5,225 research outputs found
The transition temperature of the dilute interacting Bose gas for internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and the scattering length. This
result is non-perturbative, and a direct perturbative calculation of the
amplitude is impossible due to infrared divergences familiar from the study of
the superfluid helium lambda transition. Therefore we introduce here another
standard expansion scheme, generalizing the initial model which depends on one
complex field to one depending on real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large result agrees remarkably well with
recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter
A Convergent Iterative Solution of the Quantum Double-well Potential
We present a new convergent iterative solution for the two lowest quantum
wave functions and of the Hamiltonian with a quartic
double well potential in one dimension. By starting from a trial function,
which is by itself the exact lowest even or odd eigenstate of a different
Hamiltonian with a modified potential , we construct the Green's
function for the modified potential. The true wave functions, or
, then satisfies a linear inhomogeneous integral equation, in which
the inhomogeneous term is the trial function, and the kernel is the product of
the Green's function times the sum of , the potential difference, and
the corresponding energy shift. By iterating this equation we obtain successive
approximations to the true wave function; furthermore, the approximate energy
shift is also adjusted at each iteration so that the approximate wave function
is well behaved everywhere. We are able to prove that this iterative procedure
converges for both the energy and the wave function at all .Comment: 76 pages, Latex, no figure, 1 tabl
Discrete holomorphicity and quantized affine algebras
We consider non-local currents in the context of quantized affine algebras,
following the construction introduced by Bernard and Felder. In the case of
and , these currents can be identified with
configurations in the six-vertex and Izergin--Korepin nineteen-vertex models.
Mapping these to their corresponding Temperley--Lieb loop models, we directly
identify non-local currents with discretely holomorphic loop observables. In
particular, we show that the bulk discrete holomorphicity relation and its
recently derived boundary analogue are equivalent to conservation laws for
non-local currents
Application of finite element techniques in predicting the acoustic properties of turbofan inlets
An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow
Non-Equilibrium Time Evolution in Quantum Field Theory
The time development of equal-time correlation functions in quantum mechanics
and quantum field theory is described by an exact evolution equation for
generating functionals. This permits a comparison between classical and quantum
evolution in non-equilibrium systems.Comment: 7 pages, LaTe
Symmetry Principle Preserving and Infinity Free Regularization and renormalization of quantum field theories and the mass gap
Through defining irreducible loop integrals (ILIs), a set of consistency
conditions for the regularized (quadratically and logarithmically) divergent
ILIs are obtained to maintain the generalized Ward identities of gauge
invariance in non-Abelian gauge theories. Overlapping UV divergences are
explicitly shown to be factorizable in the ILIs and be harmless via suitable
subtractions. A new regularization and renormalization method is presented in
the initial space-time dimension of the theory. The procedure respects
unitarity and causality. Of interest, the method leads to an infinity free
renormalization and meanwhile maintains the symmetry principles of the original
theory except the intrinsic mass scale caused conformal scaling symmetry
breaking and the anomaly induced symmetry breaking. Quantum field theories
(QFTs) regularized through the new method are well defined and governed by a
physically meaningful characteristic energy scale (CES) and a physically
interesting sliding energy scale (SES) which can run from to a dynamically generated mass gap or to in the
absence of mass gap and infrared (IR) problem. It is strongly indicated that
the conformal scaling symmetry and its breaking mechanism play an important
role for understanding the mass gap and quark confinement.Comment: 59 pages, Revtex, 4 figures, 1 table, Erratum added, published
versio
Derivative Expansion of the Exact Renormalization Group
The functional flow equations for the Legendre effective action, with respect
to changes in a smooth cutoff, are approximated by a derivative expansion; no
other approximation is made. This results in a set of coupled non-linear
differential equations. The corresponding differential equations for a fixed
point action have at most a countable number of solutions that are well defined
for all values of the field. We apply the technique to the fixed points of
one-component real scalar field theory in three dimensions. Only two
non-singular solutions are found: the gaussian fixed point and an approximation
to the Wilson fixed point. The latter is used to compute critical exponents, by
carrying the approximation to second order. The results appear to converge
rapidly.Comment: 14 pages (with figures), Plain TeX, uses psfig, 4 postscript figures
appended as uuencoded compressed tar file, SHEP 93/94-16, CERN-TH.7203/94.
(Added small details and minor improvements in rigour : the version to be
published in Phys.Lett.B
Measurements of admittances and characteristic combustion times of reactive gaseous propellant coaxial injectors
The results of an experimental investigation that was concerned with the quantitative determination of the capabilities of combustion processes associated with coaxial injectors to amplify and sustain combustor oscillations was described. The driving provided by the combustion process was determined by employing the modified standing-wave method utilizing coaxial injectors and air-acetylene mixtures. Analyses of the measured data indicate that the investigated injectors are capable of initiating and amplifying combustion instabilities under favorable conditions of injector-combustion coupling and over certain frequency ranges. These frequency ranges and the frequency at which an injector's driving capacity is maximum are observed to depend upon the equivalence ratio, the pressure drop across the injector orifices and the number of injector elements. The characteristic combustion times of coaxial injectors were determined from steady state temperature measurements
Characteristics of response factors of coaxial gaseous rocket injectors
The results of an experimental investigation undertaken to determine the frequency dependence of the response factors of various gaseous propellant rocket injectors subject to axial instabilities are presented. The injector response factors were determined, using the modified impedance-tube technique, under cold-flow conditions simulating those observed in unstable rocket motors. The tested injectors included a gaseous-fuel injector element, a gaseous-oxidizer injector element and a coaxial injector with both fuel and oxidizer elements. Emphasis was given to the determination of the dependence of the injector response factor upon the open-area ratio of the injector, the length of the injector orifice, and the pressure drop across the injector orifices. The measured data are shown to be in reasonable agreement with the corresponding injector response factor data predicted by the Feiler and Heidmann model
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