20,118 research outputs found
Schwinger Algebra for Quaternionic Quantum Mechanics
It is shown that the measurement algebra of Schwinger, a characterization of
the properties of Pauli measurements of the first and second kinds, forming the
foundation of his formulation of quantum mechanics over the complex field, has
a quaternionic generalization. In this quaternionic measurement algebra some of
the notions of quaternionic quantum mechanics are clarified. The conditions
imposed on the form of the corresponding quantum field theory are studied, and
the quantum fields are constructed. It is shown that the resulting quantum
fields coincide with the fermion or boson annihilation-creation operators
obtained by Razon and Horwitz in the limit in which the number of particles in
physical states .Comment: 20 pages, Plain Te
Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check
We show that when the Hornberger--Sipe calculation of collisional decoherence
is carried out with the squared delta function a delta of energy instead of a
delta of the absolute value of momentum, following a method introduced by
Di\'osi, the corrected formula for the decoherence rate is simply obtained. The
results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As
an independent cross-check, we calculate the mean squared coordinate diffusion
of a hard sphere implied by the corrected decoherence master equation, and show
that it agrees precisely with the same quantity as calculated by a classical
Brownian motion analysis.Comment: Tex: 14 pages 7/30/06: revisions to introduction, and references
added 9/29/06: further minor revisions and references adde
Collapse models with non-white noises
We set up a general formalism for models of spontaneous wave function
collapse with dynamics represented by a stochastic differential equation driven
by general Gaussian noises, not necessarily white in time. In particular, we
show that the non-Schrodinger terms of the equation induce the collapse of the
wave function to one of the common eigenstates of the collapsing operators, and
that the collapse occurs with the correct quantum probabilities. We also
develop a perturbation expansion of the solution of the equation with respect
to the parameter which sets the strength of the collapse process; such an
approximation allows one to compute the leading order terms for the deviations
of the predictions of collapse models with respect to those of standard quantum
mechanics. This analysis shows that to leading order, the ``imaginary'' noise
trick can be used for non-white Gaussian noise.Comment: Latex, 20 pages;references added and minor revisions; published as J.
Phys. A: Math. Theor. {\bf 40} (2007) 15083-1509
Breaking quantum linearity: constraints from human perception and cosmological implications
Resolving the tension between quantum superpositions and the uniqueness of
the classical world is a major open problem. One possibility, which is
extensively explored both theoretically and experimentally, is that quantum
linearity breaks above a given scale. Theoretically, this possibility is
predicted by collapse models. They provide quantitative information on where
violations of the superposition principle become manifest. Here we show that
the lower bound on the collapse parameter lambda, coming from the analysis of
the human visual process, is ~ 7 +/- 2 orders of magnitude stronger than the
original bound, in agreement with more recent analysis. This implies that the
collapse becomes effective with systems containing ~ 10^4 - 10^5 nucleons, and
thus falls within the range of testability with present-day technology. We also
compare the spectrum of the collapsing field with those of known cosmological
fields, showing that a typical cosmological random field can yield an efficient
wave function collapse.Comment: 13 pages, LaTeX, 3 figure
Towards Quantum Superpositions of a Mirror: an Exact Open Systems Analysis - Calculational Details
We give details of calculations analyzing the proposed mirror superposition
experiment of Marshall, Simon, Penrose, and Bouwmeester within different
stochastic models for state vector collapse. We give two methods for exactly
calculating the fringe visibility in these models, one proceeding directly from
the equation of motion for the expectation of the density matrix, and the other
proceeding from solving a linear stochastic unravelling of this equation. We
also give details of the calculation that identifies the stochasticity
parameter implied by the small displacement Taylor expansion of the CSL model
density matrix equation. The implications of the two results are briefly
discussed. Two pedagogical appendices review mathematical apparatus needed for
the calculations.Comment: 9 pages, LaTeX. Minor changes mad
On Measurement of Helicity Parameters in Top Quark Decay
To enable an evaluation of future measurements of the helicity parameters for
" t --> W b " decay in regard to " T_FS violation", this paper considers the
effects of an additional pure-imaginary coupling, (i g/2 Lambda) or (i g),
associated with a specific, single additional Lorentz structure, i = S, P, S +
P, ... Sizable " T_FS violation" signatures can occur for low-effective mass
scales (< 320 GeV), but in most cases can be more simply excluded by 10%
precision measurement of the probabilities P(W_L) and P(b_L). Signatures for
excluding the presence of " T_FS violation" associated with the two dynamical
phase-type ambiguities are investigated.Comment: 15 pages, 1 table, 7 figures, no macro
Multi-particle Correlations in Quaternionic Quantum Systems
We investigate the outcomes of measurements on correlated, few-body quantum
systems described by a quaternionic quantum mechanics that allows for regions
of quaternionic curvature. We find that a multi-particle interferometry
experiment using a correlated system of four nonrelativistic, spin-half
particles has the potential to detect the presence of quaternionic curvature.
Two-body systems, however, are shown to give predictions identical to those of
standard quantum mechanics when relative angles are used in the construction of
the operators corresponding to measurements of particle spin components.Comment: REVTeX 3.0, 16 pages, no figures, UM-P-94/54, RCHEP-94/1
Alternative Descriptions in Quaternionic Quantum Mechanics
We characterize the quasianti-Hermitian quaternionic operators in QQM by
means of their spectra; moreover, we state a necessary and sufficient condition
for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian
with respect to a uniquely defined positive scalar product in a infinite
dimensional (right) quaternionic Hilbert space. According to such results we
obtain two alternative descriptions of a quantum optical physical system, in
the realm of quaternionic quantum mechanics, while no alternative can exist in
complex quantum mechanics, and we discuss some differences between them.Comment: 16 page
Comment about pion electro-production and the axial form factors
The claim by Haberzettl (Phys.Rev.Lett.85 (2000) 3576) that the axial form
factor of the nucleon cannot be accessed through threshold pion
electroproduction is unfounded
Collapse models with non-white noises II: particle-density coupled noises
We continue the analysis of models of spontaneous wave function collapse with
stochastic dynamics driven by non-white Gaussian noise. We specialize to a
model in which a classical "noise" field, with specified autocorrelator, is
coupled to a local nonrelativistic particle density. We derive general results
in this model for the rates of density matrix diagonalization and of state
vector reduction, and show that (in the absence of decoherence) both processes
are governed by essentially the same rate parameters. As an alternative route
to our reduction results, we also derive the Fokker-Planck equations that
correspond to the initial stochastic Schr\"odinger equation. For specific
models of the noise autocorrelator, including ones motivated by the structure
of thermal Green's functions, we discuss the qualitative and qantitative
dependence on model parameters, with particular emphasis on possible
cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision
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