Misleading signposts along the de Broglie-Bohm road to quantum mechanics

Eighty years after de Broglie's, and a little more than half a century after Bohm's seminal papers, the de Broglie--Bohm theory (a.k.a. Bohmian mechanics), which is presumably the simplest theory which explains the orthodox quantum mechanics formalism, has reached an exemplary state of conceptual clarity and mathematical integrity. No other theory of quantum mechanics comes even close. Yet anyone curious enough to walk this road to quantum mechanics is soon being confused by many misleading signposts that have been put up, and not just by its detractors, but unfortunately enough also by some of its proponents. This paper outlines a road map to help navigate ones way.Comment: Dedicated to Jeffrey Bub on occasion of his 65th birthday. Accepted for publication in Foundations of Physics. A "slip of pen" in the bibliography has been corrected -- thanks go to Oliver Passon for catching it

Irreversible Quantum Mechanics in the Neutral K-System

The neutral Kaon system is used to test the quantum theory of resonance scattering and decay phenomena. The two dimensional Lee-Oehme-Yang theory with complex Hamiltonian is obtained by truncating the complex basis vector expansion of the exact theory in Rigged Hilbert space. This can be done for K_1 and K_2 as well as for K_S and K_L, depending upon whether one chooses the (self-adjoint, semi-bounded) Hamiltonian as commuting or non-commuting with CP. As an unexpected curiosity one can show that the exact theory (without truncation) predicts long-time 2 pion decays of the neutral Kaon system even if the Hamiltonian conserves CP.Comment: 36 pages, 1 PostScript figure include

Symmetry Representations in the Rigged Hilbert Space Formulation of Quantum Mechanics

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space

The density matrix in the de Broglie-Bohm approach

If the density matrix is treated as an objective description of individual systems, it may become possible to attribute the same objective significance to statistical mechanical properties, such as entropy or temperature, as to properties such as mass or energy. It is shown that the de Broglie-Bohm interpretation of quantum theory can be consistently applied to density matrices as a description of individual systems. The resultant trajectories are examined for the case of the delayed choice interferometer, for which Bell appears to suggest that such an interpretation is not possible. Bell's argument is shown to be based upon a different understanding of the density matrix to that proposed here.Comment: 15 pages, 4 figure

Hypersurface Bohm-Dirac models

We define a class of Lorentz invariant Bohmian quantum models for N entangled but noninteracting Dirac particles. Lorentz invariance is achieved for these models through the incorporation of an additional dynamical space-time structure provided by a foliation of space-time. These models can be regarded as the extension of Bohm's model for N Dirac particles, corresponding to the foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to more general foliations. As with Bohm's model, there exists for these models an equivariant measure on the leaves of the foliation. This makes possible a simple statistical analysis of position correlations analogous to the equilibrium analysis for (the nonrelativistic) Bohmian mechanics.Comment: 17 pages, 3 figures, RevTex. Completely revised versio

Entanglement and State Preparation

When a subset of particles in an entangled state is measured, the state of the subset of unmeasured particles is determined by the outcome of the measurement. This first measurement may be thought of as a state preparation for the remaining particles. In this paper, we examine how the duration of the first measurement effects the state of the unmeasured subsystem. The state of the unmeasured subsytem will be a pure or mixed state depending on the nature of the measurement. In the case of quantum teleportation we show that there is an eigenvalue equation which must be satisfied for accurate teleportation. This equation provides a limitation to the states that can be accurately teleported.Comment: 24 pages, 3 figures, submitted to Phys. Rev.

Time Asymmetric Quantum Physics

Mathematical and phenomenological arguments in favor of asymmetric time evolution of micro-physical states are presented.Comment: Tex file with 2 figure

Measuring ^{12}C(&alpha,&gamma)^{16}O from White Dwarf Asteroseismology

During helium burning in the core of a red giant, the relative rates of the 3&alpha and ^{12}C(&alpha,&gamma)^{16}O reactions largely determine the final ratio of carbon to oxygen in the resulting white dwarf star. The uncertainty in the 3&alpha reaction at stellar energies due to the extrapolation from high-energy laboratory measurements is relatively small, but this is not the case for the ^{12}C(&alpha,&gamma)^{16}O reaction. Recent advances in the analysis of asteroseismological data on pulsating white dwarf stars now make it possible to obtain precise measurements of the central ratio of carbon to oxygen, providing a more direct way to measure the ^{12}C(&alpha,&gamma)^{16}O reaction rate at stellar energies. We assess the systematic uncertainties of this approach and quantify small shifts in the measured central oxygen abundance originating from the observations and from model settings that are kept fixed during the optimization. Using new calculations of white dwarf internal chemical profiles, we find a rate for the ^{12}C(&alpha,&gamma)^{16}O reaction that is significantly higher than most published values. The accuracy of this method may improve as we modify some of the details of our description of white dwarf interiors that were not accessible through previous model-fitting methods.Comment: 8 pages, 4 figures, 3 tables, uses emulateapj5.sty, Accepted for publication in the Astrophysical Journa

Controlled Flow of Spin-Entangled Electrons via Adiabatic Quantum Pumping

We propose a method to dynamically generate and control the flow of spin-entangled electrons, each belonging to a spin-singlet, by means of adiabatic quantum pumping. The pumping cycle functions by periodic time variation of localized two-body interactions. We develop a generalized approach to adiabatic quantum pumping as traditional methods based on scattering matrix in one dimension cannot be applied here. We specifically compute the flow of spin-entangled electrons within a Hubbard-like model of quantum dots, and discuss possible implementations and identify parameters that can be used to control the singlet flow.Comment: 4 pages, 3 figure