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We give an overview of the basic definitions of condensed categories, as well as the internal Hom of condensed abelian groups. We give a construction for the internal Hom of condensed sets and apply it to obtain a new proof of a theorem of Clausen and Scholze. Finally, we give a detailed account of a construction of the real numbers from discrete spaces, which is an intermediate step of a theorem by Clausen and Scholze.
We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the measure of cer
When the isospin chemical potential exceeds the pion mass, charged pions condense in the zero-momentum state forming a superfluid. Chiral perturbation theory provides a very powerful tool for studying this phase. However, the formalism that is usuall
Our understanding of various states of matter usually relies on the assumption of thermodynamic equilibrium. However, the transitions between different phases of matter can be strongly affected by non-equilibrium phenomena. Here we demonstrate and ex
We show that a correct formulation of the cold collision frequency shift for two photon spectroscopy of Bose-condensed and cold non-Bose-condensed hydrogen is consistent with experimental data. Our treatment includes transport and inhomogeneity into
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here Ill supply some broad, unifying context, both conceptual and historical, for the abundance of res