19,642 research outputs found
Efficient Simulation of Quantum State Reduction
The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.Comment: 4 pages, No Figur
Nuclear modification at sqrt{s_{NN}}=17.3 GeV, measured at NA49
Transverse momentum spectra up to 4.5 GeV/c were measured around midrapidity
in Pb+Pb reactions at sqrt{s_{NN}}=17.3 GeV, for pi^{+/-}, p, pbar and K^{+/-},
by the NA49 experiment. The nuclear modification factors R_{AA}, R_{AA/pA} and
R_{CP} were extracted and are compared to RHIC results at sqrt{s_{NN}}=200 GeV.
The modification factor R_{AA} shows a rapid increase with transverse momentum
in the covered region. The modification factor R_{CP} shows saturation well
below unity in the pi^{+/-} channel. The extracted R_{CP} values follow the 200
GeV RHIC results closely in the available transverse momentum range for all
particle species. For pi^{+/-} above 2.5 GeV/c transverse momentum, the
measured suppression is smaller than that observed at RHIC. The nuclear
modification factor R_{AA/pA} for pi^{+/-} stays well below unity.Comment: Proceedings of Quark Matter 2008 conferenc
Octonionic Version of Dirac Equations
It is shown that a simple continuity condition in the algebra of split
octonions suffices to formulate a system of differential equations that are
equivalent to the standard Dirac equations. In our approach the particle mass
and electro-magnetic potentials are part of an octonionic gradient function
together with the space-time derivatives. As distinct from previous attempts to
translate the Dirac equations into different number systems here the wave
functions are real split octonions and not bi-spinors. To formulate positively
defined probability amplitudes four different split octonions (transforming
into each other by discrete transformations) are necessary, rather then two
complex wave functions which correspond to particles and antiparticles in usual
Dirac theory.Comment: Version accepted by Int. J Mod. Phy
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
Representations of U(1,q) and Constructive Quaternion Tensor Products
The representation theory of the group U(1,q) is discussed in detail because
of its possible application in a quaternion version of the Salam-Weinberg
theory.
As a consequence, from purely group theoretical arguments we demonstrate that
the eigenvalues must be right-eigenvalues and that the only consistent scalar
products are the complex ones. We also define an explicit quaternion tensor
product which leads to a set of additional group representations for integer
``spin''.Comment: 28 pages, Latex, Dipartimento di Fisica, Universita di Lecce
INFN-Sezione di Lecc
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
Symmetry Breaking for Matter Coupled to Linearized Supergravity From the Perspective of the Current Supermultiplet
We consider a generic supersymmetric matter theory coupled to linearized
supergravity, and analyze scenarios for spontaneous symmetry breaking in terms
of vacuum expectation values of components of the current supermultiplet. When
the vacuum expectation of the energy momentum tensor is zero, but the scalar
current or pseudoscalar current gets an expectation, evaluation of the
gravitino self energy using the supersymmetry current algebra shows that there
is an induced gravitino mass term. The structure of this term generalizes the
supergravity action with cosmological constant to theories with CP violation.
When the vacuum expectation of the energy momentum tensor is nonzero,
supersymmetry is broken; requiring cancellation of the cosmological constant
gives the corresponding generalized gravitino mass formula.Comment: 11 page
Regular subspaces of a quaternionic Hilbert space from quaternionic Hermite polynomials and associated coherent states
We define quaternionic Hermite polynomials by analogy with two families of
complex Hermite polynomials. As in the complex case, these polynomials
consatitute orthogonal families of vectors in ambient quaternionic
-spaces. Using these polynomials, we then define regular and anti-regular
subspaces of these -spaces, the associated reproducing kernels and the
ensuing quaternionic coherent states
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
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