Hilbert-Post completeness for the state and the exception effects

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.Comment: Siegfried Rump (Hamburg University of Technology), Chee Yap (Courant Institute, NYU). Sixth International Conference on Mathematical Aspects of Computer and Information Sciences , Nov 2015, Berlin, Germany. 2015, LNC

Patterns for computational effects arising from a monad or a comonad

This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used for proving properties of different effects. The first pattern provides inference rules which can be interpreted in the Kleisli category of a monad and the coKleisli category of the associated comonad. In a dual way, the second pattern provides inference rules which can be interpreted in the coKleisli category of a comonad and the Kleisli category of the associated monad. The logics combine a 3-tier effect system for terms consisting of pure terms and two other kinds of effects called 'constructors/observers' and 'modifiers', and a 2-tier system for 'up-to-effects' and 'strong' equations. Each pattern provides generic rules for dealing with any monad (respectively comonad), and it can be extended with specific rules for each effect. The paper presents two use cases: a language with exceptions (using the standard monadic semantics), and a language with state (using the less standard comonadic semantics). Finally, we prove that the obtained inference system for states is Hilbert-Post complete

The Ongoing Impact of Modular Localization on Particle Theory

Modular localization is the concise conceptual formulation of causal localization in the setting of local quantum physics. Unlike QM it does not refer to individual operators but rather to ensembles of observables which share the same localization region, as a result it explains the probabilistic aspects of QFT in terms of the impure KMS nature arising from the local restriction of the pure vacuum. Whereas it played no important role in the perturbation theory of low spin particles, it becomes indispensible for interactions which involve higher spin $s\geq1$ fields, where is leads to the replacement of the operator (BRST) gauge theory setting in Krein space by a new formulation in terms of stringlocal fields in Hilbert space. The main purpose of this paper is to present new results which lead to a rethinking of important issues of the Standard Model concerning massive gauge theories and the Higgs mechanism. We place these new findings into the broader context of ongoing conceptual changes within QFT which already led to new nonperturbative constructions of models of integrable QFTs. It is also pointed out that modular localization does not support ideas coming from string theory, as extra dimensions and Kaluza-Klein dimensional reductions outside quasiclassical approximations. Apart from hologarphic projections on null-surfaces, holograhic relations between QFT in different spacetime dimensions violate the causal completeness property, this includes in particular the Maldacena conjecture. Last not least, modular localization sheds light onto unsolved problems from QFT's distant past since it reveals that the Einstein-Jordan conundrum is really an early harbinger of the Unruh effect.Comment: a small text overlap with unpublished arXiv:1201.632

Clean Positive Operator Valued Measures

In quantum mechanics the statistics of the outcomes of a measuring apparatus is described by a positive operator valued measure (POVM). A quantum channel transforms POVM's into POVM's, generally irreversibly, thus loosing some of the information retrieved from the measurement. This poses the problem of which POVM's are "undisturbed", namely they are not irreversibly connected to another POVM. We will call such POVM clean. In a sense, the clean POVM's would be "perfect", since they would not have any additional "extrinsical" noise. Quite unexpectedly, it turns out that such cleanness property is largely unrelated to the convex structure of POVM's, and there are clean POVM's that are not extremal and vice-versa. In this paper we solve the cleannes classification problem for number n of outcomes n<=d (d dimension of the Hilbert space), and we provide a a set of either necessary or sufficient conditions for n>d, along with an iff condition for the case of informationally complete POVM's for n=d^2.Comment: Minor changes. amsart 21 pages. Accepted for publication on J. Math. Phy

Full configuration interaction approach to the few-electron problem in artificial atoms

We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong interaction regime. The implementation relies on a single-particle representation, but it is independent of the choice of the single-particle basis and, therefore, of the details of the device and configuration of external fields. Assuming no truncation of the Fock space of Slater determinants generated from the chosen single-particle basis, the code may tackle regimes where Coulomb interaction very effectively mixes many determinants. Typical strongly correlated systems lead to very large diagonalization problems; in our implementation, the secular equation is reduced to its minimal rank by exploiting the symmetry of the effective-mass interacting Hamiltonian, including square total spin. The resulting Hamiltonian is diagonalized via parallel implementation of the Lanczos algorithm. The code gives access to both wave functions and energies of first excited states. Excellent code scalability in a parallel environment is demonstrated; accuracy is tested for the case of up to eight electrons confined in a two-dimensional harmonic trap as the density is progressively diluted and correlation becomes dominant. Comparison with previous Quantum Monte Carlo simulations in the Wigner regime demonstrates power and flexibility of the method.Comment: RevTeX 4.0, 18 pages, 6 tables, 9 postscript b/w figures. Final version with new material. Section 6 on the excitation spectrum has been added. Some material has been moved to two appendices, which appear in the EPAPS web depository in the published versio