Moyal products -- a new perspective on quasi-hermitian quantum mechanics

The rationale for introducing non-hermitian Hamiltonians and other observables is reviewed and open issues identified. We present a new approach based on Moyal products to compute the metric for quasi-hermitian systems. This approach is not only an efficient method of computation, but also suggests a new perspective on quasi-hermitian quantum mechanics which invites further exploration. In particular, we present some first results which link the Berry connection and curvature to non-perturbative properties and the metric.Comment: 14 pages. Submitted to J Phys A special issue on The Physics of Non-Hermitian Operator

Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations

The family of metric operators, constructed by Musumbu {\sl et al} (2007 {\sl J. Phys. A: Math. Theor.} {\bf 40} F75), for a harmonic oscillator Hamiltonian augmented by a non-Hermitian $\cal PT$-symmetric part, is re-examined in the light of an su(1,1) approach. An alternative derivation, only relying on properties of su(1,1) generators, is proposed. Being independent of the realization considered for the latter, it opens the way towards the construction of generalized non-Hermitian (not necessarily $\cal PT$-symmetric) oscillator Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.Comment: 11 pages, no figure; changes in title and in paragraphs 3 and 5; final published versio

Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem

In a previous paper (arXiv:math-ph/0604055) we introduced a very simple PT-symmetric non-Hermitian Hamiltonian with real spectrum and derived a closed formula for the metric operator relating the problem to a Hermitian one. In this note we propose an alternative formula for the metric operator, which we believe is more elegant and whose construction -- based on a backward use of the spectral theorem for self-adjoint operators -- provides new insights into the nature of the model.Comment: LaTeX, 6 page

Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations

A harmonic oscillator Hamiltonian augmented by a non-Hermitian \pt-symmetric part and its su(1,1) generalizations, for which a family of positive-definite metric operators was recently constructed, are re-examined in a supersymmetric context. Quasi-Hermitian supersymmetric extensions of such Hamiltonians are proposed by enlarging su(1,1) to a ${\rm su}(1,1/1) \sim {\rm osp}(2/2, \R)$ superalgebra. This allows the construction of new non-Hermitian Hamiltonians related by similarity to Hermitian ones. Some examples of them are reviewed.Comment: 15 pages, no figure; published versio

Loosely bound hyperons in the SU(3) Skyrme model

Hyperon pairs bound in deuteron like states are obtained within the SU(3) Skyrme model in agreement with general expectations from boson exchange models. The central binding from the flavor symmetry breaking terms increases with the strangeness contents of the interacting baryons whereas the kinetic non-linear $\sigma$-model term fixes the spin and isospin of the bound pair. We give a complete account of the interactions of octet baryons within the product approximation to baryon number $B=2$ configurations.Comment: 35 pages REVTEX including 2 figs, with 3 further figs available on request from [email protected] or from [email protected] SI-94-TP3S2; STPHY-Th/94-

Experimental evidence of non-Amontons behaviour at a multicontact interface

We report on normal stress field measurements at the multicontact interface between a rough elastomeric film and a smooth glass sphere under normal load, using an original MEMS-based stress sensing device. These measurements are compared to Finite Elements Method calculations with boundary conditions obeying locally Amontons' rigid-plastic-like friction law with a uniform friction coefficient. In dry contact conditions, significant deviations are observed which decrease with increasing load. In lubricated conditions, the measured profile recovers almost perfectly the predicted profile. These results are interpreted as a consequence of the finite compliance of the multicontact interface, a mechanism which is not taken into account in Amontons' law

Quantum Big Bang without fine-tuning in a toy-model

The question of possible physics before Big Bang (or after Big Crunch) is addressed via a schematic non-covariant simulation of the loss of observability of the Universe. Our model is drastically simplified by the reduction of its degrees of freedom to the mere finite number. The Hilbert space of states is then allowed time-dependent and singular at the critical time $t=t_c$. This option circumvents several traditional theoretical difficulties in a way illustrated via solvable examples. In particular, the unitary evolution of our toy-model quantum Universe is shown interruptible, without any fine-tuning, at the instant of its bang or collapse $t= t_c$.Comment: 20 pp., 1 fig., invited talk for the conference "10th Workshop on Quantization, Dualities and Integrable Systems" (April 22 - 24, 2011), http://qdis.emu.edu.tr/index.htm

Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry and iii) the -x^4-potential, which serves as a toy model for the quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos correcte

Testing earthquake links in Mexico from 1978 to the 2017 M = 8.1 Chiapas and M = 7.1 Puebla Shocks

The M = 8.1 Chiapas and the M = 7.1 Puebla earthquakes occurred in the bending part of the subducting Cocos plate 11 days and ~600 km apart, a range that puts them well outside the typical aftershock zone. We find this to be a relatively common occurrence in Mexico, with 14% of M > 7.0 earthquakes since 1900 striking more than 300 km apart and within a 2 week interval, not different from a randomized catalog. We calculate the triggering potential caused by crustal stress redistribution from large subduction earthquakes over the last 40 years. There is no evidence that static stress transfer or dynamic triggering from the 8 September Chiapas earthquake promoted the 19 September earthquake. Both recent earthquakes were promoted by past thrust events instead, including delayed afterslip from the 2012 M = 7.5 Oaxaca earthquake. A repeated pattern of shallow thrust events promoting deep intraslab earthquakes is observed over the past 40 years

Neurodevelopmental evaluation and referral practices in children with congenital heart disease in central South Africa

Introduction: Children with congenital heart disease (CHD) are at higher risk for developmental delays than the general population. The American Heart Association (AHA) published a guideline to address these concerns in 2012. This study determined the neurodevelopmental evaluation and referral practices of practitioners in central South Africa.Method: An online survey was administered to practitioners (n=45) including paediatric cardiologists (n=4), cardiothoracic surgeons (n=4) and general paediatricians (n=37). Information on practitioner characteristics, awareness of the 2012 AHA guideline; and neurodevelopmental evaluation and referral practices was collected.Results: Twenty-one practitioners responded, including paediatric cardiologists (n=4), cardiothoracic surgeons (n=2) and paediatricians (n=15). Data for 20 practitioners was included. Despite most practitioners (n=18) indicating guidelines for the management of development were important, the majority (n=16; 80%) were unaware of the guideline. Most practitioners (n=18; 90%) failed to risk stratify children to identify those to be evaluated. Children with developmental delays were referred for formal developmental evaluation (n=11; 55%) and to intervention therapies (n= 15; 75%).Conclusion: Most practitioners are unaware of the 2012 AHA guideline. Awareness of the developmental risks associated with CHD and implementation of the guideline could promote early identification of developmental delays with referral to intervention therapies