A topos for algebraic quantum theory

The aim of this paper is to relate algebraic quantum mechanics to topos theory, so as to construct new foundations for quantum logic and quantum spaces. Motivated by Bohr's idea that the empirical content of quantum physics is accessible only through classical physics, we show how a C*-algebra of observables A induces a topos T(A) in which the amalgamation of all of its commutative subalgebras comprises a single commutative C*-algebra. According to the constructive Gelfand duality theorem of Banaschewski and Mulvey, the latter has an internal spectrum S(A) in T(A), which in our approach plays the role of a quantum phase space of the system. Thus we associate a locale (which is the topos-theoretical notion of a space and which intrinsically carries the intuitionistic logical structure of a Heyting algebra) to a C*-algebra (which is the noncommutative notion of a space). In this setting, states on A become probability measures (more precisely, valuations) on S(A), and self-adjoint elements of A define continuous functions (more precisely, locale maps) from S(A) to Scott's interval domain. Noting that open subsets of S(A) correspond to propositions about the system, the pairing map that assigns a (generalized) truth value to a state and a proposition assumes an extremely simple categorical form. Formulated in this way, the quantum theory defined by A is essentially turned into a classical theory, internal to the topos T(A).Comment: 52 pages, final version, to appear in Communications in Mathematical Physic

Isospin influences on particle emission and critical phenomenon in nuclear dissociation

Features of particle emission and critical point behavior are investigated as functions of the isospin of disassembling sources and temperature at a moderate freeze-out density for medium-size Xe isotopes in the framework of isospin dependent lattice gas model. Multiplicities of emitted light particles, isotopic and isobaric ratios of light particles show the strong dependence on the isospin of the dissociation source, but double ratios of light isotope pairs and the critical temperature determined by the extreme values of some critical observables are insensitive to the isospin of the systems. Values of the power law parameter of cluster mass distribution, mean multiplicity of intermediate mass fragments ($IMF$), information entropy ($H$) and Campi's second moment ($S_2$) also show a minor dependence on the isospin of Xe isotopes at the critical point. In addition, the slopes of the average multiplicites of the neutrons ($N_n$), protons ($N_p$), charged particles ($N_{CP}$), and IMFs ($N_{imf}$), slopes of the largest fragment mass number ($A_{max}$), and the excitation energy per nucleon of the disassembling source ($E^*/A$) to temperature are investigated as well as variances of the distributions of $N_n$, $N_p$, $N_{CP}$, $N_{IMF}$, $A_{max}$ and $E^*/A$. It is found that they can be taken as additional judgements to the critical phenomena.Comment: 9 Pages, 8 figure

Biomass offsets little or none of permafrost carbon release from soils, streams, and wildfire: an expert assessment

As the permafrost region warms, its large organic carbon pool will be increasingly vulnerable to decomposition, combustion, and hydrologic export. Models predict that some portion of this release will be offset by increased production of Arctic and boreal biomass; however, the lack of robust estimates of net carbon balance increases the risk of further overshooting international emissions targets. Precise empirical or model-based assessments of the critical factors driving carbon balance are unlikely in the near future, so to address this gap, we present estimates from 98 permafrost-region experts of the response of biomass, wildfire, and hydrologic carbon flux to climate change. Results suggest that contrary to model projections, total permafrost-region biomass could decrease due to water stress and disturbance, factors that are not adequately incorporated in current models. Assessments indicate that end-of-the-century organic carbon release from Arctic rivers and collapsing coastlines could increase by 75% while carbon loss via burning could increase four-fold. Experts identified water balance, shifts in vegetation community, and permafrost degradation as the key sources of uncertainty in predicting future system response. In combination with previous findings, results suggest the permafrost region will become a carbon source to the atmosphere by 2100 regardless of warming scenario but that 65%–85% of permafrost carbon release can still be avoided if human emissions are actively reduced