2,867 research outputs found
Matrix factorizations for nonaffine LG-models
We propose a natural definition of a category of matrix factorizations for
nonaffine Landau-Ginzburg models. For any LG-model we construct a fully
faithful functor from the category of matrix factorizations defined in this way
to the triangulated category of singularities of the corresponding fiber. We
also show that this functor is an equivalence if the total space of the
LG-model is smooth.Comment: 12 pages, minor corrections of TEX fil
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
In this paper we establish an equivalence between the category of graded
D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W
and the triangulated category of singularities of the fiber of W over zero. The
main result is a theorem that shows that the graded triangulated category of
singularities of the cone over a projective variety is connected via a fully
faithful functor to the bounded derived category of coherent sheaves on the
base of the cone. This implies that the category of graded D-branes of type B
in Landau-Ginzburg models with homogeneous superpotential W is connected via a
fully faithful functor to the derived category of coherent sheaves on the
projective variety defined by the equation W=0.Comment: 26 pp., LaTe
Derived categories of Burniat surfaces and exceptional collections
We construct an exceptional collection of maximal possible length
6 on any of the Burniat surfaces with , a 4-dimensional family of
surfaces of general type with . We also calculate the DG algebra of
endomorphisms of this collection and show that the subcategory generated by
this collection is the same for all Burniat surfaces.
The semiorthogonal complement of is an "almost
phantom" category: it has trivial Hochschild homology, and K_0(\mathcal
A)=\bZ_2^6.Comment: 15 pages, 1 figure; further remarks expande
Critical thermodynamics of two-dimensional N-vector cubic model in the five-loop approximation
The critical behavior of the two-dimensional N-vector cubic model is studied
within the field-theoretical renormalization-group (RG) approach. The
beta-functions and critical exponents are calculated in the five-loop
approximation, RG series obtained are resummed using Pade-Borel-Leroy and
conformal mapping techniques. It is found that for N = 2 the continuous line of
fixed points is well reproduced by the resummed RG series and an account for
the five-loop terms makes the lines of zeros of both beta-functions closer to
each another. For N > 2 the five-loop contributions are shown to shift the
cubic fixed point, given by the four-loop approximation, towards the Ising
fixed point. This confirms the idea that the existence of the cubic fixed point
in two dimensions under N > 2 is an artifact of the perturbative analysis. In
the case N = 0 the results obtained are compatible with the conclusion that the
impure critical behavior is controlled by the Ising fixed point.Comment: 18 pages, 4 figure
Single-electron latch with granular film charge leakage suppressor
A single-electron latch is a device that can be used as a building block for
Quantum-dot Cellular Automata (QCA) circuits. It consists of three nanoscale
metal "dots" connected in series by tunnel junctions; charging of the dots is
controlled by three electrostatic gates. One very important feature of a
single-electron latch is its ability to store ("latch") information represented
by the location of a single electron within the three dots. To obtain latching,
the undesired leakage of charge during the retention time must be suppressed.
Previously, to achieve this goal, multiple tunnel junctions were used to
connect the three dots. However, this method of charge leakage suppression
requires an additional compensation of the background charges affecting each
parasitic dot in the array of junctions. We report a single-electron latch
where a granular metal film is used to fabricate the middle dot in the latch
which concurrently acts as a charge leakage suppressor. This latch has no
parasitic dots, therefore the background charge compensation procedure is
greatly simplified. We discuss the origins of charge leakage suppression and
possible applications of granular metal dots for various single-electron
circuits.Comment: 21 pages, 4 figure
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
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