Calabi--Yau complete intersections in exceptional Grassmannians
June 13, 2016
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Mathematics
Algebraic Geometry
We classify completely reducible equivariant vector bundles on Grassmannians
of exceptional Lie groups which give Calabi--Yau 3-folds as complete
intersections. In particular, we find a new family of Calabi--Yau 3-folds in an
E6-Grassman...
Rate of convergence of attractors for semilinear singularly perturbed
problems: scalar parabolic equations with localized large diffusion
June 12, 2016
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Mathematics
Analysis of PDEs
In this paper we study the asymptotic nonlinear dynamics of scalar semilinear
parabolic problems reaction-diffusion type when the diffusion coefficient
becomes large in a subregion which is interior to the domain. We obtain, under
suitable ...
Universal Quantum Emulator
June 8, 2016
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Physics
Quantum Physics
We propose a quantum algorithm that emulates the action of an unknown unitary
transformation on a given input state, using multiple copies of some unknown
sample input states of the unitary and their corresponding output states. The
algorit...
Holographic Space-time, Newton's Law and the Dynamics of Black Holes
June 3, 2016
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Physics
High Energy Physics - Theory
We revisit the construction of models of quantum gravity in d dimensional
Minkowski space in terms of random tensor models, and correct some mistakes in
our previous treatment of the subject. We find a large class of models in which
the lar...
Matrix Product Density Operators: Renormalization Fixed Points and
Boundary Theories
June 2, 2016
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Physics
Quantum Physics
Strongly Correlated Electrons
Quantum Physics
Strongly Correlated Electrons
We consider the tensors generating matrix product states and density
operators in a spin chain. For pure states, we revise the renormalization
procedure introduced by F. Verstraete et al. in 2005 and characterize the
tensors corresponding t...
Pfaffian Schur processes and last passage percolation in a half-quadrant
June 1, 2016
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Mathematics
Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
Probability
Statistical Mechanics
Mathematical Physics
Mathematical Physics
We study last passage percolation in a half-quadrant, which we analyze within
the framework of Pfaffian Schur processes. For the model with exponential
weights, we prove that the fluctuations of the last passage time to a point on
the diago...
The real parts of the nontrivial Riemann zeta function zeros
June 1, 2016
Mathematics
General Mathematics
This theorem is based on holomorphy of studied functions and the fact that
near a singularity point the real part of some rational function can take an
arbitrary preassigned value....
Riemann hypothesis equivalences, Robin inequality, Lagarias criterion,
and Riemann hypothesis
May 25, 2016
Mathematics
General Mathematics
In this paper, we briefly review most of accomplished research in Riemann
Zeta function and Riemann hypothesis since Riemann's age including Riemann
hypothesis equivalences as well. We then make use of Robin and Lagarias'
criteria to prove ...
Differential forms on diffeological spaces and diffeological gluing, I
May 24, 2016
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Mathematics
Differential Geometry
Differential Geometry
This paper aims to describe the behavior of diffeological differential forms
under the operation of gluing of diffeological spaces along a smooth map. In
the diffeological context, two ways of looking at diffeological forms are
available, t...
Impact of post-Born lensing on the CMB
May 18, 2016
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Physics
Cosmology and Nongalactic Astrophysics
General Relativity and Quantum Cosmology
Lensing of the CMB is affected by post-Born lensing, producing corrections to
the convergence power spectrum and introducing field rotation. We show
numerically that the lensing convergence power spectrum is affected at the
≲0.2%...