5,943 research outputs found
Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases
We investigate some exact static and dynamic properties of one-dimensional
fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive
p-wave interactions induced by a Feshbach resonance. A closed form solution for
the one-body density matrix for harmonic trapping is analyzed in terms of its
natural orbitals, with the surprising result that for odd, but not for even,
numbers of fermions the maximally occupied natural orbital coincides with the
ground harmonic oscillator orbital and has the maximally allowed fermionic
occupancy of unity. The exact dynamics of the trapped gas following turnoff of
the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR
PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold
The symmetric potential has
a completely real spectrum for , and begins to develop complex
eigenvalues for . At the symmetry-breaking threshold
some of the eigenvectors become degenerate, giving rise to a Jordan-block
structure for each degenerate eigenvector. In general this is expected to
result in a secular growth in the amplitude of the wave. However, it has been
shown in a recent paper by Longhi, by numerical simulation and by the use of
perturbation theory, that for a broad initial wave packet this growth is
suppressed, and instead a saturation leading to a constant maximum amplitude is
observed. We revisit this problem by explicitly constructing the Bloch
wave-functions and the associated Jordan functions and using the method of
stationary states to find the dependence on the longitudinal distance for a
variety of different initial wave packets. This allows us to show in detail how
the saturation of the linear growth arises from the close connection between
the contributions of the Jordan functions and those of the neighbouring Bloch
waves.Comment: 15 pages, 7 figures Minor corrections, additional reference
The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
An S-matrix satisying the Yang-Baxter equation with symmetries relevant to
the AdS_5xS^5 superstring has recently been determined up to an unknown scalar
factor. Such scalar factors are typically fixed using crossing relations,
however due to the lack of conventional relativistic invariance, in this case
its determination remained an open problem.
In this paper we propose an algebraic way to implement crossing relations for
the AdS_5xS^5 superstring worldsheet S-matrix. We base our construction on a
Hopf-algebraic formulation of crossing in terms of the antipode and introduce
generalized rapidities living on the universal cover of the parameter space
which is constructed through an auxillary, coupling constant dependent,
elliptic curve. We determine the crossing transformation and write functional
equations for the scalar factor of the S-matrix in the generalized rapidity
plane.Comment: 27 pages, no figures; v2: sign typo fixed in (24), everything else
unchange
Modelling and analysis of current and concept vehicles for the purpose of enhancing vehicle handling: executive summary
In this document, research into the modelling and analysis of current and concept vehicles for the purpose of enhancing vehicle handling is summarised. This work is recounted in detail in a portfolio of reports that has been submitted for the degree of Doctor of Engineering.
The portfolio includes fifteen submissions, eleven of which are concerned with the analysis and simulation of drivers' steering behaviour. Two relate to a novel suspension concept. One addresses a current problem caused by suspension variability and one introduces a process for selecting between new suspension concepts. Each of these fifteen submissions is summarised in this document. In addition, the order in which it is recommended that these submissions be read is listed.
In section 4, a project summary of the research into the analysis and simulation of drivers' steering behaviour is presented. Existing models of drivers' steering behaviour are reviewed. Vehicle tests that illustrate the different steering styles used by different drivers are recounted. A driver model that simulates the steering behaviour exhibited in these tests is formulated . Then, this driver model is used to develop a switching strategy for variable dampers. It is demonstrated that the switching strategy enhances vehicle handling and reduces the roll experienced by drivers during a handling manoeuvre.
Finally, it is verified that this research complies with the requirement of the degree of Doctor of Engineering to demonstrate innovation in the application of knowledge to the engineering business environment. This is achieved by specifying eight examples of where new ideas and methods have been applied to address current issues within the automotive industry
Fracture, Fatigue, and Structural Integrity of Metallic Materials and Components Undergoing Random or Variable Amplitude Loadings
When quickly reviewing engineering and industrial fields, one often discovers that a
large number of metallic components and structures are subjected, in service, to random or variable amplitude loadings. The examples are many: vehicles subjected to loadings and vibrations caused by road irregularity and engine, structures exposed to wind, off-shore platforms undergoing wave-loadings, and so on. Just like constant amplitude loadings, random and variable amplitude loadings can make fatigue cracks initiate and propagate, even up to catastrophic failures. Engineers faced with the problem of estimating the structural integrity and the fatigue strength of metallic structures, or their propensity to fracture, usually make use of theoretical or experimental approaches, or both. Counting methods (e.g., rainflow) provide information on the fatigue cycles in the load, whereas damage accumulation laws (as the celebrated Palmgren–Miner linear rule) establish how to sum up the damage of each counted cycle. In structural integrity, this is named as the “time-domain” approach. Over recent years, the “frequency-domain” approach has also received increasing and widespread use, especially with random loadings; this approach estimates fatigue life based on load statistical properties represented, in the frequency domain, by a power spectral density. Neither of the previous approaches, however, can do without the support of experimental laboratory testing, which provides a means to collect material strength data under specific loading conditions, or to verify preliminary estimations. The purpose of this Special Issue is to collect articles aimed at providing an up-todate overview of approaches and case studies—theoretical, numerical or experimental—on several topics in the field of fracture, fatigue strength, and the structural integrity of metallic components subjected to random or variable amplitude loadings
Vafa-Witten theorem and Lee-Yang singularities
We prove the analyticity of the finite volume QCD partition function for
complex values of the theta-vacuum parameter. The absence of singularities
different from Lee-Yang zeros only permits ^ cusp singularities in the vacuum
energy density and never v cusps. This fact together with the Vafa-Witten
diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros
at theta=0 and has an important consequence: the absence of a first order phase
transition at theta=0. The result provides a key missing link in the
Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories
and follows from renormalizability, unitarity, positivity and existence of BPS
bounds. Generalizations of this theorem to other physical systems are also
discussed, with particular interest focused on the non-linear CPn sigma model.Comment: 9 page
Kernel functions and B\"acklund transformations for relativistic Calogero-Moser and Toda systems
We obtain kernel functions associated with the quantum relativistic Toda
systems, both for the periodic version and for the nonperiodic version with its
dual. This involves taking limits of previously known results concerning kernel
functions for the elliptic and hyperbolic relativistic Calogero-Moser systems.
We show that the special kernel functions at issue admit a limit that yields
generating functions of B\"acklund transformations for the classical
relativistic Calogero-Moser and Toda systems. We also obtain the
nonrelativistic counterparts of our results, which tie in with previous results
in the literature.Comment: 76 page
Family memories in the home: contrasting physical and digital mementos
We carried out fieldwork to characterise and compare physical and digital mementos in the home. Physical mementos are highly valued, heterogeneous and support different types of recollection. Contrary to expectations, we found physical mementos are not purely representational, and can involve appropriating common objects and more idiosyncratic forms. In contrast, digital mementos were initially perceived as less valuable, although participants later reconsidered this. Digital mementos were somewhat limited in function and expression, largely involving representational photos and videos, and infrequently accessed. We explain these digital limitations and conclude with design guidelines for digital mementos, including better techniques for accessing and integrating these into everyday life, allowing them to acquire the symbolic associations and lasting value that characterise their physical counterparts
Zero modes on cosmic strings in an external magnetic field
A classical analysis suggests that an external magnetic field can cause
trajectories of charge carriers on a superconducting domain wall or cosmic
string to bend, thus expelling charge carriers with energy above the mass
threshold into the bulk. We study this process by solving the Dirac equation
for a fermion of mass and charge , in the background of a domain wall
and a magnetic field of strength . We find that the modes of the charge
carriers get shifted into the bulk, in agreement with classical expectations.
However the dispersion relation for the zero modes changes dramatically --
instead of the usual linear dispersion relation, , the new
dispersion relation is well fit by where
for a thin wall in the weak field limit, and for a thick
wall of width . This result shows that the energy of the charge carriers on
the domain wall remains below the threshold for expulsion even in the presence
of an external magnetic field. If charge carriers are expelled due to an
additional perturbation, they are most likely to be ejected at the threshold
energy .Comment: 9 pages, 4 figure
Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again
We show that a simple approximation based on concepts underlying the
Kibble-Zurek theory of second order phase transition dynamics can be used to
treat avoided level crossing problems. The approach discussed in this paper
provides an intuitive insight into quantum dynamics of two level systems, and
may serve as a link between the theory of dynamics of classical and quantum
phase transitions. To illustrate these ideas we analyze dynamics of a
paramagnet-ferromagnet quantum phase transition in the Ising model. We also
present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys.
Rev.
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