Sequential measurement of conjugate variables as an alternative quantum state tomography

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by measuring sequentially two conjugate variables. The procedure relies on the quasi-characteristic function, the Fourier-transform of the Wigner quasi-probability. The proper characteristic function obtained by Fourier-transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasi-characteristic function of the two detectors and that, unknown, of the quantum system. This allows state reconstruction through the sequence: data collection, Fourier-transform, algebraic operation, inverse Fourier-transform. The strength of the measurement should be intermediate for the procedure to work.Comment: v2, 5 pages, no figures, substantial improvements in the presentation, thanks to an anonymous referee. v3, close to published versio

Interference in Bohmian Mechanics with Complex Action

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex [JCP {125}, 231103 (2006)]. In the alternative formulation there is a significant reduction in the magnitude of the quantum force as compared with the conventional Bohmian formulation, at the price of propagating complex trajectories. In this paper we show that Bohmian mechanics with complex action is able to overcome the main computational limitation of conventional Bohmian methods -- the propagation of wavefunctions once nodes set in. In the vicinity of nodes, the quantum force in conventional Bohmian formulations exhibits rapid oscillations that pose severe difficulties for existing numerical schemes. We show that within complex Bohmian mechanics, multiple complex initial conditions can lead to the same real final position, allowing for the description of nodes as a sum of the contribution from two or more crossing trajectories. The idea is illustrated on the reflection amplitude from a one-dimensional Eckart barrier. We believe that trajectory crossing, although in contradiction to the conventional Bohmian trajectory interpretation, provides an important new tool for dealing with the nodal problem in Bohmian methods

Self-induced decoherence approach: Strong limitations on its validity in a simple spin bath model and on its general physical relevance

The "self-induced decoherence" (SID) approach suggests that (1) the expectation value of any observable becomes diagonal in the eigenstates of the total Hamiltonian for systems endowed with a continuous energy spectrum, and (2), that this process can be interpreted as decoherence. We evaluate the first claim in the context of a simple spin bath model. We find that even for large environments, corresponding to an approximately continuous energy spectrum, diagonalization of the expectation value of random observables does in general not occur. We explain this result and conjecture that SID is likely to fail also in other systems composed of discrete subsystems. Regarding the second claim, we emphasize that SID does not describe a physically meaningful decoherence process for individual measurements, but only involves destructive interference that occurs collectively within an ensemble of presupposed "values" of measurements. This leads us to question the relevance of SID for treating observed decoherence effects.Comment: 11 pages, 4 figures. Final published versio

Tube Model for Light-Front QCD

We propose the tube model as a first step in solving the bound state problem in light-front QCD. In this approach we neglect transverse variations of the fields, producing a model with 1+1 dimensional dynamics. We then solve the two, three, and four particle sectors of the model for the case of pure glue SU(3). We study convergence to the continuum limit and various properties of the spectrum.Comment: 29 page

Quantum Theory and Galois Fields

We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one. The paper has been prepared as a presentation to the ICSSUR' 2005 conference (Besancon, France, May 2-6, 2005).Comment: Latex, 24 pages, 1 figur

Masses of the physical mesons from an effective QCD--Hamiltonian

The front form Hamiltonian for quantum chromodynamics, reduced to an effective Hamiltonian acting only in the $q\bar q$ space, is solved approximately. After coordinate transformation to usual momentum space and Fourier transformation to configuration space a second order differential equation is derived. This retarded Schr\"odinger equation is solved by variational methods and semi-analytical expressions for the masses of all 30 pseudoscalar and vector mesons are derived. In view of the direct relation to quantum chromdynamics without free parameter, the agreement with experiment is remarkable, but the approximation scheme is not adequate for the mesons with one up or down quark. The crucial point is the use of a running coupling constant $\alpha_s(Q^2)$, in a manner similar but not equal to the one of Richardson in the equal usual-time quantization. Its value is fixed at the Z mass and the 5 flavor quark masses are determined by a fit to the vector meson quarkonia.Comment: 18 pages, 4 Postscript figure

Klein-Gordon Equation in Hydrodynamical Form

We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities. We find that the equation of motion for the probability densities is in the form of relativistic hydrodynamics where various forces have their classical counterparts, with the additional element of the quantum stress tensor that depends on the derivatives of the amplitude of the wave function. We derive the equation of motion for the Wigner function and we find that its approximate classical weak-field limit coincides with the equation of motion for the distribution function in the collisionless kinetic theory.Comment: 13 page

A 3+1 Dimensional Light-Front Model with Spontaneous Breaking of Chiral Symmetry

We investigate a 3+1 dimensional toy model that exhibits spontaneous breakdown of chiral symmetry, both in a light-front (LF) Hamiltonian and in a Euclidean Schwinger-Dyson (SD) formulation. We show that both formulations are completely equivalent --- provided the renormalization is properly done. For the model considered, this means that if one uses the same transverse momentum cutoff on the SD and LF formulations then the vertex mass in the LF calculation must be taken to be the same as the current quark mass in the SD calculation. The kinetic mass term in the LF calculation is renormalized non-trivially, which is eventually responsible for the mass generation of the physical fermion of the model.Comment: 6 pages, REVTE

String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.Comment: 20 pages (7 figures available from authors as postscipt files), PUPT-134

The Reconstruction Problem and Weak Quantum Values

Quantum Mechanical weak values are an interference effect measured by the cross-Wigner transform W({\phi},{\psi}) of the post-and preselected states, leading to a complex quasi-distribution {\rho}_{{\phi},{\psi}}(x,p) on phase space. We show that the knowledge of {\rho}_{{\phi},{\psi}}(z) and of one of the two functions {\phi},{\psi} unambiguously determines the other, thus generalizing a recent reconstruction result of Lundeen and his collaborators.Comment: To appear in J.Phys.: Math. Theo