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Complete Segal spaces arising from simplicial categories | In this paper, we compare several functors which take simplicial categories
or model categories to complete Segal spaces, which are particularly nice
simplicial spaces which, like simplicial categories, can be considered to be
models for homotopy theories. We then give a characterization, up to weak
equivalence, of complete Segal spaces arising from these functors.
|
Semiclassical scattering amplitude at the maximum point of the potential | We compute the scattering amplitude for Schr\"odinger operators at a critical
energy level, corresponding to the maximum point of the potential. We follow
the wrok of Robert and Tamura, '89, using Isozaki and Kitada's representation
formula for the scattering amplitude, together with results from Bony, Fujiie,
Ramond and Zerzeri '06 in order to analyze the contribution of trapped
trajectories.
|
Riggings of locally compact abelian groups | We obtain a set of generalized eigenvectors that provides a generalized
spectral decomposition for a given unitary representation of a commutative,
locally compact topological group. These generalized eigenvectors are
functionals belonging to the dual space of a rigging on the space of square
integrable functions on the character group. These riggings are obtained
through suitable spectral measure spaces.
|
The LIL for $U$-statistics in Hilbert spaces | We give necessary and sufficient conditions for the (bounded) law of the
iterated logarithm for $U$-statistics in Hilbert spaces. As a tool we also
develop moment and tail estimates for canonical Hilbert-space valued
$U$-statistics of arbitrary order, which are of independent interest.
|
Circulating Current States in Bilayer Fermionic and Bosonic Systems | It is shown that fermionic polar molecules or atoms in a bilayer optical
lattice can undergo the transition to a state with circulating currents, which
spontaneously breaks the time reversal symmetry. Estimates of relevant
temperature scales are given and experimental signatures of the circulating
current phase are identified. Related phenomena in bosonic and spin systems
with ring exchange are discussed.
|
Possible polarisation and spin dependent aspects of quantum gravity | We argue that quantum gravity theories that carry a Lie algebraic
modification of the Poincare' and Heisenberg algebras inevitably provide
inhomogeneities that may serve as seeds for cosmological structure formation.
Furthermore, in this class of theories one must expect a strong polarisation
and spin dependence of various quantum-gravity effects.
|
Two center multipole expansion method: application to macromolecular
systems | We propose a new theoretical method for the calculation of the interaction
energy between macromolecular systems at large distances. The method provides a
linear scaling of the computing time with the system size and is considered as
an alternative to the well known fast multipole method. Its efficiency,
accuracy and applicability to macromolecular systems is analyzed and discussed
in detail.
|
Spectral averaging for trace compatible operators | In this note the notions of trace compatible operators and infinitesimal
spectral flow are introduced. We define the spectral shift function as the
integral of infinitesimal spectral flow. It is proved that the spectral shift
function thus defined is absolutely continuous and Krein's formula is
established. Some examples of trace compatible affine spaces of operators are
given.
|
Gravitating Global k-monopole | A gravitating global k-monopole produces a tiny gravitational field outside
the core in addition to a solid angular deficit in the k-field theory. As a new
feature, the gravitational field can be attractive or repulsive depending on
the non-canonical kinetic term.
|
Pair production with neutrinos in an intense background magnetic field | We present a detailed calculation of the electron-positron production rate
using neutrinos in an intense background magnetic field. The computation is
done for the process nu -> nu e- e+ (where nu can be nu_e, nu_mu, or nu_tau)
within the framework of the Standard Model. Results are given for various
combinations of Landau-levels over a range of possible incoming neutrino
energies and magnetic field strengths.
|
Theoretical Aspects of the SOM Algorithm | The SOM algorithm is very astonishing. On the one hand, it is very simple to
write down and to simulate, its practical properties are clear and easy to
observe. But, on the other hand, its theoretical properties still remain
without proof in the general case, despite the great efforts of several
authors. In this paper, we pass in review the last results and provide some
conjectures for the future work.
|
Retract rationality and Noether's problem | Let K be any field and G be a finite group. We will prove that, if K is any
field, p an odd prime number, and G is a non-abelian group of exponent p with
|G|=p^3 or p^4 satisfying [K(\zeta_p):K] <= 2, then K(G) is rational over K. We
will also show that K(G) is retract rational if G belongs to a much larger
class of p-groups. In particular, generic G-polynomials of G-Galois extensions
exist for these groups.
|
Noether's problem for some p-groups | Let K be any field and G be a finite group. Noether's problem asks whether
the fixed field is rational (=purely transcendental) over K. We will prove that
if G is a non-abelian p-group of order p^n containing a cyclic subgroup of
index p and K is any field containing a primitive p^{n-2}-th root of unity,
then K(G) is rational over K.
|
The canonical volume of threefolds of general type with $\chi<1$ | We prove that the canonical volume $K^3\geq {1/30}$ for all projective
3-folds of general type with $\chi(\mathcal{O})\leq 0$. This bound is sharp.
|
Dynamical Equilibrium, trajectories study in an economical system. The
case of the labor market | The paper deals with the study of labor market dynamics, and aims to
characterize its equilibriums and possible trajectories. The theoretical
background is the theory of the segmented labor market. The main idea is that
this theory is well adapted to interpret the observed trajectories, due to the
heterogeneity of the work situations.
|
Borromean Entanglement Revisited | An interesting analogy between quantum entangled states and topological links
was suggested by Aravind. In particular, he emphasized a connection between the
Greenberger-Horne-Zeilinger (GHZ) state and the Borromean rings. However, he
made the connection in a way that depends on the choice of measurement basis.
We reconsider it in a basis-independent way by using the reduced density
matrix.
|
One-parameter families of functions in the Pick class | In the one-parameter family of power-law maps of the form
$f_a(x)=-|x|^{\alpha}+a,$ $\alpha >1,$ we give examples of mutually related
dynamically determined quantities, depending on the parameter $a$, such that
one is a Pick function of the following one. These Pick functions are
extendable by reflection through the $(1,+\infty)$ half-axis and have
completely monotone derivatives there.
|
The homology of the Steinberg variety and Weyl group coinvariants | Let G be a complex, connected, reductive algebraic group with Weyl group W
and Steinberg variety Z. We show that the graded Borel-Moore homology of Z is
isomorphic to the smash product of the coinvariant algebra of W and the group
algebra of W.
|
Inhomogeneous color superconductivity and the cooling of compact stars | In this talk I discuss the inhomogeneous (LOFF) color superconductive phases
of Quantum Chromodynamics (QCD). In particular, I show the effect of a core of
LOFF phase on the cooling of a compact star.
|
Wormholes in the accelerating universe | We discuss different arguments that have been raised against the viability of
the big trip process, reaching the conclusions that this process can actually
occur by accretion of phantom energy onto the wormholes and that it is stable
and might occur in the global context of a multiverse model. We finally argue
that the big trip does not contradict any holographic bounds on entropy and
information.
|
The Invar Tensor Package | The Invar package is introduced, a fast manipulator of generic scalar
polynomial expressions formed from the Riemann tensor of a four-dimensional
metric-compatible connection. The package can maximally simplify any polynomial
containing tensor products of up to seven Riemann tensors within seconds. It
has been implemented both in Mathematica and Maple algebraic systems.
|
Another Riemann-Farey Computation | Another approach to constructing an upper bound for the Riemann-Farey sum is
described.
|
Fractional Generalization of Kac Integral | Generalization of the Kac integral and Kac method for paths measure based on
the Levy distribution has been used to derive fractional diffusion equation.
Application to nonlinear fractional Ginzburg-Landau equation is discussed.
|
Generalized Smirnov statistics and the distribution of prime factors | We apply recent bounds of the author (math.PR/0609224) for generalized
Smirnov statistics to the distribution of integers whose prime factors satisfy
certain systems of inequalities.
|
Le module dendriforme sur le groupe cyclique | The structure of anticyclic operad on the Dendriform operad defines in
particular a matrix of finite order acting on the vector space spanned by
planar binary trees. We compute its characteristic polynomial and propose a
(compatible) conjecture for the characteristic polynomial of the Coxeter
transformation for the Tamari lattice, which is mostly a square root of this
matrix.
|
A Way to Dynamically Overcome the Cosmological Constant Problem | The Cosmological Constant problem can be solved once we require that the full
standard Einstein Hilbert lagrangian, gravity plus matter, is multiplied by a
total derivative. We analyze such a picture writing the total derivative as the
covariant gradient of a new vector field (b_mu). The dynamics of this b_mu
field can play a key role in the explanation of the present cosmological
acceleration of the Universe.
|
Energy Functionals for the Parabolic Monge-Ampere Equation | We introduce certain energy functionals to the complex Monge-Ampere equation
over a bounded domain with inhomogeneous boundary condition, and use these
functionals to show the convergence of the solution to the parabolic
Monge-Ampere equation.
|
Compatible Actions and Cohomology of Crystallographic Groups | We compute the cohomology of crystallographic groups with holonomy of prime
order. As an application we compute the group of gerbes associated to many
six--dimensional toroidal orbifolds arising in string theory.
|
Comment on Electroweak Higgs as a Pseudo-Goldstone Boson of Broken Scale
Invariance | The first model of Foot, Kobakhidze and Volkas described in their work in
arXiv:0704.1165 [hep-ph] is a tailored version of our model on broken scale
invariance in the standard model presented in hep-th/0403039.
|
Radiation from Kinetic Poynting Flux Acceleration | We derive analytic formulas for the power output and critical frequency of
radiation by electrons accelerated by relativistic kinetic Poynting flux, and
validate these results with Particle-In-Cell plasma simulations. We find that
the in-situ radiation power output and critical frequency are much below those
predicted by the classical synchrotron formulae. We discuss potential
astrophysical applications of these results.
|
Weak type radial convolution operators on free group | Radial convolution operators on free groups with nonnegative kernel of weak
type $(2,2)$ and of restricted weak type $(2,2)$ are characterized. Estimates
of weak type $(p,p)$ are obtained as well for $1<p<2.$
|
Analycity and smoothing effect for the coupled system of equations of
Korteweg - de Vries type with a single point singularity | We study that a solution of the initial value problem associated for the
coupled system of equations of Korteweg - de Vries type which appears as a
model to describe the strong interaction of weakly nonlinear long waves, has
analyticity in time and smoothing effect up to real analyticity if the initial
data only has a single point singularity at $x=0.$
|
Smoothing properties for the higher order nonlinear Schr\"{o}dinger
equation with constant coefficients | We study local and global existence and smoothing properties for the initial
value problem associated to a higher order nonlinear Schr\"odinger equation
with constant coefficients which appears as a model for propagation of pulse in
optical fiber.
|
Parameter estimation for power-law distributions by maximum likelihood
methods | Distributions following a power-law are an ubiquitous phenomenon. Methods for
determining the exponent of a power-law tail by graphical means are often used
in practice but are intrinsically unreliable. Maximum likelihood estimators for
the exponent are a mathematically sound alternative to graphical methods.
|
The Weil representation and Hecke operators for vector valued modular
forms | We define Hecke operators on vector valued modular forms transforming with
the Weil representation associated to a discriminant form. We describe the
properties of the corresponding algebra of Hecke operators and study the action
on modular forms.
|
On the energy spectrum of the one-dimensional Klein-Gordon Oscillator | In the present article, we describe a method of introducing the harmonic
potential into the Klein-Gordon equation, leading to genuine bound states. The
eigenfunctions and eigenenergies are worked out explicitly.
|
New versions of Schur-Weyl duality | After reviewing classical Schur-Weyl duality, we present some other contexts
which enjoy similar features, relating to Brauer algebras and classical groups.
|
Lower bounds in some power sum problems | We study the power sum problem max_{v=1,...,m} | sum_{k=1}^n z_k^v | and by
using features of Fejer kernels we give new lower bounds in the case of
unimodular complex numbers z_k and m cn^2 for constants c>1.
|
Coloring ordinals by reals | We study combinatorial principles we call Homogeneity Principle HP(\kappa)
and Injectivity Principle IP(\kappa,\lambda) for regular \kappa>\aleph_1 and
\lambda\leq\kappa which are formulated in terms of coloring the ordinals
<\kappa by reals.
|
Axioms for a local Reidemeister trace in fixed point and coincidence
theory on differentiable manifolds | We give axioms which characterize the local Reidemeister trace for orientable
differentiable manifolds. The local Reidemeister trace in fixed point theory is
already known, and we provide both uniqueness and existence results for the
local Reidemeister trace in coincidence theory.
|
On (n+2)-dimensional n-Lie algebras | I show that an (n+2)-dimensional n-Lie algebra over an algebraically closed
field must have a subalgeba of codimension 1.
|
Non-Associativity of Lorentz Transformation and Associative Reflection
Symmetric Transformation | Each of the two moving observers observes the relative velocity of the other.
The two velocities should be equal and opposite. We have shown that this
relativistic requirement is not fulfilled by Lorentz transformation. We have
also shown that the reason is that Lorentz transformation is not associative.
Reciprocal symmetric transformation is associative and fulfills relativistic
requirements.
|
Jamming dynamics in grain mixtures : An extended hydrodynamic approach | We study jamming in granular mixtures from the novel point of view of
extended hydrodynamics. Using a hard sphere binary mixture model we predict
that a few large grains are expected to get caged more effectively in a matrix
of small grains compared to a few small grains in a matrix of larger ones. A
similar effect has been experimentally seen in the context of colloidal
mixtures.
|
Causal vs. Analytic constraints on anomalous quartic gauge couplings | We derive one loop constraints on the anomalous quartic gauge couplings using
a general non-forward dispersion relation for the elastic scattering amplitude
of two longitudinally polarized vector bosons. We compare this result with
another one derived by the assumption that the underlying theory satisfies the
causality principle of Special Relativity and show that this latter is more
constraining.
|
Non-linear electromagnetic response of graphene | It is shown that the massless energy spectrum of electrons and holes in
graphene leads to the strongly non-linear electromagnetic response of this
system. We predict that the graphene layer, irradiated by electromagnetic
waves, emits radiation at higher frequency harmonics and can work as a
frequency multiplier. The operating frequency of the graphene frequency
multiplier can lie in a broad range from microwaves to the infrared.
|
Bone Cancer Rates in Dinosaurs Compared with Modern Vertebrates | Data on the prevalence of bone cancer in dinosaurs is available from past
radiological examination of preserved bones. We statistically test this data
for consistency with rates extrapolated from information on bone cancer in
modern vertebrates, and find that there is no evidence of a different rate.
Thus, this test provides no support for a possible role of ionizing radiation
in the K-T extinction event.
|
Finite Representations of the braid group commutator subgroup | We study the representations of the commutator subgroup K_{n} of the braid
group B_{n} into a finite group . This is done through a symbolic dynamical
system. Some experimental results enable us to compute the number of subgroups
of K_{n} of a given (finite) index, and, as a by-product, to recover the well
known fact that every representation of K_{n} into S_{r}, with n > r, must be
trivial.
|
Solutions of certain fractional kinetic equations and a fractional
diffusion equation | In view of the usefulness and importance of the kinetic equation in certain
physical problems, the authors derive the explicit solution of a fractional
kinetic equation of general character, that unifies and extends earlier
results. Further, an alternative shorter method based on a result developed by
the authors is given to derive the solution of a fractional diffusion equation.
|
Addendum: A Classification of Plane Symmetric Kinematic Self-similar
Solutions | In our recent paper, we classified plane symmetric kinematic self-similar
perfect fluid and dust solutions of the second, zeroth and infinite kinds.
However, we have missed some solutions during the process. In this short
communication, we add up those missing solutions. We have found a total of
seven solutions, out of which five turn out to be independent and cannot be
found in the earlier paper
|
Identities for number series and their reciprocals: Dirac delta function
approach | Dirac delta function (delta-distribution) approach can be used as efficient
method to derive identities for number series and their reciprocals. Applying
this method, a simple proof for identity relating prime counting function
(pi-function) and logarithmic integral (Li-function) can be obtained.
|
The Chow ring of the moduli space and its related homogeneous space of
bundles on P^2 with charge 1 | For an algebraically closed field K with ch K \not = 2, we determine the Chow
ring of the moduli space of holomorphic bundles on a projective plane with the
structure group SO(n,K) and half the first Pontryagin index being equal to 1,
each of which is trivial on a fixed line and has a fixed holomorphic
trivialization there.
|
Additional Explanatory Notes on the Analytic Proof of the Finite
Generation of the Canonical Ring | This set of notes provides some additional explanatory material on the
analytic proof of the finite generation of the canonical ring for a compact
complex algebraic manifold of general type.
|
Quadratic centers defining elliptic surfaces | Let $X$ be a quadratic vector field with a center whose generic orbits are
algebraic curves of genus one. To each $X$ we associate an elliptic surface (a
smooth complex compact surface which is a genus one fibration). We give the
list of all such vector fields and determine the corresponding elliptic
surfaces.
|
Search for exclusive events using the dijet mass fraction at the
Tevatron | In this paper, we discuss the observation of exclusive events using the dijet
mass fraction as measured by the CDF collaboration at the Tevatron. We compare
the data to pomeron exchange inspired models as well as Soft color interaction
ones. We also provide the prediction on dijet mass fraction at the LHC using
both exclusive and inclusive diffractive events.
|
Entanglement Cost for Sequences of Arbitrary Quantum States | The entanglement cost of arbitrary sequences of bipartite states is shown to
be expressible as the minimization of a conditional spectral entropy rate over
sequences of separable extensions of the states in the sequence. The expression
is shown to reduce to the regularized entanglement of formation when the n-th
state in the sequence consists of n copies of a single bipartite state.
|
Growth rates for geometric complexities and counting functions in
polygonal billiards | We introduce a new method for estimating the growth of various quantities
arising in dynamical systems. We apply our method to polygonal billiards on
surfaces of constant curvature. For instance, we obtain power bounds of degree
two plus epsilon in length for the number of billiard orbits between almost all
pairs of points in a planar polygon.
|
The Jumping Phenomenon of Hodge Numbers | Let $X$ be a compact complex manifold, consider a small deformation $\phi:
\mathcal{X} \to B$ of $X$, the dimension of the Dolbeault cohomology groups
$H^q(X_t,\Omega_{X_t}^p)$ may vary under this defromation. This paper will
study such phenomenons by studying the obstructions to deform a class in
$H^q(X,\Omega_X^p)$ with the parameter $t$ and get the formula for the
obstructions.
|
V-cycle optimal convergence for DCT-III matrices | The paper analyzes a two-grid and a multigrid method for matrices belonging
to the DCT-III algebra and generated by a polynomial symbol. The aim is to
prove that the convergence rate of the considered multigrid method (V-cycle) is
constant independent of the size of the given matrix. Numerical examples from
differential and integral equations are considered to illustrate the claimed
convergence properties.
|
Characterization of Closed Vector Fields in Finsler Geometry | The $\pi$-exterior derivative ${\o}d$, which is the Finslerian generalization
of the (usual) exterior derivative $d$ of Riemannian geometry, is defined. The
notion of a ${\o}d$-closed vector field is introduced and investigated. Various
characterizations of ${\o}d$-closed vector fields are established. Some results
concerning ${\o}d$-closed vector fields in relation to certain special Finsler
spaces are obtained.
|
Yukawa's Pion, Low-Energy QCD and Nuclear Chiral Dynamics | A survey is given of the evolution from Yukawa's early work, via the
understanding of the pion as a Nambu-Goldstone boson of spontaneously broken
chiral symmetry in QCD, to modern developments in the theory of the nucleus
based on the chiral effective field theory representing QCD in its low-energy
limit.
|
On Virasoro Constraints for Orbifold Gromov-Witten Theory | Virasoro constraints for orbifold Gromov-Witten theory are described. These
constraints are applied to the degree zreo, genus zero orbifold Gromov-Witten
potentials of the weighted projective stacks $\mathbb{P}(1,N)$,
$\mathbb{P}(1,1,N)$ and $\mathbb{P}(1,1,1,N)$ to obtain formulas of descendant
cyclic Hurwitz-Hodge integrals.
|
The author replies | I respond to the Bernard et al. comment on my letter ``Chiral anomalies and
rooted staggered fermions.''
|
On a new version of the Ito's formula for the stochastic heat equation | We derive an It\^o's-type formula for the one dimensional stochastic heat
equation driven by a space-time white noise. The proof is based on elementary
properties of the $\mathcal{S}$-transform and on the explicit representation of
the solution process. We also discuss the relationship with other versions of
this It\^o's-type formula existing in literature.
|
A Note on Sums of Powers | We improve a result of Bennett concerning certain sequences involving sums of
powers of positive integers.
|
Quantum teleportation with atoms: quantum process tomography | The performance of a quantum teleportation algorithm implemented on an ion
trap quantum computer is investigated. First the algorithm is analyzed in terms
of the teleportation fidelity of six input states evenly distributed over the
Bloch sphere. Furthermore, a quantum process tomography of the teleportation
algorithm is carried out which provides almost complete knowledge about the
algorithm.
|
Hyperbolic Balance Laws with a Non Local Source | This paper is devoted to hyperbolic systems of balance laws with non local
source terms. The existence, uniqueness and Lipschitz dependence proved here
comprise previous results in the literature and can be applied to physical
models, such as Euler system for a radiating gas and Rosenau regularization of
the Chapman-Enskog expansion.
|
The Quantum Interference Computer: an experimental proposal | An experiment is proposed to test the interference aspect of the Quantum
Interference Computer approach
|
Vacuum as a less hostile environment to entanglement | We derive sufficient conditions for infinite-dimensional systems whose
entanglement is not completely lost in a finite time during its decoherence by
a passive interaction with local vacuum environments. The sufficient conditions
allow us to clarify a class of bipartite entangled states which preserve their
entanglement or, in other words, are tolerant against decoherence in a vacuum.
We also discuss such a class for entangled qubits.
|
Non-Viability of a Counter-Argument to Bell's Theorem | It is demonstrated that a recently suggested model for the EPR-Bohm spin
experiment, based on Clifford algebra valued local variables and observables,
runs into very serious difficulties and can therefore not be taken as
constituting a viable counter-example to Bell's theorem.
|
Bi-Lipschitz geometry of weighted homogeneous surface singularities | We show that a weighted homogeneous complex surface singularity is metrically
conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest
weights are equal. We also give an example of a pair of weighted homogeneous
complex surface singularities that are topologically equivalent but not
bi-Lipschitz equivalent.
|
The No-Boundary Probability for the Universe starting at the top of the
hill | We use the Hartle-Hawking No-Boundary Proposal to make a comparison between
the probabilities of the universe starting near, and at, the top of a hill in
the effective potential. In the context of top-down cosmology, our calculation
finds that the universe doesn't start at the top.
|
A biased view of symplectic cohomology | These are lecture notes from my talks at the "Current Developments in
Mathematics" conference (Harvard, 2006). They cover a variety of topics
involving symplectic cohomology. In particular, a discussion of (algorithmic)
classification issues in symplectic and contact topology is included.
|
Symmetry properties of the nodal superconductor PrOs4Sb12 | We present a theoretical study of the superconducting gap function in
PrOs4Sb12 using a symmetry-based approach. A three-component order parameter in
the triplet channel best describes superconductivity. The gap function is
non-degenerate and the lower branch has four cusp nodes at unusual points of
the Fermi surface, which lead to power law behaviours in the density of states,
specific heat and nuclear spin relaxation rate.
|
Three-manifolds of positive Ricci curvature and convex weakly umbilic
boundary | In this paper we consider three-manifolds with weakly umbilic boundary (the
Second Fundamental form of the boundary is a constant multiple of the metric).
We show that if the initial manifold has positive Ricci curvature and the
boundary is convex (nonnegative Second Fundamental form), its metric can be
deformed via the Ricci flow to a metric of constant curvature and totally
geodesic boundary.
|
Comment on ``Analysis of Floquet formulation of time-dependent
density-functional theory'' [Chem. Phys. Lett. {\bf 433} (2006), 204] | We discuss the relationship between modern time-dependent density functional
theory and earlier time-periodic versions, and why the criticisms in a recent
paper (Chem. Phys. Lett. {\bf 433} (2006) 204) of our earlier analysis (Chem.
Phys. Lett. {\bf 359} (2002) 237) are incorrect.
|
The SLOCC invariant and the residual entanglement for n-qubits | In this paper, we find the invariant for $n$-qubits and propose the residual
entanglement for $n$-qubits by means of the invariant. Thus, we establish a
relation between SLOCC entanglement and the residual entanglement. The
invariant and the residual entanglement can be used for SLOCC entanglement
classification for $n$-qubits.
|
On the energy equality for weak solutions of the 3D Navier-Stokes
equations | We prove that the energy equality holds for weak solutions of the 3D
Navier-Stokes equations in the functional class $L^3([0,T);V^{5/6})$, where
$V^{5/6}$ is the domain of the fractional power of the Stokes operator
$A^{5/12}$.
|
Discrete quantum Fourier transform in coupled semiconductor double
quantum dot molecules | In this Letter, we present a physical scheme for implementing the discrete
quantum Fourier transform in a coupled semiconductor double quantum dot system.
The main controlled-R gate operation can be decomposed into many simple and
feasible unitary transformations. The current scheme would be a useful step
towards the realization of complex quantum algorithms in the quantum dot
system.
|
Estimation of Bond Percolation Thresholds on the Archimedean Lattices | We give accurate estimates for the bond percolation critical probabilities on
seven Archimedean lattices, for which the critical probabilities are unknown,
using an algorithm of Newman and Ziff.
|
A Remark on Compact Minimal Surfaces in $S^5$ with Non-Negative Gaussian
Curvature | In this paper we classify compact minimal surfaces in $S^5$ with non-negative
Gaussian curvature using the notion of a contact angle.
|
Zig Zag symmetry in AdS/CFT duality | The validity of the Bianchi identity, which is intimately connected with the
zig zag symmetry, is established, for piecewise continuous contours, in the
context of Polakov's gauge field-string connection in the large 'tHooft
coupling limit, according to which the chromoelectric `string' propagates in
five dimensions with its ends attached on a Wilson loop in four dimensions. An
explicit check in the wavy line approximation is presented.
|
Associated Graded Algebras and Coalgebras | We investigate the notion of associated graded coalgebra (algebra) of a
bialgebra with respect to a subbialgebra (quotient bialgebra) and characterize
those which are bialgebras of type one in the framework of abelian braided
monoidal categories.
|
ABCD and ODEs | We outline a relationship between conformal field theories and spectral
problems of ordinary differential equations, and discuss its generalisation to
models related to classical Lie algebras.
|
The Jumping Phenomenon of the Dimensions of Cohomology Groups of Tangent
Sheaf | Let $X$ be a compact complex manifold, consider a small deformation $\phi:
\mathcal{X} \to B$ of $X$, the dimensions of the cohomology groups of tangent
sheaf $H^q(X_t,\mathcal{T}_{X_t})$ may vary under this deformation. This paper
will study such phenomenons by studying the obstructions to deform a class in
$H^q(X,\mathcal{T}_X)$ with the parameter $t$ and get the formula for the
obstructions.
|
Conformal Structures in Noncommutative Geometry | It is well-known that a compact Riemannian spin manifold can be reconstructed
from its canonical spectral triple which consists of the algebra of smooth
functions, the Hilbert space of square integrable spinors and the Dirac
operator. It seems to be a folklore fact that the metric can be reconstructed
up to conformal equivalence if one replaces the Dirac operator D by sign(D). We
give a precise formulation and proof of this fact.
|
Nonadditive quantum error-correcting code | We report the first nonadditive quantum error-correcting code, namely, a
$((9,12,3))$ code which is a 12-dimensional subspace within a 9-qubit Hilbert
space, that outperforms the optimal stabilizer code of the same length by
encoding more levels while correcting arbitrary single-qubit errors.
|
L-theory of groups with unstable derived series | In this short note we prove that the Farrell-Jones Fibered Isomorphism
Conjecture in L-theory, after inverting 2, is true for a group whose some
derived subgroup is free.
|
An algebraic proof of Gabrielov's theorem about analytic homomorphisms
in any characteristic | The proof of proposition 3.6 is not correct
|
On action of the Virasoro algebra on the space of univalent functions | We obtain explicit expressions for differential operators defining the action
of the Virasoro algebra on the space of univalent functions. We also obtain an
explicit Taylor decomposition for Schwarzian derivative and a formula for the
Grunsky coefficients.
|
Comment on "Liquids on Topologically Nanopatterned Surfaces" | Comment on "Liquids on Topologically Nanopatterned Surfaces" by O. Gang et
al, Phys. Rev. Lett. 95, 217801 (2005).
See also an erratum published by O. Gang et al (Phys Rev Lett, to appear)
|
Free pre-Lie algebras are free as Lie algebras | We prove that free pre-Lie algebras, when considered as Lie algebras, are
free. Working in the category of S-modules, we define a natural filtration on
the space of generators. We also relate the symmetric group action on
generators with the structure of the anticyclic PreLie operad.
|
Charmed Meson Production in Deep Inelastic Scattering | Charmed meson production in semi-inclusive deep inelastic scattering is
investigated in the color dipole formalism. The transverse momentum
distributions are calculated. We find good agreement with the H1 data using a
hard fragmentation function.
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Electroweak Chiral Lagrangian for Left-right Symmetric Models | The complete list of electroweak chiral Lagrangian up to order of p4 for
left-right symmetric models with a neutral light higgs is provided. The
connection of these operators to left and right gauge boson mixings and masses
is made and their contribution to conventional generalized electroweak chiral
Lagrangian with a neutral light higgs included in is estimated.
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Metal and molecule cooling in simulations of structure formation | This submission has been withdrawn by arXiv administrators because it is a
duplicate of 0704.2182.
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Casimir Friction I: Friction of a vacuum on a spinning dielectric | We introduce the concept of Casimir friction, i.e. friction due to quantum
fluctuations. In this first article we describe the calculation of a constant
torque, arising from the scattering of quantum fluctuations, on a dielectric
rotating in an electromagnetic vacuum.
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Braneworld Cosmology | A brief review of the field of braneworld cosmology, from its inception with
the large extra dimension scenario, to aspects of cosmology in warped extra
dimensions, including the RS-I and RS-II models, braneworld inflation, the
Goldberger-Wise mechanism, mirage cosmology, the radion-induced phase
transition in RS-I, possible gravity wave signals, and the DGP model.
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Equilibrium states for interval maps: the potential $-t\log |Df|$ | Let $f:I \to I$ be a $C^2$ multimodal interval map satisfying polynomial
growth of the derivatives along critical orbits. We prove the existence and
uniqueness of equilibrium states for the potential $\phi_t:x\mapsto
-t\log|Df(x)|$ for $t$ close to 1, and also that the pressure function $t
\mapsto P(\phi_t)$ is analytic on an appropriate interval near $t = 1$.
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Factor Analysis and Alternating Minimization | In this paper we make a first attempt at understanding how to build an
optimal approximate normal factor analysis model. The criterion we have chosen
to evaluate the distance between different models is the I-divergence between
the corresponding normal laws. The algorithm that we propose for the
construction of the best approximation is of an the alternating minimization
kind.
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The Picard group of $M_{1,1}$ | We compute the Picard group of the moduli stack of elliptic curves and its
canonical compactification over general base schemes.
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Pomeranchuk instability: symmetry breaking and experimental signatures | We discuss the emergence of symmetry-breaking {\it via} the Pomeranchuk
instability from interactions that respect the underlying point-group symmetry.
We use a variational mean-field theory to consider a 2D continuum and a square
lattice. We describe two experimental signatures: a symmetry-breaking pattern
of Friedel oscillations around an impurity; and a structural transition.
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