Reciprocal relativity of noninertial frames: quantum mechanics

Noninertial transformations on time-position-momentum-energy space {t,q,p,e} with invariant Born-Green metric ds^2=-dt^2+dq^2/c^2+(1/b^2)(dp^2-de^2/c^2) and the symplectic metric -de/\dt+dp/\dq are studied. This U(1,3) group of transformations contains the Lorentz group as the inertial special case. In the limit of small forces and velocities, it reduces to the expected Hamilton transformations leaving invariant the symplectic metric and the nonrelativistic line element ds^2=dt^2. The U(1,3) transformations bound relative velocities by c and relative forces by b. Spacetime is no longer an invariant subspace but is relative to noninertial observer frames. Born was lead to the metric by a concept of reciprocity between position and momentum degrees of freedom and for this reason we call this reciprocal relativity. For large b, such effects will almost certainly only manifest in a quantum regime. Wigner showed that special relativistic quantum mechanics follows from the projective representations of the inhomogeneous Lorentz group. Projective representations of a Lie group are equivalent to the unitary reprentations of its central extension. The same method of projective representations of the inhomogeneous U(1,3) group is used to define the quantum theory in the noninertial case. The central extension of the inhomogeneous U(1,3) group is the cover of the quaplectic group Q(1,3)=U(1,3)*s H(4). H(4) is the Weyl-Heisenberg group. A set of second order wave equations results from the representations of the Casimir operators

Virtual copies of semisimple Lie algebras in enveloping algebras of semidirect products and Casimir operators

Given a semidirect product $\frak{g}=\frak{s}\uplus\frak{r}$ of semisimple Lie algebras $\frak{s}$ and solvable algebras $\frak{r}$, we construct polynomial operators in the enveloping algebra $\mathcal{U}(\frak{g})$ of $\frak{g}$ that commute with $\frak{r}$ and transform like the generators of $\frak{s}$, up to a functional factor that turns out to be a Casimir operator of $\frak{r}$. Such operators are said to generate a virtual copy of $\frak{s}$ in $\mathcal{U}(\frak{g})$, and allow to compute the Casimir operators of $\frak{g}$ in closed form, using the classical formulae for the invariants of $\frak{s}$. The behavior of virtual copies with respect to contractions of Lie algebras is analyzed. Applications to the class of Hamilton algebras and their inhomogeneous extensions are given.Comment: 20 pages, 2 Appendice

Electronic marking and identification techniques to discourage document copying

Modern computer networks make it possible to distribute documents quickly and economically by electronic means rather than by conventional paper means. However, the widespread adoption of electronic distribution of copyrighted material is currently impeded by the ease of illicit copying and dissemination. In this paper we propose techniques that discourage illicit distribution by embedding each document with a unique codeword. Our encoding techniques are indiscernible by readers, yet enable us to identify the sanctioned recipient of a document by examination of a recovered document. We propose three coding methods, describe one in detail, and present experimental results showing that our identification techniques are highly reliable, even after documents have been photocopied

Simulation of the Spin Field Effect Transistors: Effects of Tunneling and Spin Relaxation on its Performance

A numerical simulation of spin-dependent quantum transport for a spin field effect transistor (spinFET) is implemented in a widely used simulator nanoMOS. This method includes the effect of both spin relaxation in the channel and the tunneling barrier between the source/drain and the channel. Account for these factors permits setting more realistic performance limits for the transistor, especially the magnetoresistance, which is found to be lower compared to earlier predictions. The interplay between tunneling and spin relaxation is elucidated by numerical simulation. Insertion of the tunneling barrier leads to an increased magnetoresistance. Numerical simulations are used to explore the tunneling barrier design issues.Comment: 31 pages, 14 figures, submitted to Journal of Applied Physic

Projective Representations of the Inhomogeneous Hamilton Group: Noninertial Symmetry in Quantum Mechanics

Symmetries in quantum mechanics are realized by the projective representations of the Lie group as physical states are defined only up to a phase. A cornerstone theorem shows that these representations are equivalent to the unitary representations of the central extension of the group. The formulation of the inertial states of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group, and its nonrelativistic limit in terms of the Galilei group, are fundamental examples. Interestingly, neither of these symmetries includes the Weyl-Heisenberg group; the hermitian representations of its algebra are the Heisenberg commutation relations that are a foundation of quantum mechanics. The Weyl-Heisenberg group is a one dimensional central extension of the abelian group and its unitary representations are therefore a particular projective representation of the abelian group of translations on phase space. A theorem involving the automorphism group shows that the maximal symmetry that leaves invariant the Heisenberg commutation relations are essentially projective representations of the inhomogeneous symplectic group. In the nonrelativistic domain, we must also have invariance of Newtonian time. This reduces the symmetry group to the inhomogeneous Hamilton group that is a local noninertial symmetry of Hamilton's equations. The projective representations of these groups are calculated using the Mackey theorems for the general case of a nonabelian normal subgroup

Integrating heterogeneous distributed COTS discrete-event simulation packages: An emerging standards-based approach

This paper reports on the progress made toward the emergence of standards to support the integration of heterogeneous discrete-event simulations (DESs) created in specialist support tools called commercial-off-the-shelf (COTS) discrete-event simulation packages (CSPs). The general standard for heterogeneous integration in this area has been developed from research in distributed simulation and is the IEEE 1516 standard The High Level Architecture (HLA). However, the specific needs of heterogeneous CSP integration require that the HLA is augmented by additional complementary standards. These are the suite of CSP interoperability (CSPI) standards being developed under the Simulation Interoperability Standards Organization (SISO-http://www.sisostds.org) by the CSPI Product Development Group (CSPI-PDG). The suite consists of several interoperability reference models (IRMs) that outline different integration needs of CSPI, interoperability frameworks (IFs) that define the HLA-based solution to each IRM, appropriate data exchange representations to specify the data exchanged in an IF, and benchmarks termed CSP emulators (CSPEs). This paper contributes to the development of the Type I IF that is intended to represent the HLA-based solution to the problem outlined by the Type I IRM (asynchronous entity passing) by developing the entity transfer specification (ETS) data exchange representation. The use of the ETS in an illustrative case study implemented using a prototype CSPE is shown. This case study also allows us to highlight the importance of event granularity and lookahead in the performance and development of the Type I IF, and to discuss possible methods to automate the capture of appropriate values of lookahead

Dynamical Expansion of H II Regions from Ultracompact to Compact Sizes in Turbulent, Self-Gravitating Molecular Clouds

The nature of ultracompact H II regions (UCHRs) remains poorly determined. In particular, they are about an order of magnitude more common than would be expected if they formed around young massive stars and lasted for one dynamical time, around 10^4 yr. We here perform three-dimensional numerical simulations of the expansion of an H II region into self-gravitating, radiatively cooled gas, both with and without supersonic turbulent flows. In the laminar case, we find that H II region expansion in a collapsing core produces nearly spherical shells, even if the ionizing source is off-center in the core. This agrees with analytic models of blast waves in power-law media. In the turbulent case, we find that the H II region does not disrupt the central collapsing region, but rather sweeps up a shell of gas in which further collapse occurs. Although this does not constitute triggering, as the swept-up gas would eventually have collapsed anyway, it does expose the collapsing regions to ionizing radiation. We suggest that these regions of secondary collapse, which will not all themselves form massive stars, may form the bulk of observed UCHRs. As the larger shell will take over 10^5 years to complete its evolution, this could solve the timescale problem. Our suggestion is supported by the ubiquitous observation of more diffuse emission surrounding UCHRs.Comment: accepted to ApJ, 40 pages, 13 b/w figures, changes from v1 include analytic prediction of radio luminosity, better description of code testing, and many minor changes also in response to refere