5,176 research outputs found
Bousfield localization on formal schemes
Let (X, O_X) be a noetherian formal scheme and consider D_qct(X) its derived
category of sheaves with quasi-coherent torsion homology. We show that there is
a bijection between the set of rigid (i.e. \tensor-ideals) localizing
subcategories of D_qct(X) and subsets in X, generalizing previous work by
Neeman. If moreover X is separated, the associated localization and
acyclization functors are described in certain cases. When Z is a stable for
specialization subset of X, its associated acyclization is \Gamma_Z. When X is
an scheme, the corresponding localizing subcategories are generated by perfect
complexes and we recover Thomason's classification of thick subcategories. On
the other hand, if Y is a generically stable subset of X, we give an expression
for the associated localization functor.Comment: Relaxed the separation hypothesis. Added connection with Thomason's
classification of thick subcategorie
Thermodynamics of weakly measured quantum systems
We consider continuously monitored quantum systems and introduce definitions
of work and heat along individual quantum trajectories that are valid for
coherent superpositions of energy eigenstates. We use these quantities to
extend the first and second laws of stochastic thermodynamics to the quantum
domain. We illustrate our results with the case of a weakly measured driven
two-level system and show how to distinguish between quantum work and heat
contributions. We finally employ quantum feedback control to suppress detector
backaction and determine the work statistics.Comment: 6 pages, 3 figure
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