110 research outputs found
The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values
A which-way measurement destroys the twin-slit interference pattern. Bohr
argued that distinguishing between two slits a distance s apart gives the
particle a random momentum transfer \wp of order h/s. This was accepted for
more than 60 years, until Scully, Englert and Walther (SEW) proposed a
which-way scheme that, they claimed, entailed no momentum transfer. Storey,
Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed,
showed that Bohr was right. This work reviews and extends a recent proposal
[Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a
weak-valued probability distribution for momentum transfer, P_wv(\wp). We show
that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero
because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is
measurable in a way understandable to a classical physicist. We introduce a new
measure of spread for P_wv(\wp): half of the unit-confidence interval, and
conjecture that it is never less than h/4s. For an idealized example with
infinitely narrow slits, the moments of P_wv(\wp) and of the momentum
distributions are undefined unless a process of apodization is used. We show
that by considering successively smoother initial wave functions, successively
more moments of both P_wv(\wp) and the momentum distributions become defined.
For this example the moments of P_wv(\wp) are zero, and these are equal to the
changes in the moments of the momentum distribution. We prove that this
relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but
only for the first two moments. We also compare these moments to those of two
other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find
agreement between all of these, but again only for the first two moments.Comment: 14 pages, 6 figures, submitted to J. Opt.
Electroweak baryogenesis induced by a scalar field
A cosmological pseudoscalar field coupled to hypercharge topological number
density can exponentially amplify hyperelectric and hypermagnetic fields while
coherently rolling or oscillating, leading to the formation of a time-dependent
condensate of topological number density. The topological condensate can be
converted, under certain conditions, into baryons in sufficient quantity to
explain the observed baryon asymmetry in the universe. The amplified
hypermagnetic field can perhaps sufficiently strengthen the electroweak phase
transition, and by doing so, save any pre-existing baryon number asymmetry from
extinction.Comment: 8 pages, 4 figure
Grounding Bohmian Mechanics in Weak Values and Bayesianism
Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in
which particles have real positions. The velocity of a point x in configuration
space is defined as the standard probability current j(x) divided by the
probability density P(x). However, this ``standard'' j is in fact only one of
infinitely many that transform correctly and satisfy \dot P + \del . j=0. In
this article I show that there is a unique j that can be determined
experimentally as a weak value using techniques that would make sense to a
classical physicist. Moreover, this operationally defined j equals the standard
j, so, assuming \dot x = j/P, the possible Bohmian paths can also be determined
experimentally from a large enough ensemble. Furthermore, this approach to
deriving BM singles out x as the hidden variable, because (for example) the
operationally defined momentum current is in general incompatible with the
evolution of the momentum distribution. Finally I discuss how, in this setting,
the usual quantum probabilities can be derived from a Bayesian standpoint, via
the principle of indifference.Comment: 11 page
Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era
We study the generation of large scale primordial magnetic fields by a
cosmological phase transition during the radiation dominated era. The setting
is a theory of N charged scalar fields coupled to an abelian gauge field, that
undergoes a phase transition at a critical temperature much larger than the
electroweak scale. The dynamics after the transition features two distinct
stages: a spinodal regime dominated by linear long-wavelength instabilities,
and a scaling stage in which the non-linearities and backreaction of the scalar
fields are dominant. This second stage describes the growth of horizon sized
domains. We implement a recently introduced formulation to obtain the spectrum
of magnetic fields that includes the dissipative effects of the plasma. We find
that large scale magnetogenesis is very efficient during the scaling regime.
The ratio between the energy density on scales larger than L and that in the
background radiation r(L,T) = rho_B(L,T)/rho_{cmb}(T) is r(L,T) \sim 10^{-34}
at the Electroweak scale and r(L,T) \sim 10^{-14} at the QCD scale for L \sim 1
Mpc. The resulting spectrum is insensitive to the magnetic diffusion length. We
conjecture that a similar mechanism could be operative after the QCD chiral
phase transition.Comment: LaTex, 25 pages, no figures, to appear in Phys. Rev.
Magnetic field generation from non-equilibrium phase transitions
We study the generation of magnetic fields during the stage of particle
production resulting from spinodal instabilities during phase transitions out
of equilibrium. The main premise is that long-wavelength instabilities that
drive the phase transition lead to strong non-equilibrium charge and current
fluctuations which generate electromagnetic fields. We present a formulation
based on the non-equilibrium Schwinger-Dyson equations that leads to an exact
expression for the spectrum of electromagnetic fields valid for general
theories and cosmological backgrounds and whose main ingredient is the
transverse photon polarization out of equilibrium. This formulation includes
the dissipative effects of the conductivity in the medium. As a prelude to
cosmology we study magnetogenesis in Minkowski space-time in a theory of N
charged scalar fields to lowest order in the gauge coupling and to leading
order in the large N within two scenarios of cosmological relevance. The
long-wavelength power spectrum for electric and magnetic fields at the end of
the phase transition is obtained explicitly.
It follows that equipartition between electric and magnetic fields does not
hold out of equilibrium. In the case of a transition from a high temperature
phase, the conductivity of the medium severely hinders the generation of
magnetic fields, however the magnetic fields generated are correlated on scales
of the order of the domain size, which is much larger than the magnetic
diffusion length. Implications of the results to cosmological phase transitions
driven by spinodal unstabilities are discussed.Comment: Preprint no. LPTHE 02-55, 30 pages, latex, 2 eps figures. Added one
reference. To appear in Phys. Rev.
Speculations on Primordial Magnetic Helicity
We speculate that above or just below the electroweak phase transition
magnetic fields are generated which have a net helicity (otherwise said, a
Chern-Simons term) of order of magnitude , where is the
baryon or lepton number today. (To be more precise requires much more knowledge
of B,L-generating mechanisms than we currently have.) Electromagnetic helicity
generation is associated (indirectly) with the generation of electroweak
Chern-Simons number through B+L anomalies. This helicity, which in the early
universe is some 30 orders of magnitude greater than what would be expected
from fluctuations alone in the absence of B+L violation, should be reasonably
well-conserved through the evolution of the universe to around the times of
matter dominance and decoupling, because the early universe is an excellent
conductor. Possible consequences include early structure formation; macroscopic
manifestations of CP violation in the cosmic magnetic field (measurable at
least in principle, if not in practice); and an inverse-cascade dynamo
mechanism in which magnetic fields and helicity are unstable to transfer to
larger and larger spatial scales. We give a quasi-linear treatment of the
general-relativistic MHD inverse cascade instability, finding substantial
growth for helicity of the assumed magnitude out to scales , where is roughly the B+L to photon ratio and
is the magnetic correlation length. We also elaborate further on an
earlier proposal of the author for generation of magnetic fields above the EW
phase transition.Comment: Latex, 23 page
A complete 3D numerical study of the effects of pseudoscalar-photon mixing on quasar polarizations
We present the results of three-dimensional simulations of quasar
polarizations in the presence of pseudoscalar-photon mixing in the
intergalactic medium. The intergalactic magnetic field is assumed to be
uncorrelated in wave vector space but correlated in real space. Such a field
may be obtained if its origin is primordial. Furthermore we assume that the
quasars, located at cosmological distances, have negligible initial
polarization. In the presence of pseudoscalar-photon mixing we show, through a
direct comparison with observations, that this may explain the observed large
scale alignments in quasar polarizations within the framework of big bang
cosmology. We find that the simulation results give a reasonably good fit to
the observed data.Comment: 15 pages, 8 figures, significant changes, to appear in EPJ
Magnetogenesis and the dynamics of internal dimensions
The dynamical evolution of internal space-like dimensions breaks the
invariance of the Maxwell's equations under Weyl rescaling of the (conformally
flat) four-dimensional metric. Depending upon the number and upon the dynamics
of internal dimensions large scale magnetic fields can be created. The
requirements coming from magnetogenesis together with the other cosmological
constraints are examined under the assumption that the internal dimensions
either grow or shrink (in conformal time) prior to a radiation dominated epoch.
If the internal dimensions are growing the magnitude of the generated magnetic
fields can seed the galactic dynamo mechanism.Comment: 27 in RevTex style, four figure
Recommended from our members
Disorder-specific functional abnormalities during sustained attention in youth with Attention Deficit Hyperactivity Disorder (ADHD) and with Autism
Attention Deficit Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) are often comorbid and share behavioural-cognitive abnormalities in sustained attention. A key question is whether this shared cognitive phenotype is based on common or different underlying pathophysiologies. To elucidate this question, we compared 20 boys with ADHD to 20 age and IQ matched ASD and 20 healthy boys using functional magnetic resonance imaging (fMRI) during a parametrically modulated vigilance task with a progressively increasing load of sustained attention. ADHD and ASD boys had significantly reduced activation relative to controls in bilateral striato–thalamic regions, left dorsolateral prefrontal cortex (DLPFC) and superior parietal cortex. Both groups also displayed significantly increased precuneus activation relative to controls. Precuneus was negatively correlated with the DLPFC activation, and progressively more deactivated with increasing attention load in controls, but not patients, suggesting problems with deactivation of a task-related default mode network in both disorders. However, left DLPFC underactivation was significantly more pronounced in ADHD relative to ASD boys, which furthermore was associated with sustained performance measures that were only impaired in ADHD patients. ASD boys, on the other hand, had disorder-specific enhanced cerebellar activation relative to both ADHD and control boys, presumably reflecting compensation. The findings show that ADHD and ASD boys have both shared and disorder-specific abnormalities in brain function during sustained attention. Shared deficits were in fronto–striato–parietal activation and default mode suppression. Differences were a more severe DLPFC dysfunction in ADHD and a disorder-specific fronto–striato–cerebellar dysregulation in ASD
Hypermagnetic Knots, Chern-Simons Waves and the Baryon Asymmetry
At finite hyperconductivity and finite fermionic density the flux lines of
long range hypermagnetic fields may not have a topologically trivial structure.
The combined evolution of the chemical potentials and of pseudoscalar fields
(like the axial Higgs), possibly present for temperatures in the TeV range, can
twist the hypercharge flux lines, producing, ultimately, hypermagnetic knots
(HK). The dynamical features of the HK depend upon the various particle physics
parameters of the model (pseudoscalar masses and couplings, strength of the
electroweak phase transition, hyperconductivity of the plasma) and upon the
magnitude of the primordial flux sitting in topologically trivial
configurations of the hypermagnetic field. We study different cosmological
scenarios where HK can be generated. We argue that the fermionic number sitting
in HK can be released producing a seed for the Baryon Asymmetry of the Universe
(BAU) provided the typical scale of the knot is larger than the diffusivity
length scale. We derive constraints on the primordial hypermagnetic flux
required by our mechanism and we provide a measure of the parity breaking by
connecting the degree of knottedness of the flux lines to the BAU. We rule out
the ordinary axion as a possible candidate for production (around temperatures
of the order of the GeV) of {\em magnetic} knots since the produced {\em
electromagnetic} helicity is negligible (for cosmological standard) if the
initial amplitude of the axion oscillations is of the order of the Peccei-Quinn
breaking scale.Comment: 30 pages in Revtex style, 8 figure
- …