11,224 research outputs found
Etale realization on the A^1-homotopy theory of schemes
We compare Friedlander's definition of the etale topological type for
simplicial schemes to another definition involving realizations of
pro-simplicial sets. This can be expressed as a notion of hypercover descent
for etale homotopy. We use this result to construct a homotopy invariant
functor from the category of simplicial presheaves on the etale site of schemes
over S to the category of pro-spaces. After completing away from the
characteristics of the residue fields of S, we get a functor from the
Morel-Voevodsky A^1-homotopy category of schemes to the homotopy category of
pro-spaces
Class of exact memory-kernel master equations
A well-known situation in which a non-Markovian dynamics of an open quantum
system arises is when this is coherently coupled to an auxiliary system
in contact with a Markovian bath. In such cases, while the joint dynamics of
- is Markovian and obeys a standard (bipartite) Lindblad-type master
equation (ME), this is in general not true for the reduced dynamics of .
Furthermore, there are several instances (\eg the dissipative Jaynes-Cummings
model) in which a {\it closed} ME for the 's state {\it cannot} even be
worked out. Here, we find a class of bipartite Lindblad-type MEs such that the
reduced ME of can be derived exactly and in a closed form for any initial
product state of -. We provide a detailed microscopic derivation of our
result in terms of a mapping between two collision modelsComment: 9 pages, 1 figur
Equivariant localization and completion in cyclic homology and derived loop spaces
We prove an equivariant localization theorem over an algebraically closed
field of characteristic zero for smooth quotient stacks by reductive groups
in the setting of derived loop spaces as well as Hochschild homology and
its cyclic variants. We show that the derived loop spaces of the stack
and its classical -fixed point stack become equivalent
after completion along a semisimple parameter , implying the
analogous statement for Hochschild and cyclic homology of the dg category of
perfect complexes . We then prove an analogue of the
Atiyah-Segal completion theorem in the setting of periodic cyclic homology,
where the completion of the periodic cyclic homology of at
the identity is identified with a 2-periodic version of the
derived de Rham cohomology of . Together, these results identify the
completed periodic cyclic homology of a stack over a parameter with the 2-periodic derived de Rham cohomology of its -fixed points.Comment: Pre-publication version. 42 pages. Comments welcom
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