Sum rules for leading and subleading form factors in Heavy Quark Effective Theory using the non-forward amplitude

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and L_mag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil. This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the chi_i(w) and the shape of the elastic IW function xi(w). An important theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) = chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should be taken into account in the exclusive determination of |V_(cb)|.Comment: Invited talk to the International Workshop on Quantum Chromodynamics : Theory and Experiment, Conversano (Bari, Italy), 16-20 June 200

Lagrangian perturbations at order 1/mQ_{\bf Q} and the non-forward amplitude in Heavy Quark Effective Theory

We pursue the program of the study of the non-forward amplitude in HQET. We obtain new sum rules involving the elastic subleading form factors $\chi_i(w)$ $(i = 1,2, 3)$ at order $1/m_Q$ that originate from the ${\cal L}_{kin}$ and ${\cal L}_{mag}$ perturbations of the Lagrangian. To obtain these sum rules we use two methods. On the one hand we start simply from the definition of these subleading form factors and, on the other hand, we use the Operator Product Expansion. To the sum rules contribute only the same intermediate states $(j^P, J^P) = ({1 \over 2}^-, 1^-), ({3\over 2}^-, 1^-)$ that enter in the $1/m_Q^2$ corrections of the axial form factor $h_{A_1}(w)$ at zero recoil. This allows to obtain a lower bound on $- \delta_{1/m^2}^{(A_1)}$ in terms of the $\chi_i(w)$ and the shape of the elastic IW function $\xi (w)$. We find also lower bounds on the $1/m_Q^2$ correction to the form factors $h_+(w)$ and $h_1(w)$ at zero recoil. An important theoretical implication is that $\chi '_1(1)$, $\chi_2(1)$ and $\chi '_3(1)$ ($\chi_1(1) = \chi_3(1) = 0$ from Luke theorem) must vanish when the slope and the curvature attain their lowest values $\rho^2 \to {3 \over 4}$, $\sigma^2 \to {15 \over 16}$. We discuss possible implications on the precise determination of $|V_{cb}|$

Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination

We present a criterion, based on three commutator relations, that allows to decide whether two self-adjoint matrices with non-overlapping support are simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they can be simultaneously brought into a diagonal structure with 2x2-dimensional blocks. Application of this criterion to unambiguous state discrimination provides a systematic test whether the given problem is reducible to a solvable structure. As an example, we discuss unambiguous state comparison.Comment: 5 pages, discussion of related work adde

Mass transfer characteristics in structured packing for CO2 emission reduction processes

Acid gas treating and CO2 capture from flue gas by absorption have gained wide importance over the past few decades. With the implementation of more stringent environmental regulations and the awareness of the greenhouse effect, the need for efficient removal of acid gases such as CO2 (carbon dioxide) has increased significantly. Therefore, additional effort for research in this field is inevitable. For flue gas processes the ratio of absorption solvent to gas throughput is very different compared to acid gas treating processes owing to the atmospheric pressures and the dilution effect of combustion air. Moreover, in flue gas applications pressure drop is a very important process parameter. Packing types are required that allow for low pressure drop in combination with high interfacial areas at low liquid loading per square meter. The determination of interfacial areas in gas-liquid contactors by means of the chemical method (Danckwerts, P. V. Gas-liquid reactions; McGraw-Hill: London, 1970) has been very frequently applied. Unfortunately, many of the model systems proposed in the literature are reversible and therefore this condition possibly is not met. Versteeg et al. (Versteeg, G. F.; Kuipers, J. A. M.; Beckum, F. P. H.; van Swaaij, W. P. M. Chem. Eng. Sci. 1989, 44, 2292) have demonstrated that for reversible reactions the conditions for the determination of the interfacial area by means of the chemical method are much more severe. In a study by Raynal et al. (Raynal, L.; Ballaguet, J. P.; Berrere-Tricca, C. Chem. Eng. Sci. 2004, 59, 5395), it has been shown that there is a dependency of the interfacial area on the packing height. Unfortunately, most model systems used, e.g., CO2-caustic soda (as used by Raynal et al.), are much more complex and consist of (a set of) reversible reaction(s). The natures of these systems make the conditions at which the interfacial area can be determined much more severe and put more limitations on the process conditions and experimental equipment than a priori can be expected. Therefore, an extended absorption model is required to determine the conditions at which the interfacial area can be measured without detailed knowledge of the values of the liquid-side mass transfer coefficient, k1, beforehand.

On Verifying Causal Consistency

Causal consistency is one of the most adopted consistency criteria for distributed implementations of data structures. It ensures that operations are executed at all sites according to their causal precedence. We address the issue of verifying automatically whether the executions of an implementation of a data structure are causally consistent. We consider two problems: (1) checking whether one single execution is causally consistent, which is relevant for developing testing and bug finding algorithms, and (2) verifying whether all the executions of an implementation are causally consistent. We show that the first problem is NP-complete. This holds even for the read-write memory abstraction, which is a building block of many modern distributed systems. Indeed, such systems often store data in key-value stores, which are instances of the read-write memory abstraction. Moreover, we prove that, surprisingly, the second problem is undecidable, and again this holds even for the read-write memory abstraction. However, we show that for the read-write memory abstraction, these negative results can be circumvented if the implementations are data independent, i.e., their behaviors do not depend on the data values that are written or read at each moment, which is a realistic assumption.Comment: extended version of POPL 201

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.Comment: 19 page

Optimality of entropic uncertainty relations

The entropic uncertainty relation proven by Maassen and Uffink for arbitrary pairs of two observables is known to be non-optimal. Here, we call an uncertainty relation optimal, if the lower bound can be attained for any value of either of the corresponding uncertainties. In this work we establish optimal uncertainty relations by characterising the optimal lower bound in scenarios similar to the Maassen-Uffink type. We disprove a conjecture by Englert et al. and generalise various previous results. However, we are still far from a complete understanding and, based on numerical investigation and analytical results in small dimension, we present a number of conjectures.Comment: 24 pages, 10 figure