Compatible Quantum Theory

Formulations of quantum mechanics can be characterized as realistic, operationalist, or a combination of the two. In this paper a realistic theory is defined as describing a closed system entirely by means of entities and concepts pertaining to the system. An operationalist theory, on the other hand, requires in addition entities external to the system. A realistic formulation comprises an ontology, the set of (mathematical) entities that describe the system, and assertions, the set of correct statements (predictions) the theory makes about the objects in the ontology. Classical mechanics is the prime example of a realistic physical theory. The present realistic formulation of the histories approach originally introduced by Griffiths, which we call 'Compatible Quantum Theory (CQT)', consists of a 'microscopic' part (MIQM), which applies to a closed quantum system of any size, and a 'macroscopic' part (MAQM), which requires the participation of a large (ideally, an infinite) system. The first (MIQM) can be fully formulated based solely on the assumption of a Hilbert space ontology and the noncontextuality of probability values, relying in an essential way on Gleason's theorem and on an application to dynamics due in large part to Nistico. The microscopic theory does not, however, possess a unique corpus of assertions, but rather a multiplicity of contextual truths ('c-truths'), each one associated with a different framework. This circumstance leads us to consider the microscopic theory to be physically indeterminate and therefore incomplete, though logically coherent. The completion of the theory requires a macroscopic mechanism for selecting a physical framework, which is part of the macroscopic theory (MAQM). Detailed definitions and proofs are presented in the appendice

An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, mean-field theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial dimensions, where it can be replaced by a scaling phenomenology. The Ginzburg-Landau formalism can then be used to justify the phenomenological theory using the renormalization group, which elucidates the physical and mathematical mechanism for universality. In the second part of the paper it is shown how near pattern forming linear instabilities of dynamical systems, a formally similar Ginzburg-Landau theory can be derived for nonequilibrium macroscopic phenomena. The real and complex Ginzburg-Landau equations thus obtained yield nontrivial solutions of the original dynamical system, valid near the linear instability. Examples of such solutions are plane waves, defects such as dislocations or spirals, and states of temporal or spatiotemporal (extensive) chaos

A simple system with two temperatures

We study the stationary nonequilibrium regime which settles in when two single-spin paramagnets each in contact with its own thermal bath are coupled. The response vs. correlation plot exhibits some features of aging systems, in particular the existence, in some regimes, of effective temperatures.Comment: 7 pages, 3 figure

Dynamic aspect of the chiral phase transition in the mode coupling theory

We analyze the dynamic aspect of the chiral phase transition. We apply the mode coupling theory to the linear sigma model and derive the kinetic equation for the chiral phase transition. We challenge Hohenberg and Halperin's classification scheme of dynamic critical phenomena in which the dynamic universality class of the chiral phase transition has been identified with that of the antiferromagnet. We point out a crucial difference between the chiral dynamics and the antiferromagnet system. We also calculate the dynamic critical exponent for the chiral phase transition. Our result is $z=1-\eta/2\cong 0.98$ which is contrasted with $z=d/2=1.5$ of the antiferromagnet.Comment: 57 pages, no figure

Development of a Kohn-Sham like potential in the Self-Consistent Atomic Deformation Model

This is a brief description of how to derive the local ``atomic'' potentials from the Self-Consistent Atomic Deformation (SCAD) model density function. Particular attention is paid to the spherically averaged case.Comment: 5 Pages, LaTeX, no figure

Conditions for extreme sensitivity of protein diffusion in membranes to cell environments

We study protein diffusion in multicomponent lipid membranes close to a rigid substrate separated by a layer of viscous fluid. The large-distance, long-time asymptotics for Brownian motion are calculated using a nonlinear stochastic Navier-Stokes equation including the effect of friction with the substrate. The advective nonlinearity, neglected in previous treatments, gives only a small correction to the renormalized viscosity and diffusion coefficient at room temperature. We find, however, that in realistic multicomponent lipid mixtures, close to a critical point for phase separation, protein diffusion acquires a strong power-law dependence on temperature and the distance to the substrate $H$, making it much more sensitive to cell environment, unlike the logarithmic dependence on $H$ and very small thermal correction away from the critical point.Comment: 19 pages, 4 figure

Maximum thickness of a two-dimensional trapped Bose system

The trapped Bose system can be regarded as two-dimensional if the thermal fluctuation energy is less than the lowest energy in the perpendicular direction. Under this assumption, we derive an expression for the maximum thickness of an effective two-dimensional trapped Bose system.Comment: 1 pages, 0 figure

Electronic structure of amorphous germanium disulfide via density functional molecular dynamics simulations

Using density functional molecular dynamics simulations we study the electronic properties of glassy g-GeS$_2$. We compute the electronic density of states, which compares very well with XPS measurements, as well as the partial EDOS and the inverse participation ratio. We show the electronic contour plots corresponding to different structural environments, in order to determine the nature of the covalent bonds between the atoms. We finally study the local atomic charges, and analyze the impact of the local environment on the charge transfers between the atoms. The broken chemical order inherent to amorphous systems leads to locally charged zones when integrating the atomic charges up to nearest-neighbor distances.Comment: 13 pages, 9 figures; to appear in Phys. Rev.