Common Axioms for Inferring Classical Ensemble Dynamics and Quantum Theory

The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrodingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted.Comment: Final proceedings version. 6 pages. Presented at the 3rd QTRF conference at Vaxjo, Sweden, June6-11 200

Resummation in a Hot Scalar Field Theory

A resummed perturbative expansion is used to obtain the self-energy in the high-temperature $g^2\phi^4$ field theory model up to order $g^4$. From this the zero momentum pole of the effective propagator is evaluated to determine the induced thermal mass and damping rate for the bosons in the plasma to order $g^3$. The calculations are performed in the imaginary time formalism and a simple diagrammatic analysis is used to identify the relevant diagrams at each order. Results are compared with similar real-time calculations found in the literature.Comment: 26 pages (figures not included

Why is Schrodinger's Equation Linear?

Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrodinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear corrections to quantum theory. Nonlinear corrections can also appear in a Lorentz invariant theory in the form of higher derivative terms that are determined by a length scale, possibly the Planck length. It is suggested that the best place to look for evidence of such quantum nonlinear effects is in neutrino physics and cosmology.Comment: 3 pages; Presented at the DICE 2004 workshop; Sept 2004, Piombino Italy. Minor corrections: this is the proceedings Versio

Joint Source-Channel Coding over a Fading Multiple Access Channel with Partial Channel State Information

In this paper we address the problem of transmission of correlated sources over a fast fading multiple access channel (MAC) with partial channel state information available at both the encoders and the decoder. We provide sufficient conditions for transmission with given distortions. Next these conditions are specialized to a Gaussian MAC (GMAC). We provide the optimal power allocation strategy and compare the strategy with various levels of channel state information. Keywords: Fading MAC, Power allocation, Partial channel state information, Correlated sources.Comment: 7 Pages, 3 figures. To Appear in IEEE GLOBECOM, 200

Phase transitions in a system of hard rectangles on the square lattice

The phase diagram of a system of monodispersed hard rectangles of size $m\times m k$ on a square lattice is numerically determined for $m=2,3$ and aspect ratio $k= 1,2,\ldots, 7$. We show the existence of a disordered phase, a nematic phase with orientational order, a columnar phase with orientational and partial translational order, and a solid-like phase with sublattice order, but no orientational order. The asymptotic behavior of the phase boundaries for large $k$ are determined using a combination of entropic arguments and a Bethe approximation. This allows us to generalize the phase diagram to larger $m$ and $k$, showing that for $k \geq 7$, the system undergoes three entropy driven phase transitions with increasing density. The nature of the different phase transitions are established and the critical exponents for the continuous transitions are determined using finite size scaling.Comment: 16 pages, 20 figure