The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ 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 $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

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

A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase

Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model reformulated with two auxiliary fields in a background breaking the symmetry to U(n) are studied in the so-called bare vertex approximation. A large n solution is constructed under the supplementary assumption so that the scalar components are much heavier than the pseudoscalars. The renormalizability of the solution is investigated by explicit construction of the counterterms.Comment: RevTeX4, 14 pages, 2 figures. Version published in Phys. Rev.

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) $M_c$ and a physically interesting sliding energy scale (SES) $\mu_s$ which can run from $\mu_s \sim M_c$ to a dynamically generated mass gap $\mu_s=\mu_c$ or to $\mu_s =0$ 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

Acoustic properties of turbofan inlets

The acoustic field within a duct containing a nonuniform steady flow was predicted. This analysis used the finite element method to calculate the velocity potential within the duct

Many-body physics in the radio frequency spectrum of lattice bosons

We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. Using random phase and local density approximations we produce both trap averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the deep superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the $f$-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A \textbf{79}, 043422 (2009)], we also discuss the features which arise in a spin-dependent optical lattice.Comment: 6 pages, 4 figures, 13 subfigure

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Sep. - 31 Dec. 1969

Theoretical studies and test facility installation for investigating behavior of rocket nozzles and acoustic liners in three dimensional acoustic field

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Dec. 1969 - 28 Feb. 1970

Frequency responses of supercritical nozzles and acoustic liner

Behavior of nozzles and acoustic liners in three-dimensional acoustic fields Quarterly report, 1 Jun. - 31 Aug. 1970

Updating computer program for determining nozzle admittances to eliminate double-root solution and to fit resultant admittance data curves by statistical mean