions of low (or high) permeability
embedded in a matrix of high (respectively low) permeability. Our
method is H^1- conforming, with degrees of freedom at the nodes of a triangular
mesh and requiring the solution of subgrid problems for the basis functions on
elements which straddle the coefficient interface but which use standard linear
approximation otherwise. A key point is the introduction of novel coefficientdependent
boundary conditions for the subgrid problems. Under moderate
assumptions, we prove that our methods have (optimal) convergence rate of
O(h) in the energy norm and O(h^2) in the L_2 norm where h is the (coarse)
mesh diameter and the hidden constants in these estimates are independent
of the “contrast” (i.e. ratio of largest to smallest value) of the PDE coefficient.
For standard elements the best estimate in the energy norm would be
O(h^(1/2−ε)) with a hidden constant which in general depends on the contrast.
The new interior boundary conditions depend not only on the contrast of the
coefficients, but also on the angles of intersection of the interface with the
element edges
Dynamical Symmetry Breaking With a Fourth Generation
Adding a fourth generation to the Standard Model and assuming it to be valid
up to some cutoff \Lambda, we show that electroweak symmetry is broken by
radiative corrections due to the fourth generation. The effects of the fourth
generation are isolated using a Lagrangian with a genuine scalar without
self-interactions at the classical level. For masses of the fourth generation
consistent with electroweak precision data (including the B \rightarrow K \pi\
CP asymmetries) we obtain a Higgs mass of the order of a few hundreds GeV and a
cutoff \Lambda\ around 1-2 TeV. We study the reliability of the perturbative
treatment used to obtain these results taking into account the running of the
Yukawa couplings of the fourth quark generation with the aid of the
Renormalization Group (RG) equations, finding similar allowed values for the
Higgs mass but a slightly lower cut-off due to the breaking of the perturbative
regime. Such low cut-off means that the effects of new physics needed to
describe electroweak interactions at energy above \Lambda\ should be measurable
at the LHC. We use the minimal supersymmetric extension of the standard model
with four generations as an explicit example of models realizing the dynamical
electroweak symmetry breaking by radiative corrections and containing new
physics. Here, the cutoff is replaced by the masses of the squarks and
electroweak symmetry breaking by radiative corrections requires the squark
masses to be of the order of 1 TeV.Comment: 20 pages, 7 figures. New section adde
Kondo effect in coupled quantum dots with RKKY interaction: Finite temperature and magnetic field effects
We study transport through two quantum dots coupled by an RKKY interaction as
a function of temperature and magnetic field. By applying the Numerical
Renormalization Group (NRG) method we obtain the transmission and the linear
conductance. At zero temperature and magnetic field, we observe a quantum phase
transition between the Kondo screened state and a local spin singlet as the
RKKY interaction is tuned. Above the critical RKKY coupling the Kondo peak is
split. However, we find that both finite temperature and magnetic field restore
the Kondo resonance. Our results agree well with recent transport experiments
on gold grain quantum dots in the presence of magnetic impurities.Comment: 4 pages, 5 figure
Formation of Electronic Nematic Phase in Interacting Systems
We study the formation of an electronic nematic phase characterized by a
broken point-group symmetry in interacting fermion systems within the weak
coupling theory. As a function of interaction strength and chemical potential,
the phase transition between the isotropic Fermi liquid and nematic phase is
first order at zero temperature and becomes second order at a finite
temperature. The transition is present for all typical, including quasi-2D,
electronic dispersions on the square lattice and takes place for arbitrarily
small interaction when at van Hove filling, thus suppressing the Lifshitz
transition. In connection with the formation of the nematic phase, we discuss
the origin of the first order transition and competition with other broken
symmetry states.Comment: revtex4, 6 pages, 6 figures; revised introduction, updated reference
Direct CP Violation in Angular Distribution of Decays
We show that the study of certain observables in the angular distribution in
provide clear test for CP vioaltion beyond the Standard
Model. These observables vanish in SM, but in models beyond SM some of them can
be large enough to be measured at B factories.Comment: 7 pages, Revte
Two-stage Kondo effect in side-coupled quantum dots: Renormalized perturbative scaling theory and Numerical Renormalization Group analysis
We study numerically and analytically the dynamical (AC) conductance through
a two-dot system, where only one of the dots is coupled to the leads but it is
also side-coupled to the other dot through an antiferromagnetic exchange (RKKY)
interaction. In this case the RKKY interaction gives rise to a ``two-stage
Kondo effect'' where the two spins are screened by two consecutive Kondo
effects. We formulate a renormalized scaling theory that captures remarkably
well the cross-over from the strongly conductive correlated regime to the low
temperature low conductance state. Our analytical formulas agree well with our
numerical renormalization group results. The frequency dependent current noise
spectrum is also discussed.Comment: 6 pages, 7 figure
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