Parameters for Twisted Representations

The study of Hermitian forms on a real reductive group $G$ gives rise, in the unequal rank case, to a new class of Kazhdan-Lusztig-Vogan polynomials. These are associated with an outer automorphism $\delta$ of $G$, and are related to representations of the extended group $$. These polynomials were defined geometrically by Lusztig and Vogan in "Quasisplit Hecke Algebras and Symmetric Spaces", Duke Math. J. 163 (2014), 983--1034. In order to use their results to compute the polynomials, one needs to describe explicitly the extension of representations to the extended group. This paper analyzes these extensions, and thereby gives a complete algorithm for computing the polynomials. This algorithm is being implemented in the Atlas of Lie Groups and Representations software

Coarsening of "clouds" and dynamic scaling in a far-from-equilibrium model system

A two-dimensional lattice gas of two species, driven in opposite directions by an external force, undergoes a jamming transition if the filling fraction is sufficiently high. Using Monte Carlo simulations, we investigate the growth of these jams ("clouds"), as the system approaches a non-equilibrium steady state from a disordered initial state. We monitor the dynamic structure factor $S(k_x,k_y;t)$ and find that the $k_x=0$ component exhibits dynamic scaling, of the form $S(0,k_y;t)=t^\beta \tilde{S}(k_yt^\alpha)$. Over a significant range of times, we observe excellent data collapse with $\alpha=1/2$ and $\beta=1$. The effects of varying filling fraction and driving force are discussed

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Geometrical view of quantum entanglement

Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which apparently has no classical counterpart. We demonstrate here how quantum entanglement may be within the de Broglie-Bohm interpretation of quantum mechanics visualized in geometrical terms, giving new insight into this mysterious phenomenon and a language to describe it. On the basis of our analysis of the dynamics of a pair of qubits, quantum entanglement is linked to concurrent motion of angular momenta in the Bohmian space of hidden variables and to the average angle between these momenta

Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."Comment: 11 pages, 3 figures, v2: Minor change

Transverse Momentum Correlations in Relativistic Nuclear Collisions

From the correlation structure of transverse momentum $p_t$ in relativistic nuclear collisions we observe for the first time temperature/velocity structure resulting from low-$Q^2$ partons. Our novel analysis technique does not invoke an {\em a priori} jet hypothesis. $p_t$ autocorrelations derived from the scale dependence of $$ fluctuations reveal a complex parton dissipation process in RHIC heavy ion collisions. We also observe structure which may result from collective bulk-medium recoil in response to parton stopping.Comment: 10 pages, 10 figures, proceedings, MIT workshop on fluctuations and correlations in relativistic nuclear collision

The harmonic measure of diffusion-limited aggregates including rare events

We obtain the harmonic measure of diffusion-limited aggregate (DLA) clusters using a biased random-walk sampling technique which allows us to measure probabilities of random walkers hitting sections of clusters with unprecedented accuracy; our results include probabilities as small as 10- 80. We find the multifractal D(q) spectrum including regions of small and negative q. Our algorithm allows us to obtain the harmonic measure for clusters more than an order of magnitude larger than those achieved using the method of iterative conformal maps, which is the previous best method. We find a phase transition in the singularity spectrum f(α) at α≈14 and also find a minimum q of D(q), qmin=0.9±0.05

Experimental data on the single spin asymmetry and their interpretations by the chromo-magnetic string model

An attempt is made to interpret the various existing experimental data on the single spin asymmetries in inclusive pion production by the polarized proton and antiproton beams. As the basis of analysis the chromo-magnetic string model is used. A whole measured kinematic region is covered. The successes and fails of such approach are outlined. The possible improvements of model are discussed.Comment: 17 pages, 3 figure

False Vacuum Chaotic Inflation: The New Paradigm?

Recent work is reported on inflation model building in the context of supergravity and superstrings, with special emphasis on False Vacuum (`Hybrid') Chaotic Inflation. Globally supersymmetric models do not survive in generic supergravity theories, but fairly simple conditions can be formulated which do ensure successful supergravity inflation. The conditions are met in some of the versions of supergravity that emerge from superstrings.Comment: 4 pages, LATEX, LANCASTER-TH 94-1