Dense Molecular Gas Excitation at High Redshift: Detection of HCO+(J=4-3) Emission in the Cloverleaf Quasar

We report the detection of HCO+(J=4-3) emission in the Cloverleaf Quasar at z=2.56, using the IRAM Plateau de Bure Interferometer. HCO+ emission is a star formation indicator similar to HCN, tracing dense molecular hydrogen gas (n(H2) ~= 10^5 cm^-3) within star-forming molecular clouds. We derive a lensing-corrected HCO+(J=4-3) line luminosity of L'(HCO+(4-3)) = (1.6+/-0.3) x 10^9 (mu_L/11)^-1 K km/s pc^2, which corresponds to only 48% of the HCO+(J=1=0) luminosity, and <~4% of the CO(J=3-2) luminosity. The HCO+ excitation thus is clearly subthermal in the J=4-3 transition. Modeling of the HCO+ line radiative transfer suggests that the HCO+ emission emerges from a region with physical properties comparable to that exhibiting the CO line emission, but 2x higher gas density. This suggests that both HCO+ and CO lines trace the warm, dense molecular gas where star formation actively takes place. The HCO+ lines have only ~2/3 the width of the CO lines, which may suggest that the densest gas is more spatially concentrated. In contrast to the z=3.91 quasar APM08279+5255, the dense gas excitation in the Cloverleaf is consistent with being purely collisional, rather than being enhanced by radiative processes. Thus, the physical properties of the dense gas component in the Cloverleaf are consistent with those in the nuclei of nearby starburst galaxies. This suggests that the conditions in the dense, star-forming gas in active galactic nucleus-starburst systems at early cosmic times like the Cloverleaf are primarily affected by the starburst itself, rather than the central active black hole.Comment: 4 pages, 3 figures, to appear in ApJ (accepted November 3, 2010

Beyond the Spectral Theorem: Spectrally Decomposing Arbitrary Functions of Nondiagonalizable Operators

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This curse is well known. It also occurs for finite-dimensional linear operators. We circumvent it by developing a meromorphic functional calculus that can decompose arbitrary functions of nondiagonalizable linear operators in terms of their eigenvalues and projection operators. It extends the spectral theorem of normal operators to a much wider class, including circumstances in which poles and zeros of the function coincide with the operator spectrum. By allowing the direct manipulation of individual eigenspaces of nonnormal and nondiagonalizable operators, the new theory avoids spurious divergences. As such, it yields novel insights and closed-form expressions across several areas of physics in which nondiagonalizable dynamics are relevant, including memoryful stochastic processes, open non unitary quantum systems, and far-from-equilibrium thermodynamics. The technical contributions include the first full treatment of arbitrary powers of an operator. In particular, we show that the Drazin inverse, previously only defined axiomatically, can be derived as the negative-one power of singular operators within the meromorphic functional calculus and we give a general method to construct it. We provide new formulae for constructing projection operators and delineate the relations between projection operators, eigenvectors, and generalized eigenvectors. By way of illustrating its application, we explore several, rather distinct examples.Comment: 29 pages, 4 figures, expanded historical citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/bst.ht

Diffraction Patterns of Layered Close-packed Structures from Hidden Markov Models

We recently derived analytical expressions for the pairwise (auto)correlation functions (CFs) between modular layers (MLs) in close-packed structures (CPSs) for the wide class of stacking processes describable as hidden Markov models (HMMs) [Riechers \etal, (2014), Acta Crystallogr.~A, XX 000-000]. We now use these results to calculate diffraction patterns (DPs) directly from HMMs, discovering that the relationship between the HMMs and DPs is both simple and fundamental in nature. We show that in the limit of large crystals, the DP is a function of parameters that specify the HMM. We give three elementary but important examples that demonstrate this result, deriving expressions for the DP of CPSs stacked (i) independently, (ii) as infinite-Markov-order randomly faulted 2H and 3C stacking structures over the entire range of growth and deformation faulting probabilities, and (iii) as a HMM that models Shockley-Frank stacking faults in 6H-SiC. While applied here to planar faulting in CPSs, extending the methods and results to planar disorder in other layered materials is straightforward. In this way, we effectively solve the broad problem of calculating a DP---either analytically or numerically---for any stacking structure---ordered or disordered---where the stacking process can be expressed as a HMM.Comment: 18 pages, 6 figures, 3 tables; http://csc.ucdavis.edu/~cmg/compmech/pubs/dplcps.ht

Ultimate limit on learning non-Markovian behavior: Fisher information rate and excess information

We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized class of candidate models, the Fisher information of observed sequence probabilities lower-bounds the variance in model estimation from finite data. As sequence-length increases, the minimal variance scales as the square inverse of the length -- with constant coefficient given by the information rate. We discover a simple closed-form expression for this information rate, even in the case of infinite Markov order. We furthermore obtain the exact analytic lower bound on model variance from the observation-induced metadynamic among belief states. We discover ephemeral, exponential, and more general modes of convergence to the asymptotic information rate. Surprisingly, this myopic information rate converges to the asymptotic Fisher information rate with exactly the same relaxation timescales that appear in the myopic entropy rate as it converges to the Shannon entropy rate for the process. We illustrate these results with a sequence of examples that highlight qualitatively distinct features of stochastic processes that shape optimal learning

A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression

The causal structure of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one, an advantage that increases with codeword length. While previously difficult to compute, we express the quantum advantage in closed form using spectral decomposition, leading to direct computation of the quantum communication cost at all encoding lengths, including infinite. This makes clear how finite-codeword compression is controlled by the classical process' cryptic order and allows us to analyze structure within the length-asymptotic regime of infinite-cryptic order (and infinite Markov order) processes.Comment: 21 pages, 13 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/eqc.ht

The impossibility of Landauer's bound for almost every quantum state

The thermodynamic cost of resetting an arbitrary initial state to a particular desired state is lower bounded by Landauer's bound. However, here we demonstrate that this lower bound is necessarily unachievable for nearly every initial state, for any reliable reset mechanism. Since local heating threatens rapid decoherence, this issue is of substantial importance beyond mere energy efficiency. For the case of qubit reset, we find the minimally dissipative state analytically for any reliable reset protocol, in terms of the entropy-flow vector introduced here. This allows us to verify a recent theorem about initial-state dependence of entropy production for any finite-time transformation, as it pertains to quantum state preparation.Comment: 9 pages plus 3 pages of appendices, 3 figure

Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process

New exact results about the nonequilibrium thermodynamics of open quantum systems at arbitrary timescales are obtained by considering all possible variations of initial conditions of a system, its environment, and correlations between them. First we obtain a new quantum-information theoretic equality for entropy production, valid for an arbitrary initial joint state of system and environment. For any finite-time process with a fixed initial environment, we then show that the contraction of the system's distinction -- relative to the minimally dissipative state -- exactly quantifies its thermodynamic dissipation. The quantum component of this dissipation is the change in coherence relative to the minimally dissipative state. Implications for quantum state preparation and local control are explored. For nonunitary processes -- like the preparation of any particular quantum state -- we find that mismatched expectations lead to divergent dissipation as the actual initial state becomes orthogonal to the anticipated one.Comment: 6 pages plus 14 pages of appendices, 1 figur

The evolutionary connection between QSOs and SMGs: molecular gas in far-infrared luminous QSOs at z ∼ 2.5

We present Institut de Radioastronomie Millimétrique Plateau de Bure Interferometer observations of the ^(12)CO (3–2) emission from two far-infrared luminous QSOs at z ∼ 2.5 selected from the Herschel-Astrophysical Tetrahertz Large Area Survey. These far-infrared bright QSOs were selected to have supermassive black holes (SMBHs) with masses similar to those thought to reside in submillimetre galaxies (SMGs) at z ∼ 2.5, making them ideal candidates as systems in the potential transition from an ultraluminous infrared galaxy phase to a submillimetre faint, unobscured, QSO. We detect ^(12)CO (3–2) emission from both QSOs and we compare their baryonic, dynamical and SMBH masses to those of SMGs at the same epoch. We find that these far-infrared bright QSOs have similar dynamical but lower gas masses than SMGs. We combine our results with literature values and find that at a fixed LFIR, far-infrared bright QSOs have ∼50 ± 30 per cent less warm/dense gas than SMGs. Taken together with previous results, which show that QSOs lack the extended, cool reservoir of gas seen in SMGs, this suggests that far-infrared bright QSOs are at a different evolutionary stage. This is consistent with the hypothesis that far-infrared bright QSOs represent a short (∼1 Myr) but ubiquitous phase in the transformation of dust-obscured, gas-rich, starburst-dominated SMGs into unobscured, gas-poor, QSOs