Space of State Vectors in PT Symmetrical Quantum Mechanics

Space of states of PT symmetrical quantum mechanics is examined. Requirement that eigenstates with different eigenvalues must be orthogonal leads to the conclusion that eigenfunctions belong to the space with an indefinite metric. The self consistent expressions for the probability amplitude and average value of operator are suggested. Further specification of space of state vectors yield the superselection rule, redefining notion of the superposition principle. The expression for the probability current density, satisfying equation of continuity and vanishing for the bound state, is proposed.Comment: Revised version, explicit expressions for average values and probability amplitude adde

Common Space of Spin and Spacetime

Given Lorentz invariance in Minkowski spacetime, we investigate a common space of spin and spacetime. To obtain a finite spinor representation of the non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an indefinite inner product space (IIPS) with a normalized positive probability. In this IIPS, the common momentum and common variable of a massive fermion turn out to be ``doubly strict plus-operators''. Due to this nice property, it is straightforward to show an uncertainty relation between fermion mass and proper time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint, and the fermion field equations are derivable from the Lagrangians. Finally, the nonlinear QED equations and Lagrangians are presented as an example.Comment: 17 pages, a reference corrected, final version published on Foundations of Physics Letters in June of 2005, as a personal tribute to Einstein and Dira

Pseudo-Hermitian Hamiltonians, indefinite inner product spaces and their symmetries

We extend the definition of generalized parity $P$, charge-conjugation $C$ and time-reversal $T$ operators to nondiagonalizable pseudo-Hermitian Hamiltonians, and we use these generalized operators to describe the full set of symmetries of a pseudo-Hermitian Hamiltonian according to a fourfold classification. In particular we show that $TP$ and $CTP$ are the generators of the antiunitary symmetries; moreover, a necessary and sufficient condition is provided for a pseudo-Hermitian Hamiltonian $H$ to admit a $P$-reflecting symmetry which generates the $P$-pseudounitary and the $P$-pseudoantiunitary symmetries. Finally, a physical example is considered and some hints on the $P$-unitary evolution of a physical system are also given.Comment: 20 page

Resummation of mass terms in perturbative massless quantum field theory

The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form $-\frac{m^2}{2} \Phi^2$ to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde

Robustness of circadian clocks to daylight fluctuations: hints from the picoeucaryote Ostreococcus tauri

The development of systemic approaches in biology has put emphasis on identifying genetic modules whose behavior can be modeled accurately so as to gain insight into their structure and function. However most gene circuits in a cell are under control of external signals and thus quantitative agreement between experimental data and a mathematical model is difficult. Circadian biology has been one notable exception: quantitative models of the internal clock that orchestrates biological processes over the 24-hour diurnal cycle have been constructed for a few organisms, from cyanobacteria to plants and mammals. In most cases, a complex architecture with interlocked feedback loops has been evidenced. Here we present first modeling results for the circadian clock of the green unicellular alga Ostreococcus tauri. Two plant-like clock genes have been shown to play a central role in Ostreococcus clock. We find that their expression time profiles can be accurately reproduced by a minimal model of a two-gene transcriptional feedback loop. Remarkably, best adjustment of data recorded under light/dark alternation is obtained when assuming that the oscillator is not coupled to the diurnal cycle. This suggests that coupling to light is confined to specific time intervals and has no dynamical effect when the oscillator is entrained by the diurnal cycle. This intringuing property may reflect a strategy to minimize the impact of fluctuations in daylight intensity on the core circadian oscillator, a type of perturbation that has been rarely considered when assessing the robustness of circadian clocks

MOST light-curve analysis of the γ Doradus pulsator HR 8799, showing resonances and amplitude variations

Context. The central star of the HR 8799 system is a γ Doradus-type pulsator. The system harbours four planetary-mass companions detected by direct imaging, and is a good solar system analogue. The masses of the companions are not accurately known because the estimation depends greatly on the age of the system, which is also not known with sufficient accuracy. Asteroseismic studies of the star might help to better constrain the age of HR 8799. We organized an extensive photometric and multi-site spectroscopic observing campaign to study the pulsations of the central star. Aims: The aim of the present study is to investigate the pulsation properties of HR 8799 in detail via the ultra-precise 47 d nearly continuous photometry obtained with the Microvariability and Oscillations in STars (MOST) space telescope, and to find as many independent pulsation modes as possible, which is the prerequisite for an asteroseismic age determination. Methods: We carried out Fourier analysis of the wide-band photometric time series. Results: We find that resonance and sudden amplitude changes characterize the pulsation of HR 8799. The dominant frequency is always at f1 = 1.978 d-1.Many multiples of one-ninth of the dominant frequency appear in the Fourier spectrum of the MOST data: n/9 f1, where n = {1,2,3,4,5,6,7,8,9,10,13,14,17,18}. Our analysis also reveals that many of these peaks show strong amplitude decrease and phase variations even on the 47 d time scale. The dependencies between the pulsation frequencies of HR 8799 make the planned subsequent asteroseismic analysis rather difficult. We point out some resemblance between the light curve of HR 8799 and the modulated pulsation light curves of Blazhko RR Lyrae stars. Based on data from the MOST satellite, a Canadian Space Agency mission, jointly operated by Dynacon Inc., the University of Toronto Institute for Aerospace Studies and the University of British Columbia, with the assistance of the University of Vienna

Role of the electro-thermo-mechanical multiple coupling on the operation of RF microswitch

A phenomenological approach is proposed to identify some effects occurring within the structure of the microswitch conceived for radio frequency application. This microsystem is operated via a nonlinear electromechanical action imposed by the applied voltage. Unfortunately, it can be affected by residual stress, due to the microfabrication process, therefore axial and flexural behaviors are strongly coupled. This coupling increases the actuation voltage required to achieve the so-called ‘‘pull-in'' condition. Moreover, temperature may strongly affect strain and stress distributions, respectively. Environmental temperature, internal dissipation of material, thermo-elastic and Joule effects play different roles on the microswitch flexural isplacement. Sometimes buckling phenomenon evenly occurs. Literature show that all those issues make difficult an effective computation of ‘‘pull-in'' and ‘‘pull-out'' voltages for evenly distinguishing the origin of some failures detected in operation. Analysis, numerical methods and experiments are applied to an industrial test case to investigate step by step the RF-microswitch operation. Multiple electro-hermomechanical coupling is first modeled to have a preliminary and comprehensive description of the microswitch behavior and of its reliability. ‘‘Pull-in'' and ‘‘pull-out'' tests are then performed to validate the proposed models and to find suitable criteria to design the RF-MEM