Asymptotic States and the Definition of the S-matrix in Quantum Gravity

Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy-momentum naturally leads to the gauge theory of volume-preserving diffeormorphisms of an inner Minkowski space. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit - mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality - is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeormorphisms. The so defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally generalized LSZ reduction formulae for scalar, Dirac and gauge fields are established which allow to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in an earlier paper [8] any transition amplitude can in principle be computed to any order in perturbative quantum gravity.Comment: 35 page

Unified model of voltage/current mode control to predict saddle-node bifurcation

A unified model of voltage mode control (VMC) and current mode control (CMC) is proposed to predict the saddle-node bifurcation (SNB). Exact SNB boundary conditions are derived, and can be further simplified in various forms for design purpose. Many approaches, including steady-state, sampled-data, average, harmonic balance, and loop gain analyses are applied to predict SNB. Each approach has its own merits and complement the other approaches.Comment: Submitted to International Journal of Circuit Theory and Applications on December 23, 2010; Manuscript ID: CTA-10-025

Quantum stochastic integrals as operators

We construct quantum stochastic integrals for the integrator being a martingale in a von Neumann algebra, and the integrand -- a suitable process with values in the same algebra, as densely defined operators affiliated with the algebra. In the case of a finite algebra we allow the integrator to be an $L^2$--martingale in which case the integrals are $L^2$--martingales too

Heat-treatment of metal parts facilitated by sand embedment

Embedding metal parts of complex shape in sand contained in a steel box prevents strains and warping during heat treatment. The sand not only provides a simple, inexpensive support for the parts but also ensures more uniform distribution of heat to the parts

Magnetic field dependence of the antiferromagnetic phase transitions in Co-doped YbRh_2Si_2

We present first specific-heat data of the alloy Yb(Rh_(1-x)Co_x)_2Si_2 at intermediate Co-contents x=0.18, 0.27, and 0.68. The results already point to a complex magnetic phase diagram as a function of composition. Co-doping of YbRh_2Si_2 (T_N^{x=0}=72 mK) stabilizes the magnetic phase due to the volume decrease of the crystallographic unit cell. The magnetic phase transitions are clearly visible as pronounced anomalies in C^{4f}(T)/T and can be suppressed by applying a magnetic field. Going from x=0.18 to x=0.27 we observe a change from two mean-field (MF) like magnetic transitions at T_N^{0.18}=1.1 K and T_L^{0.18}=0.65 K to one sharp \lambda-type transition at T_N^{0.27}=1.3 K. Preliminary measurements under magnetic field do not confirm the field-induced first-order transition suggested in the literature. For x=0.68 we find two transitions at T_N^{0.68}=1.14 K and T_L^{0.68}=1.06 K.Comment: Accepted for the ICM proceedings 200

Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control

Sampled-data analysis and harmonic balance analysis are applied to analyze switching DC-DC converters under constant on-time control. Design-oriented boundary conditions for the period-doubling bifurcation and the saddle-node bifurcation are derived. The required ramp slope to avoid the bifurcations and the assigned pole locations associated with the ramp are also derived. The derived boundary conditions are more general and accurate than those recently obtained. Those recently obtained boundary conditions become special cases under the general modeling approach presented in this paper. Different analyses give different perspectives on the system dynamics and complement each other. Under the sampled-data analysis, the boundary conditions are expressed in terms of signal slopes and the ramp slope. Under the harmonic balance analysis, the boundary conditions are expressed in terms of signal harmonics. The derived boundary conditions are useful for a designer to design a converter to avoid the occurrence of the period-doubling bifurcation and the saddle-node bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications on August 10, 2011; Manuscript ID: CTA-11-016

Figure of merit for direct-detection optical channels

The capacity and sensitivity of a direct-detection optical channel are calculated and compared to those of a white Gaussian noise channel. Unlike Gaussian channels in which the receiver performance can be characterized using the noise temperature, the performance of the direct-detection channel depends on both signal and background noise, as well as the ratio of peak to average signal power. Because of the signal-power dependence of the optical channel, actual performance of the channel can be evaluated only by considering both transmit and receive ends of the systems. Given the background noise power and the modulation bandwidth, however, the theoretically optimum receiver sensitivity can be calculated. This optimum receiver sensitivity can be used to define the equivalent receiver noise temperature and calculate the corresponding G/T product. It should be pointed out, however, that the receiver sensitivity is a function of signal power, and care must be taken to avoid deriving erroneous projections of the direct-detection channel performance