528 research outputs found
Canonical basis and homology of local systems
Using the isomorphism between highest weight U_q(sl_2)-modules and homologies
of certain local systems on the configuration spaces, constructed by Varchenko,
we give a geometric construction of the dual of the Lusztig's canonical basis
in a tensor product of irreducible finite-dimensional U_q(sl_2)-modules.Comment: 21 pages, AMSTeX; many figures, require epsf macro packag
Knapsack problems in products of groups
The classic knapsack and related problems have natural generalizations to
arbitrary (non-commutative) groups, collectively called knapsack-type problems
in groups. We study the effect of free and direct products on their time
complexity. We show that free products in certain sense preserve time
complexity of knapsack-type problems, while direct products may amplify it. Our
methods allow to obtain complexity results for rational subset membership
problem in amalgamated free products over finite subgroups.Comment: 15 pages, 5 figures. Updated to include more general results, mostly
in Section
Entanglement Edge Modes of General Noncommutative Matrix Backgrounds
We explore the structure of entanglement edge modes on noncommutative
backgrounds that arise from matrix quantum mechanics. For the fuzzy sphere,
despite nonlocality and UV/IR mixing, we find area law behavior in the dominant
representations governing the state of the edge modes. For general
noncommutative backgrounds with no global symmetry, nonlocal effects resum into
a smoothly varying coupling constant that deforms the metric to a different
frame. The effect is analogous to the relationship between string frame and
Einstein frame in string theory.Comment: 35 pages, 11 figures, one appendi
Friction, Free Axes of Rotation and Entropy
Friction forces acting on rotators may promote their alignment and therefore
eliminate degrees of freedom in their movement. The alignment of rotators by
friction force was demonstrated by experiments performed with different
spinners, demonstrating how friction generates negentropy in a system of
rotators. A gas of rigid rotators influenced by friction force is considered.
The orientational negentropy generated by a friction force was estimated with
the Sackur-Tetrode equation. The minimal change in total entropy of a system of
rotators, corresponding to their eventual alignment, decreases with
temperature. The reported effect may be of the primary importance for a phase
equilibrium and motion of ubiquitous colloidal and granular systems.Comment: 10 pages, 7 image
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