15,487 research outputs found
A generalization of the injectivity condition for Projected Entangled Pair States
We introduce a family of tensor network states that we term semi-injective
Projected Entangled-Pair States (PEPS). They extend the class of injective PEPS
and include other states, like the ground states of the AKLT and the CZX models
in square lattices. We construct parent Hamiltonians for which semi-injective
PEPS are unique ground states. We also determine the necessary and sufficient
conditions for two tensors to generate the same family of such states in two
spatial dimensions. Using this result, we show that the third cohomology
labeling of Symmetry Protected Topological phases extends to semi-injective
PEPS.Comment: 63 page
Inverse scattering of Canonical systems and their evolution
In this work we present an analogue of the inverse scattering for Canonical
systems using theory of vessels and associated to them completely integrable
systems. Analytic coefficients fits into this setting, significantly expanding
the class of functions for which the inverse scattering exist. We also derive
an evolutionary equation, arising from canonical systems, which describes the
evolution of the logarithmic derivative of the tau function, associated to
these systemsComment: arXiv admin note: substantial text overlap with arXiv:1303.532
Krein systems
In the present paper we extend results of M.G. Krein associated to the
spectral problem for Krein systems to systems with matrix valued accelerants
with a possible jump discontinuity at the origin. Explicit formulas for the
accelerant are given in terms of the matrizant of the system in question.
Recent developments in the theory of continuous analogs of the resultant
operator play an essential role
The total coordinate ring of a wonderful variety
We study the cone of effective divisors and the total coordinate ring of
wonderful varieties, with applications to their automorphism group. We show
that the total coordinate ring of any spherical variety is obtained from that
of the associated wonderful variety by a base change of invariant subrings.Comment: Final version, to appear in Journal of Algebr
Well-posedness via Monotonicity. An Overview
The idea of monotonicity (or positive-definiteness in the linear case) is
shown to be the central theme of the solution theories associated with problems
of mathematical physics. A "grand unified" setting is surveyed covering a
comprehensive class of such problems. We elaborate the applicability of our
scheme with a number examples. A brief discussion of stability and
homogenization issues is also provided.Comment: Thoroughly revised version. Examples correcte
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