20 research outputs found
Multiple multidimensional morse wavelets
This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved
The epsilon-expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature
We discuss the application of the momentum-shell renormalization group method
to the interacting homogeneous Bose gas in the symmetric and in the
symmetry-broken phases. It is demonstrated that recently discussed
discrepancies are artifacts of not taking proper care of infrared divergencies
appearing at finite temperature. If these divergencies are taken into account
and treated properly by means of the epsilon-expansion, the resulting
renormalization group equations and the corresponding universal properties are
identical in the symmetric and the symmetry-broken phases.Comment: 11 pages, no figure
Nonperturbative Effects on T_c of Interacting Bose Gases in Power-Law Traps
The critical temperature T_c of an interacting Bose gas trapped in a general
power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of
variational perturbation theory. It is shown that the interaction-induced shift
in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+
O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the
s-wave scattering length divided by the thermal wavelength at T_c, and
eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and
D'(eta) a^{2 eta} describe the leading-order perturbative and nonperturbative
contributions to the critical temperature, respectively. This result
quantitatively shows how an increasingly inhomogeneous potential suppresses the
influence of critical fluctuations. The appearance of the a^{2 eta}
contribution is qualitatively explained in terms of the Ginzburg criterion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/35
Non-Analytic Vertex Renormalization of a Bose Gas at Finite Temperature
We derive the flow equations for the symmetry unbroken phase of a dilute
3-dimensional Bose gas. We point out that the flow equation for the interaction
contains parts which are non-analytic at the origin of the frequency-momentum
space. We examine the way this non-analyticity affects the fixed point of the
system of the flow equations and shifts the value of the critical exponent for
the correlation length closer to the experimental result in comparison with
previous work where the non-analyticity was neglected. Finally, we emphasize
the purely thermal nature of this non-analytic behaviour comparing our approach
to a previous work where non-analyticity was studied in the context of
renormalization at zero temperature.Comment: 21 pages, 4 figure
Thermodynamics of a trapped interacting Bose gas and the renormalization group
We apply perturbative renormalization group theory to the symmetric phase of
a dilute interacting Bose gas which is trapped in a three-dimensional harmonic
potential. Using Wilsonian energy-shell renormalization and the
epsilon-expansion, we derive the flow equations for the system. We relate these
equations to the flow for the homogeneous Bose gas. In the thermodynamic limit,
we apply our results to study the transition temperature as a function of the
scattering length. Our results compare well to previous studies of the problem.Comment: 14 pages, 5 figure
Effective action for QED in 2+1 dimensions at finite temperature
We calculate the effective action for a constant magnetic field and a
time-dependent time-component of the gauge field in 2+1 dimensions at finite
temperature. We also discuss the behaviour of the charge density and the
fermion condensate as order parameters of symmetry breaking.Comment: Latex, 10 pages, no figure