3,605 research outputs found
Inflationary spectra and violations of Bell inequalities
In spite of the macroscopic character of the primordial fluctuations, the
standard inflationary distribution (that obtained using linear mode equations)
exhibits inherently quantum properties, that is, properties which cannot be
mimicked by any stochastic distribution. This is demonstrated by a Gedanken
experiment for which certain Bell inequalities are violated. These violations
are {\it in principle} measurable because, unlike for Hawking radiation from
black holes, in inflationary cosmology we can have access to both members of
correlated pairs of modes delivered in the same state. We then compute the
effect of decoherence and show that the violations persist provided the
decoherence level (and thus the entropy) lies below a certain non-vanishing
threshold. Moreover, there exists a higher threshold above which no violation
of any Bell inequality can occur. In this regime, the distributions are
``separable'' and can be interpreted as stochastic ensembles of fluctuations.
Unfortunately, the precision which is required to have access to the quantum
properties is so high that, {\it in practice}, an observational verification
seems excluded.Comment: 5 pages, 1 figure; new presentation and extended discussio
Stability of spinor Fermi gases in tight waveguides
The two and three-body correlation functions of the ground state of an
optically trapped ultracold spin-1/2 Fermi gas (SFG) in a tight waveguide (1D
regime) are calculated in the plane of even and odd-wave coupling constants,
assuming a 1D attractive zero-range odd-wave interaction induced by a 3D p-wave
Feshbach resonance, as well as the usual repulsive zero-range even-wave
interaction stemming from 3D s-wave scattering. The calculations are based on
the exact mapping from the SFG to a ``Lieb-Liniger-Heisenberg'' model with
delta-function repulsions depending on isotropic Heisenberg spin-spin
interactions, and indicate that the SFG should be stable against three-body
recombination in a large region of the coupling constant plane encompassing
parts of both the ferromagnetic and antiferromagnetic phases. However, the
limiting case of the fermionic Tonks-Girardeau gas (FTG), a spin-aligned 1D
Fermi gas with infinitely attractive p-wave interactions, is unstable in this
sense. Effects due to the dipolar interaction and a Zeeman term due to a
resonance-generating magnetic field do not lead to shrinkage of the region of
stability of the SFG.Comment: 5 pages, 6 figure
Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas
The Luther-Emery liquid is a state of matter that is predicted to occur in
one-dimensional systems of interacting fermions and is characterized by a
gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a
realization of the Luther-Emery phase in a trapped cold-atom gas. We study by
means of the density-matrix renormalization-group technique a two-component
atomic Fermi gas with attractive interactions subject to parabolic trapping
inside an optical lattice. We demonstrate how this system exhibits compound
phases characterized by the coexistence of spin pairing and atomic-density
waves. A smooth crossover occurs with increasing magnitude of the atom-atom
attraction to a state in which tightly bound spin-singlet dimers occupy the
center of the trap. The existence of atomic-density waves could be detected in
the elastic contribution to the light-scattering diffraction pattern.Comment: 10 pages, 3 figures, 1 Table, submitted to Phys. Rev. on July 25th
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A Unified Framework for the Study of Anti-Windup Designs
We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework
Magnonic Goos–Hänchen Effect Induced by 1D Solitons
The spin wave spectral problem is solved in terms of the spectrum of a diagonalizable operator for a class of magnetic states that includes several types of domain walls and the chiral solitons of monoaxial helimagnets. Focusing on these latter solitons, it is shown that the spin waves reflected and transmitted by them suffer a lateral displacement analogous to the Goos-Hänchen effect of optics. The displacement is a fraction of the wavelength, but can be greatly enhanced by using an array of well separated solitons. Contrarily to the Goos–Hänchen effect recently studied in some magnetic systems, which takes place at the interfaces between different magnetic systems, the effect predicted here takes place at the soliton position, which is interesting for applications since solitons can be created at different places and moved across the material by suitable means. Moreover, the effect predicted here is not particular to monoaxial helimagnets, but it is generic of 1D solitons, although it is accidentally absent in the domain walls of ferromagnets with uniaxial anisotropy. Even though in this work the dipolar interaction is ignored for simplicity, we argue that the Goos–Hänchen shift is also present when it is taken into account. © 2021 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbH
Diffraction in time of a confined particle and its Bohmian paths
Diffraction in time of a particle confined in a box which its walls are
removed suddenly at is studied. The solution of the time-dependent
Schr\"{o}dinger equation is discussed analytically and numerically for various
initial wavefunctions. In each case Bohmian trajectories of the particles are
computed and also the mean arrival time at a given location is studied as a
function of the initial state.Comment: 8 pages, 6 figure
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