11,334 research outputs found
A note on compactly generated co-t-structures
The idea of a co-t-structure is almost "dual" to that of a t-structure, but
with some important differences. This note establishes co-t-structure analogues
of Beligiannis and Reiten's corresponding results on compactly generated
t-structures.Comment: 10 pages; details added to proofs, small correction in the main
resul
High resolution spectroscopy of single NV defects coupled with nearby C nuclear spins in diamond
We report a systematic study of the hyperfine interaction between the
electron spin of a single nitrogen-vacancy (NV) defect in diamond and nearby
C nuclear spins, by using pulsed electron spin resonance spectroscopy.
We isolate a set of discrete values of the hyperfine coupling strength ranging
from 14 MHz to 400 kHz and corresponding to C nuclear spins placed at
different lattice sites of the diamond matrix. For each lattice site, the
hyperfine interaction is further investigated through nuclear spin polarization
measurements and by studying the magnetic field dependence of the hyperfine
splitting. This work provides informations that are relevant for the
development of nuclear-spin based quantum register in diamond.Comment: 8 pages, 5 figure
Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics
We consider the following first order systems of mathematical physics.
1.The Dirac equation with scalar potential. 2.The Dirac equation with
electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The
system describing non-linear force free magnetic fields or Beltrami fields with
nonconstant proportionality factor. 5.The Maxwell equations for slowly changing
media. 6.The static Maxwell system.
We show that all this variety of first order systems reduces to a single
quaternionic equation the analysis of which in its turn reduces to the solution
of a Schroedinger equation with biquaternionic potential. In some important
situations the biquaternionic potential can be diagonalized and converted into
scalar potentials
Deriving Boltzmann Equations from Kadanoff-Baym Equations in Curved Space-Time
To calculate the baryon asymmetry in the baryogenesis via leptogenesis
scenario one usually uses Boltzmann equations with transition amplitudes
computed in vacuum. However, the hot and dense medium and, potentially, the
expansion of the universe can affect the collision terms and hence the
generated asymmetry. In this paper we derive the Boltzmann equation in the
curved space-time from (first-principle) Kadanoff-Baym equations. As one
expects from general considerations, the derived equations are covariant
generalizations of the corresponding equations in Minkowski space-time. We find
that, after the necessary approximations have been performed, only the
left-hand side of the Boltzmann equation depends on the space-time metric. The
amplitudes in the collision term on the right--hand side are independent of the
metric, which justifies earlier calculations where this has been assumed
implicitly. At tree level, the matrix elements coincide with those computed in
vacuum. However, the loop contributions involve additional integrals over the
the distribution function.Comment: 14 pages, 5 figures, extended discussion of the constraint equations
and the solution for the spectral functio
Anti-Proton Evolution in Little Bangs and Big Bang
The abundances of anti-protons and protons are considered within
momentum-integrated Boltzmann equations describing Little Bangs, i.e.,
fireballs created in relativistic heavy-ion collisions. Despite of a large
anti-proton annihilation cross section we find a small drop of the ratio of
anti-protons to protons from 170 MeV (chemical freeze-out temperature) till 100
MeV (kinetic freeze-out temperature) for CERN-SPS and BNL-RHIC energies thus
corroborating the solution of the previously exposed "ani-proton puzzle". In
contrast, the Big Bang evolves so slowly that the anti-baryons are kept for a
long time in equilibrium resulting in an exceedingly small fraction. The
adiabatic path of cosmic matter in the phase diagram of strongly interacting
matter is mapped out
Nanoscale quantum dot infrared sensors with photonic crystal cavity
We report high performance infrared sensors that are based on intersubband transitions in nanoscale self-assembled quantum dots combined with a microcavity resonator made with a high-index-contrast two-dimensional photonic crystal. The addition of the photonic crystal cavity increases the photocurrent, conversion efficiency, and the signal to noise ratio (represented by the specific detectivity D*) by more than an order of magnitude. The conversion efficiency of the detector at Vb=–2.6 V increased from 7.5% for the control sample to 95% in the PhC detector. In principle, these photonic crystal resonators are technology agnostic and can be directly integrated into the manufacturing of present day infrared sensors using existing lithographic tools in the fabrication facility
The Shapovalov determinant for the Poisson superalgebras
Among simple Z-graded Lie superalgebras of polynomial growth, there are
several which have no Cartan matrix but, nevertheless, have a quadratic even
Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields
on the (1|6)-dimensional supercircle preserving the contact form, and the
series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian
fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using
C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for
the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov
described irreducible finite dimensional representations of po(0|n) and
sh(0|n); we generalize his result for Verma modules: give criteria for
irreducibility of the Verma modules over po(0|2k) and sh(0|2k)
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
Isotypic faithful 2-representations of J-simple fiat 2-categories
We introduce the class of isotypic 2-representations for finitary 2-categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representations are equivalent to inflations of cell 2-representations
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