329 research outputs found
Super-diffusion in one-dimensional quantum lattice models
We identify a class of one-dimensional spin and fermionic lattice models
which display diverging spin and charge diffusion constants, including several
paradigmatic models of exactly solvable strongly correlated many-body dynamics
such as the isotropic Heisenberg spin chains, the Fermi-Hubbard model, and the
t-J model at the integrable point. Using the hydrodynamic transport theory, we
derive an analytic lower bound on the spin and charge diffusion constants by
calculating the curvature of the corresponding Drude weights at half filling,
and demonstrate that for certain lattice models with isotropic interactions
some of the Noether charges exhibit super-diffusive transport at finite
temperature and half filling.Comment: 4 pages + appendices, v2 as publishe
Phylogenetic toric varieties on graphs
We define phylogenetic projective toric model of a trivalent graph as a
generalization of a binary symmetric model of a trivalent phylogenetic tree.
Generators of the pro- jective coordinate ring of the models of graphs with one
cycle are explicitly described. The phylogenetic models of graphs with the same
topological invariants are deforma- tion equivalent and share the same Hilbert
function. We also provide an algorithm to compute the Hilbert function.Comment: 36 pages, improved expositio
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
We analyze the classical and quantum vacua of 2d
supersymmetric Yang-Mills theory with and gauge group,
describing the worldvolume interactions of parallel D1-branes with flat
transverse directions . We claim that the IR limit of the
theory in the superselection sector labeled --- identified with
the internal dynamics of -string bound states of Type IIB string theory
--- is described by the symmetric orbifold sigma model into
when , and by a single
massive vacuum when , generalizing the conjectures of E. Witten and
others. The full worldvolume theory of the D1-branes is the theory with
an additional 2-form gauge field coming from the string theory
Kalb-Ramond field. This theory has generalized field configurations,
labeled by the -valued generalized electric flux and an independent
-valued 't Hooft flux. We argue that in the quantum mechanical
theory, the -string sector with units of electric flux has a
-valued discrete angle specified by dual to
the 't Hooft flux. Adding the brane center-of-mass degrees of freedom to the
theory, we claim that the IR limit of the theory in the
sector with bound F-strings is described by the sigma
model into . We provide strong evidence for
these claims by computing an analog of the elliptic genus
of the UV gauge theories and of their conjectured IR limit sigma models, and
showing they agree. Agreement is established by noting that the elliptic genera
are modular-invariant Abelian (multi-periodic and meromorphic) functions, which
turns out to be very restrictive.Comment: 47 pages. Comments welcome
Complexity Theory
Computational Complexity Theory is the mathematical study of the intrinsic power and limitations of computational resources like time, space, or randomness. The current workshop focused on recent developments in various sub-areas including arithmetic complexity, Boolean complexity, communication complexity, cryptography, probabilistic proof systems, pseudorandomness, and quantum computation. Many of the developments are related to diverse mathematical fields such as algebraic geometry, combinatorial number theory, probability theory, representation theory, and the theory of error-correcting codes
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