24,463 research outputs found
Pathway from condensation via fragmentation to fermionization of cold bosonic systems
For small scattering lengths, cold bosonic atoms form a condensate the
density profile of which is smooth. With increasing scattering length, the
density {\it gradually} acquires more and more oscillations. Finally, the
number of oscillations equals the number of bosons and the system becomes {\it
fermionized}. On this pathway from condensation to fermionization intriguing
phenomena occur, depending on the shape of the trap. These include macroscopic
fragmentation and
{\it coexistence} of condensed and fermionized parts that are separated in
space.Comment: 12 pages, 2 figure
The microcanonical thermodynamics of finite systems: The microscopic origin of condensation and phase separations; and the conditions for heat flow from lower to higher temperatures
Microcanonical thermodynamics allows the application of statistical mechanics
both to finite and even small systems and also to the largest, self-gravitating
ones. However, one must reconsider the fundamental principles of statistical
mechanics especially its key quantity, entropy. Whereas in conventional
thermostatistics, the homogeneity and extensivity of the system and the
concavity of its entropy are central conditions, these fail for the systems
considered here. For example, at phase separation, the entropy, S(E), is
necessarily convex to make exp[S(E)-E/T] bimodal in E. Particularly, as
inhomogeneities and surface effects cannot be scaled away, one must be careful
with the standard arguments of splitting a system into two subsystems, or
bringing two systems into thermal contact with energy or particle exchange. Not
only the volume part of the entropy must be considered. As will be shown here,
when removing constraints in regions of a negative heat capacity, the system
may even relax under a flow of heat (energy) against a temperature slope. Thus
the Clausius formulation of the second law: ``Heat always flows from hot to
cold'', can be violated. Temperature is not a necessary or fundamental control
parameter of thermostatistics. However, the second law is still satisfied and
the total Boltzmann entropy increases. In the final sections of this paper, the
general microscopic mechanism leading to condensation and to the convexity of
the microcanonical entropy at phase separation is sketched. Also the
microscopic conditions for the existence (or non-existence) of a critical
end-point of the phase-separation are discussed. This is explained for the
liquid-gas and the solid-liquid transition.Comment: 23 pages, 2 figures, Accepted for publication in the Journal of
Chemical Physic
Beyond Mean-Field Theory for Attractive Bosons under Transverse Harmonic Confinement
We study a dilute gas of attractive bosons confined in a harmonic cylinder,
i.e. under cylindric confinement due to a transverse harmonic potential. We
introduce a many-body wave function which extends the Bethe ansatz proposed by
McGuire (J. Math. Phys. {\bf 5}, 622 (1964)) by including a variational
transverse Gaussian shape. We investigate the ground state properties of the
system comparing them with the ones of the one-dimensional (1D) attractive Bose
gas. We find that the gas becomes ultra 1D as a consequence of the attractive
interaction: the transverse width of the Bose gas reduces by increasing the
number of particles up to a critical width below which there is the collapse of
the cloud. In addition, we derive a simple analytical expression for the
simmetry-breaking solitonic density profile of the ground-state, which
generalize the one deduced by Calogero and Degasperis (Phys. Rev. A {\bf 11},
265 (1975)). This bright-soliton analytical solution shows near the collapse
small deviations with respect to the 3D mean-field numerical solution. Finally,
we show that our variational Gauss-McGuire theory is always more accurate than
the McGuire theory. In addition, we prove that for small numbers of particles
the Gauss-McGuire theory is more reliable than the mean-field theory described
by the 3D Gross-Pitaevskii equation.Comment: To be published in J. Phys. B.: At. Mol. Opt. Phy
Normalization of the covariant three-body bound state vertex function
The normalization condition for the relativistic three nucleon Bethe-Salpeter
and Gross bound state vertex functions is derived, for the first time, directly
from the three body wave equations. It is also shown that the relativistic
normalization condition for the two body Gross bound state vertex function is
identical to the requirement that the bound state charge be conserved, proving
that charge is automatically conserved by this equation.Comment: 24 pages, 9 figures, published version, minor typos correcte
Solitary wave complexes in two-component mixture condensates
Axisymmetric three-dimensional solitary waves in uniform two-component
mixture Bose-Einstein condensates are obtained as solutions of the coupled
Gross-Pitaevskii equations with equal intracomponent but varying intercomponent
interaction strengths. Several families of solitary wave complexes are found:
(1) vortex rings of various radii in each of the components, (2) a vortex ring
in one component coupled to a rarefaction solitary wave of the other component,
(3) two coupled rarefaction waves, (4) either a vortex ring or a rarefaction
pulse coupled to a localised disturbance of a very low momentum. The continuous
families of such waves are shown in the momentum-energy plane for various
values of the interaction strengths and the relative differences between the
chemical potentials of two components. Solitary wave formation, their stability
and solitary wave complexes in two-dimensions are discussed.Comment: 4 pages, 2 figures, 2 table
GNSS Signal Authentication via Power and Distortion Monitoring
We propose a simple low-cost technique that enables
civil Global Positioning System (GPS) receivers and other civil
global navigation satellite system (GNSS) receivers to reliably
detect carry-off spoofing and jamming. The technique, which
we call the Power-Distortion detector, classifies received signals
as interference-free, multipath-afflicted, spoofed, or jammed
according to observations of received power and correlatio
n
function distortion. It does not depend on external hardware or
a network connection and can be readily implemented on many
receivers via a firmware update. Crucially, the detector can with
high probability distinguish low-power spoofing from ordinary
multipath. In testing against over 25 high-quality empirical data
sets yielding over 900,000 separate detection tests, the detector
correctly alarms on all malicious spoofing or jamming attack
s
while maintaining a
<0.5% single-channel false alarm rate.Aerospace Engineering and Engineering Mechanic
Emergent bipartiteness in a society of knights and knaves
We propose a simple model of a social network based on so-called
knights-and-knaves puzzles. The model describes the formation of networks
between two classes of agents where links are formed by agents introducing
their neighbours to others of their own class. We show that if the proportion
of knights and knaves is within a certain range, the network self-organizes to
a perfectly bipartite state. However, if the excess of one of the two classes
is greater than a threshold value, bipartiteness is not observed. We offer a
detailed theoretical analysis for the behaviour of the model, investigate its
behaviou r in the thermodynamic limit, and argue that it provides a simple
example of a topology-driven model whose behaviour is strongly reminiscent of a
first-order phase transitions far from equilibrium.Comment: 12 pages, 5 figure
Duality and replicas for a unitary matrix model
In a generalized Airy matrix model, a power replaces the cubic term of
the Airy model introduced by Kontsevich. The parameter corresponds to
Witten's spin index in the theory of intersection numbers of moduli space of
curves. A continuation in down to yields a well studied unitary
matrix model, which exhibits two different phases in the weak and strong
coupling regions, with a third order critical point in-between. The application
of duality and replica to the -th Airy model allows one to recover both the
weak and strong phases of the unitary model, and to establish some new results
for these expansions. Therefore the unitary model is also indirectly a
generating function for intersection numbers.Comment: 18 page, add referece
Prospects for the Standard Model Higgs Boson Search in the LEP 2000 Run
A study has been performed of the discovery and exclusion potential of LEP expected in 2000 for the Higgs bosonpredicted by the Standard Model. The tradeoff factors betweenincreasing the luminosity at GeV and reduced integrated luminosity at GeVwere studied. It was shown that only in case some evidencefor a signal is observed it might be worth to increase the integratedluminosity at the lower center-of-mass energy, otherwise,LEP should aim at the highest possible center-of-mass energy.The ultimate expected exclusion limit (at the 95\%\ confidence level)of LEP (with GeV) is estimated to be 114 GeV
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