The Prevalence of Carbon-13 in Respiratory Carbon Dioxide As an Indicator of the Type of Endogenous Substrate. The change from lipid to carbohydrate during the respiratory rise in potato slices

Isotope discrimination is a common feature of biosynthesis in nature, with the result that different classes of carbon compounds frequently display different 13C/12C ratios. The 13C/12C ratio of lipid in potato tuber tissue is considerably lower than that for starch or protein. We have collected respiratory CO2 from potato discs in successive periods through 24 hr from the time of cutting—an interval in which the respiration rate rises 3–5-fold. The 13C/12C ratio of the evolved CO2 was determined for each period, and compared with the 13C/12C ratios of the major tissue metabolites. In the first hours the carbon isotope ratio of the CO2 matches that of lipid. With time, the ratio approaches that typical of starch or protein. An estimation has been made of the contribution of lipid and carbohydrate to the total respiration at each juncture. In connection with additional observations, it was deduced that the basal, or initial, respiration represents lipid metabolism —- possibly the alpha-oxidation of long chain fatty acids -— while the developed repiration represents conventional tricarboxylic acid cycle oxidation of the products of carbohydrate glycolysis. The true isotopic composition of the respiratory CO2 may be obscured by fractionation attending the refixation of CO2 during respiration, and by CO2 arising from dissolved CO2 and bicarbonate preexisting in the tuber. Means are described for coping with both pitfalls

Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products are local functionals of the off shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's 'Action Ward Identity'. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.Comment: 76 pages, to appear in Rev. Math. Phy

Thermoelectric Amplification of Phonons in Graphene

Amplification of acoustic phonons due to an external temperature gredient ($\nabla T$) in Graphene was studied theoretically. The threshold temperature gradient $(\nabla T)_0^{g}$ at which absorption switches over to amplification in Graphene was evaluated at various frequencies $\omega_q$ and temperatures $T$. For $T = 77K$ and frequency $\omega_q = 12THz$, $(\nabla T)_0^{g} = 0.37Km^{-1}$. The calculation was done in the regime at $ql >> 1$. The dependence of the normalized ($\Gamma/\Gamma_0$) on the frequency $\omega_q$ and the temperature gradient $(\nabla T/T)$ are evaluated numerically and presented graphically. The calculated $(\nabla T)_0^{g}$ for Graphene is lower than that obtained for homogeneous semiconductors ($n-InSb$) $(\nabla T)_0^{hom} \approx 10^3Kcm^{-1}$, Superlattices $(\nabla T)_0^{SL} = 384Kcm^{-1}$, Cylindrical Quantum Wire $(\nabla T)_0^{cqw} \approx 10^2Kcm^{-1}$. This makes Graphene a much better material for thermoelectric phonon amplifier.Comment: 12 Pages, 6 figure

Online unit clustering in higher dimensions

We revisit the online Unit Clustering and Unit Covering problems in higher dimensions: Given a set of $n$ points in a metric space, that arrive one by one, Unit Clustering asks to partition the points into the minimum number of clusters (subsets) of diameter at most one; while Unit Covering asks to cover all points by the minimum number of balls of unit radius. In this paper, we work in $\mathbb{R}^d$ using the $L_\infty$ norm. We show that the competitive ratio of any online algorithm (deterministic or randomized) for Unit Clustering must depend on the dimension $d$. We also give a randomized online algorithm with competitive ratio $O(d^2)$ for Unit Clustering}of integer points (i.e., points in $\mathbb{Z}^d$, $d\in \mathbb{N}$, under $L_{\infty}$ norm). We show that the competitive ratio of any deterministic online algorithm for Unit Covering is at least $2^d$. This ratio is the best possible, as it can be attained by a simple deterministic algorithm that assigns points to a predefined set of unit cubes. We complement these results with some additional lower bounds for related problems in higher dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

Perturbative Gravity in the Causal Approach

Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system (massless and massive). Then we investigate the interaction of massless gravity with matter (described by scalars and spinors) and massless Yang-Mills fields. We obtain a difference with respect to the classical field theory due to the fact that in quantum field theory one cannot enforce the divergenceless property on the vector potential and this spoils the divergenceless property of the usual energy-momentum tensor. To correct this one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio

Vacuum polarization around stars: nonlocal approximation

We compute the vacuum polarization associated with quantum massless fields around stars with spherical symmetry. The nonlocal contribution to the vacuum polarization is dominant in the weak field limit, and induces quantum corrections to the exterior metric that depend on the inner structure of the star. It also violates the null energy conditions. We argue that similar results also hold in the low energy limit of quantum gravity. Previous calculations of the vacuum polarization in spherically symmetric spacetimes, based on local approximations, are not adequate for newtonian stars.Comment: 8 pages, no figure

Relating on-shell and off-shell formalism in perturbative quantum field theory

In the on-shell formalism (mostly used in perturbative quantum field theory) the entries of the time ordered product T are on-shell fields (i.e. the basic fields satisfy the free field equations). With that, (multi)linearity of T is incompatible with the Action Ward identity. This can be circumvented by using the off-shell formalism in which the entries of T are off-shell fields. To relate on- and off-shell formalism correctly, a map sigma from on-shell fields to off-shell fields was introduced axiomatically by Duetsch and Fredenhagen. In that paper it was shown that, in the case of one real scalar field in N=4 dimensional Minkowski space, these axioms have a unique solution. However, this solution was given there only recursively. We solve this recurrence relation and give a fully explicit expression for sigma in the cases of the scalar, Dirac and gauge fields for arbitrary values of the dimension N.Comment: The case of gauge fields was added. 16 page

Absorption and optical selection rules of tunable excitons in biased bilayer graphene

Biased bilayer graphene, with its easily tunable band gap, presents itself as the ideal system to explore the excitonic effect in graphene-based systems. In this paper we study the excitonic optical response of such a system by combining a tight-binding model with the solution of the Bethe-Salpeter equation, the latter being solved in a semianalytical manner, requiring a single numerical quadrature, thus allowing for a transparent calculation. With our approach we start by analytically obtaining the optical selection rules, followed by the computation of the absorption spectrum for the case of a biased bilayer encapsulated in hexagonal boron nitride, a system which has been the subject of a recent experimental study. Excellent agreement is seen when we compare our theoretical prediction with the experimental data.N.M.R.P. acknowledges support from the Portuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding UIDB/04650/2020. J.C.G.H. acknowledges the Center of Physics for a grant funded by the UIDB/04650/2020 strategic project. N.M.R.P. also acknowledges support from the European Commission through the project Graphene Driven Revolutions in ICT and Beyond (Ref. No. 881603, CORE 3), COMPETE 2020, PORTUGAL 2020, FEDER, and the FCT through projects POCI-01-0145-FEDER-028114, POCI-01-0145-FEDER-02888, and PTDC/NANOPT/29265/2017

Continuity of the four-point function of massive ϕ44\phi_4^4-theory above threshold

In this paper we prove that the four-point function of massive \vp_4^4-theory is continuous as a function of its independent external momenta when posing the renormalization condition for the (physical) mass on-shell. The proof is based on integral representations derived inductively from the perturbative flow equations of the renormalization group. It closes a longstanding loophole in rigorous renormalization theory in so far as it shows the feasibility of a physical definition of the renormalized coupling.Comment: 23 pages; to appear in Rev. Math. Physics few corrections, two explanatory paragraphs adde

`Operational' Energy Conditions

I show that a quantized Klein-Gordon field in Minkowski space obeys an `operational' weak energy condition: the energy of an isolated device constructed to measure or trap the energy in a region, plus the energy it measures or traps, cannot be negative. There are good reasons for thinking that similar results hold locally for linear quantum fields in curved space-times. A thought experiment to measure energy density is analyzed in some detail, and the operational positivity is clearly manifested. If operational energy conditions do hold for quantum fields, then the negative energy densities predicted by theory have a will-o'-the-wisp character: any local attempt to verify a total negative energy density will be self-defeating on account of quantum measurement difficulties. Similarly, attempts to drive exotic effects (wormholes, violations of the second law, etc.) by such densities may be defeated by quantum measurement problems. As an example, I show that certain attempts to violate the Cosmic Censorship principle by negative energy densities are defeated. These quantum measurement limitations are investigated in some detail, and are shown to indicate that space-time cannot be adequately modeled classically in negative energy density regimes.Comment: 18 pages, plain Tex, IOP macros. Expanded treatment of measurement problems for space-time, with implications for Cosmic Censorship as an example. Accepted by Classical and Quantum Gravit