192 research outputs found
Ursell Operators in Statistical Physics III: thermodynamic properties of degenerate gases
We study in more detail the properties of the generalized Beth Uhlenbeck
formula obtained in a preceding article. This formula leads to a simple
integral expression of the grand potential of the system, where the interaction
potential appears only through the matrix elements of the second order Ursell
operator . Our results remain valid for significant degree of degeneracy
of the gas, but not when Bose Einstein (or BCS) condensation is reached, or
even too close from this transition point. We apply them to the study of the
thermodynamic properties of degenerate quantum gases: equation of state,
magnetic susceptibility, effects of exchange between bound states and free
particles, etc. We compare our predictions to those obtained within other
approaches, especially the ``pseudo potential'' approximation, where the real
potential is replaced by a potential with zero range (Dirac delta function).
This comparison is conveniently made in terms of a temperature dependent
quantity, the ``Ursell length'', which we define in the text. This length plays
a role which is analogous to the scattering length for pseudopotentials, but it
is temperature dependent and may include more physical effects than just binary
collision effects; for instance at very low temperatures it may change sign or
increase almost exponentially, an effect which is reminiscent of a precursor of
the BCS pairing transition. As an illustration, numerical results for quantum
hard spheres are given.Comment: 26 pages, 4 figures, LaTeX (amssymb), slight changes to first versio
Resonant tunneling through a C60 molecular junction in liquid environment
We present electronic transport measurements through thiolated C
molecules in liquid environment. The molecules were placed within a
mechanically controllable break junction using a single anchoring group per
molecule. When varying the electrode separation of the C-modified
junctions, we observed a peak in the conductance traces. The shape of the
curves is strongly influenced by the environment of the junction as shown by
measurements in two distinct solvents. In the framework of a simple resonant
tunneling model, we can extract the electronic tunneling rates governing the
transport properties of the junctions.Comment: 13 pages, 4 figures. To appear in Nanotechnolog
Transition Temperature of a Uniform Imperfect Bose Gas
We calculate the transition temperature of a uniform dilute Bose gas with
repulsive interactions, using a known virial expansion of the equation of
state. We find that the transition temperature is higher than that of an ideal
gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a
is the S-wave scattering length, and K_0 is a constant given in the paper. This
disagrees with all existing results, analytical or numerical. It agrees exactly
in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe
Thermodynamic properties of confined interacting Bose gases - a renormalization group approach
A renormalization group method is developed with which thermodynamic
properties of a weakly interacting, confined Bose gas can be investigated.
Thereby effects originating from a confining potential are taken into account
by periodic boundary conditions and by treating the resulting discrete energy
levels of the confined degrees of freedom properly. The resulting density of
states modifies the flow equations of the renormalization group in momentum
space. It is shown that as soon as the characteristic length of confinement
becomes comparable to the thermal wave length of a weakly interacting and
trapped Bose gas its thermodynamic properties are changed significantly. This
is exemplified by investigating characteristic bunching properties of the
interacting Bose gas which manifest themselves in the second order coherence
factor
\epsilon-regularity for systems involving non-local, antisymmetric operators
We prove an epsilon-regularity theorem for critical and super-critical
systems with a non-local antisymmetric operator on the right-hand side.
These systems contain as special cases, Euler-Lagrange equations of
conformally invariant variational functionals as Rivi\`ere treated them, and
also Euler-Lagrange equations of fractional harmonic maps introduced by Da
Lio-Rivi\`ere.
In particular, the arguments presented here give new and uniform proofs of
the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and
also the integrability results by Sharp-Topping and Sharp, not discriminating
between the classical local, and the non-local situations
Self-consistent equation for an interacting Bose gas
We consider interacting Bose gas in thermal equilibrium assuming a positive
and bounded pair potential such that 0<\int d\br V(r) = a<\infty.
Expressing the partition function by the Feynman-Kac functional integral yields
a classical-like polymer representation of the quantum gas. With Mayer graph
summation techniques, we demonstrate the existence of a self-consistent
relation between the density and the
chemical potential , valid in the range of convergence of Mayer series.
The function is equal to the sum of all rooted multiply connected graphs.
Using Kac's scaling V_{\gamma}(\br)=\gamma^{3}V(\gamma r) we prove that in
the mean-field limit only tree diagrams contribute and function
reduces to the free gas density.
We also investigate how to extend the validity of the self-consistent
relation beyond the convergence radius of Mayer series (vicinity of
Bose-Einstein condensation) and study dominant corrections to mean field. At
lowest order, the form of function is shown to depend on single polymer
partition function for which we derive lower and upper bounds and on the
resummation of ring diagrams which can be analytically performed.Comment: 33 pages, 6 figures, submitted to Phys.Rev.
Transition temperature of a dilute homogeneous imperfect Bose gas
The leading-order effect of interactions on a homogeneous Bose gas is
theoretically predicted to shift the critical temperature by an amount
\Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where
a_{scatt} is the scattering length and n is the density. There have been
several different theoretical estimates for the numerical coefficient #. We
claim to settle the issue by measuring the numerical coefficient in a lattice
simulation of O(2) phi^4 field theory in three dimensions---an effective theory
which, as observed previously in the literature, can be systematically matched
to the dilute Bose gas problem to reproduce non-universal quantities such as
the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to
improvement of analysis in the longer companion pape
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Automatic Analysis of Bees’ Waggle Dance
This work describe an algorithm for the automatic analysis of the waggle dance of honeybees. The algorithm analyses a video of a beehive with 13,624 frames, acquired at 25 frames/second. The algorithm employs the following traditional image processing steps: conversion to grayscale, low pass filtering, background subtraction, thresholding, tracking and clustering to detect run of bees that perform waggle dances. The algorithm detected 44,530 waggle events, i.e. one bee waggling in one time frame, which were then clustered into 511 waggle runs. Most of these were concentrated in one section of the hive. The accuracy of the tracking was 90% and a series of metrics like intra-dance variation in angle and duration were found to be consistent with literature. Whilst this algorithm was tested on a single video, the ideas and steps, which are simple as compared with Machine and Deep Learning techniques, should be attractive for researchers in this field who are not specialists in more complex techniques
Correlated expression of phenotypic and extended phenotypic traits across stingless bee species: worker eye morphology, foraging behaviour, and nest entrance architecture.
Abstract: Stingless bees are the most species-rich group of eusocial bees and show great diversity in behaviour, ecology, nest architecture, colony size, and worker morphology. How this variation relates to varying selection pressures and constraints is not well understood. Variation can be caused by selection acting on behavioural or morphological traits, both alone and in correlation across traits. Here we tested whether behavioural and morphological traits important for foraging and defence are linked to nest-entrance architecture, an extended phenotype relevant to both foraging and nest defence. Using 23 species we investigated whether eye size, nest entrance size, landing behaviour and foraging method show cross-species correlations. A phylogenetically-controlled comparative analysis revealed that species with relatively smaller eyes build relatively larger entrances, which in turn are associated with faster landing approaches and fewer landing errors by foragers, both of which could reduce predation risk. Concerning foraging, mass-recruiting species have c. 10-times larger entrance holes than species with a solitary foraging strategy. Larger entrances could help species with mass recruitment to rapidly increase forager traffic or mount a strong defensive response when under attack. Our results show that studying correlations among different traits helps understand phenotypic diversity in species rich groups
Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
We compute the shift of the transition temperature for a homogenous weakly
interacting Bose gas in leading order in the scattering length a for given
particle density n. Using variational perturbation theory through six loops in
a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c =
1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.Comment: 4 pages; omega' corrected: final result changes slightly to
1.25+/-0.13; references added; several minor change
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