5,536 research outputs found
Quantum effective force in an expanding infinite square-well potential and Bohmian perspective
The Schr\"{o}dinger equation is solved for the case of a particle confined to
a small region of a box with infinite walls. If walls of the well are moved,
then, due to an effective quantum nonlocal interaction with the boundary, even
though the particle is nowhere near the walls, it will be affected. It is shown
that this force apart from a minus sign is equal to the expectation value of
the gradient of the quantum potential for vanishing at the walls boundary
condition. Variation of this force with time is studied. A selection of Bohmian
trajectories of the confined particle is also computed.Comment: 7 figures, Accepted by Physica Script
On the --corrections to decay amplitudes in nonlinear and linear chiral models
The calculations of isotopic amplitudes and their results for the direct
--violating charge asymmetry in decays within the
nonlinear and linear (--model) chiral Lagrangian approach are compared
with each other. It is shown, that the latter, taking into account intermediate
scalar resonances, does not reproduce the --corrections of the nonlinear
approach introduced by Gasser and Leutwyler, being saturated mainly by vector
resonance exchange. The resulting differences concerning the violation
effect are traced in some detail.Comment: 14 page
Factorization Structure of Gauge Theory Amplitudes and Application to Hard Scattering Processes at the LHC
Previous work on electroweak radiative corrections to high energy scattering
using soft-collinear effective theory (SCET) has been extended to include
external transverse and longitudinal gauge bosons and Higgs bosons. This allows
one to compute radiative corrections to all parton-level hard scattering
amplitudes in the standard model to NLL order, including QCD and electroweak
radiative corrections, mass effects, and Higgs exchange corrections, if the
high-scale matching, which is suppressed by two orders in the log counting, and
contains no large logs, is known. The factorization structure of the effective
theory places strong constraints on the form of gauge theory amplitudes at high
energy for massless and massive gauge theories, which are discussed in detail
in the paper. The radiative corrections can be written as the sum of
process-independent one-particle collinear functions, and a universal soft
function. We give plots for the radiative corrections to q qbar -> W_T W_T, Z_T
Z_T, W_L W_L, and Z_L H, and gg -> W_T W_T to illustrate our results. The
purely electroweak corrections are large, ranging from 12% at 500 GeV to 37% at
2 TeV for transverse W pair production, and increasing rapidly with energy. The
estimated theoretical uncertainty to the partonic (hard) cross-section in most
cases is below one percent, smaller than uncertainties in the parton
distribution functions (PDFs). We discuss the relation between SCET and other
factorization methods, and derive the Magnea-Sterman equations for the Sudakov
form factor using SCET, for massless and massive gauge theories, and for light
and heavy external particles.Comment: 44 pages, 30 figures. Refs added, typos fixed. ZL ZL plots removed
because of a possible subtlet
On Epstein's trajectory model of non-relativistic quantum mechanics
In 1952 Bohm presented a theory about non-relativistic point-particles moving
along deterministic trajectories and showed how it reproduces the predictions
of standard quantum theory. This theory was actually presented before by de
Broglie in 1926, but Bohm's particular formulation of the theory inspired
Epstein to come up with a different trajectory model. The aim of this paper is
to examine the empirical predictions of this model. It is found that the
trajectories in this model are in general very different from those in the de
Broglie-Bohm theory. In certain cases they even seem bizarre and rather
unphysical. Nevertheless, it is argued that the model seems to reproduce the
predictions of standard quantum theory (just as the de Broglie-Bohm theory).Comment: 12 pages, no figures, LaTex; v2 minor improvement
Adiabatic theorems for linear and nonlinear Hamiltonians
Conditions for the validity of the quantum adiabatic approximation are
analyzed. For the case of linear Hamiltonians, a simple and general sufficient
condition is derived, which is valid for arbitrary spectra and any kind of time
variation. It is shown that in some cases the found condition is necessary and
sufficient. The adiabatic theorem is generalized for the case of nonlinear
Hamiltonians
Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality
The Fourier transform is often used to connect the Lorentzian energy
distribution for resonance scattering to the exponential time dependence for
decaying states. However, to apply the Fourier transform, one has to bend the
rules of standard quantum mechanics; the Lorentzian energy distribution must be
extended to the full real axis instead of being bounded from
below (``Fermi's approximation''). Then the Fourier transform
of the extended Lorentzian becomes the exponential, but only for times , a time asymmetry which is in conflict with the unitary group time evolution
of standard quantum mechanics. Extending the Fourier transform from
distributions to generalized vectors, we are led to Gamow kets, which possess a
Lorentzian energy distribution with and have exponential
time evolution for only. This leads to probability predictions
that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.
Typicality vs. probability in trajectory-based formulations of quantum mechanics
Bohmian mechanics represents the universe as a set of paths with a
probability measure defined on it. The way in which a mathematical model of
this kind can explain the observed phenomena of the universe is examined in
general. It is shown that the explanation does not make use of the full
probability measure, but rather of a suitable set function deriving from it,
which defines relative typicality between single-time cylinder sets. Such a set
function can also be derived directly from the standard quantum formalism,
without the need of an underlying probability measure. The key concept for this
derivation is the {\it quantum typicality rule}, which can be considered as a
generalization of the Born rule. The result is a new formulation of quantum
mechanics, in which particles follow definite trajectories, but which is only
based on the standard formalism of quantum mechanics.Comment: 24 pages, no figures. To appear in Foundation of Physic
- …