37298919
Response of an electron system to a periodic potential
We give a quantum field theoretical treatment of a one-dimensional electron system with a fixed chemical potential μ. The non-perturbative Lindhard response function is found for an electron system in a sinusoidal potential.
11500580
Renormalization-group analysis of layered sine-Gordon type models
Abstract We analyze the phase structure and the renormalization group (RG) flow of the generalized sine-Gordon models with nonvanishing mass terms, using the Wegner–Houghton RG method in the local potential approximation. Particular emphasis is laid upon the layered sine-Gordon (LSG) model, which is the bosonized version of the multi-flavour Schwinger model and approaches the sum of two “normal”, massless sine-Gordon (SG) models in the limit of a vanishing interlayer coupling J . Another model of interest is the massive sine-Gordon (MSG) model. The leading-order approximation to the UV (ultraviolet) RG flow predicts two phases for the LSG as well as for the MSG, just as it would be expected for the SG model, where the two phases are known to be separated by the Coleman fixed point. The presence of finite mass terms (for the LSG and the MSG) leads to corrections to the UV RG flow, which are naturally identified as the “mass corrections”. The leading-order mass corrections are shown to have the following consequences: (i) for the MSG model, only one phase persists, and (ii) for the LSG model, the transition temperature is modified. Within the mass-corrected UV scaling laws, the limit of J → 0 is thus nonuniform with respect to the phase structure of the model. The modified phase structure of general massive sine-Gordon models is connected with the breaking of symmetries in the internal space spanned by the field variables. For the LSG, the second-order subleading mass corrections suggest that there exists a cross-over regime before the IR scaling sets in, and the nonlinear terms show explicitly that higher-order Fourier modes appear in the periodic blocked potential.
119203296
Degeneracy induced scaling of the correlation length for periodic models
Abstract The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz–Thouless type phase transition.
54892796
Critical exponents of the O(N) model in the infrared limit from functional renormalization
We determined the critical exponent $\nu$ of the scalar O(N) model with a strategy based on the definition of the correlation length in the infrared limit. The functional renormalization group treatment of the model shows that there is an infrared fixed point in the broken phase. The appearing degeneracy induces a dynamical length scale there, which can be considered as the correlation length. It is shown that the IR scaling behavior can account either for the Ising type phase transition in the 3-dimensional O(N) model, or for the Kosterlitz-Thouless type scaling of the 2-dimensional O(2) model.
119118170
Interplay of fixed points in scalar models
We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that can be identified with the correlation length. This enables one to identify the type of the phase transition which shows similarity to the one appearing in the crossover scale. The critical exponent ν of the correlation length also proved to be equal in the crossover and the infrared scaling regimes.
85464497
Functional renormalization group for quantized anharmonic oscillator
Abstract Functional renormalization group methods formulated in the real-time formalism are applied to the O ( N ) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.
122032402
High-frequency Ramsey excitation in a Penning trap
The Ramsey excitation method for high-precision mass-measurements of highly-charged ions has been investigated and benchmarked using H2+ ions in the Penning-trap mass-spectrometer SMILETRAP. The reason for using H2+ ions are their high cyclotron frequency which is typical for the highly-charged ions usually used at SMILETRAP. Two-, three- and four-pulse Ramsey excitation data are analyzed with the help of recent theoretical work and are compared with the previously used single-pulse excitation data. An improvement factor of 2.9 in the statistical uncertainty is achieved. Furthermore the mass of 76Se, included in the previous Q-value measurement of the 76Ge neutrinoless double beta decay, is checked using 76Se25+ ions and a three-pulse Ramsey excitation. The results show a convincing agreement with the measurement when using single-pulse excitation and therefore our Q-value of 2039.006(50) keV, performed with single-pulse excitation, is confirmed.
115135571
A magic pyramid of supergravities
A bstractBy formulating $ \mathcal{N} $ = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in $ \mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O} $, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar $ \mathbb{R},\mathbb{C},\mathbb{H},\mathbb{O} $ description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4 × 4 magic square, while the higher levels are comprised of a 3 × 3 square in D = 4, a 2 × 2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of anexotic theory with G/H duality structure F4(4)/Sp(3) × Sp(1).
36063309
THE MASS-RADIUS RELATION FOR STAR-FORMING GALAXIES AT z ∼ 1.5-3.0
We present early results from a Hubble Space Telescope WFC3/IR imaging survey of star-forming galaxies in the redshift range 1.5 < z < 3.0. When complete, this survey will consist of 42 orbits of F160W imaging distributed amongst 10 survey fields on the line of sight to bright background QSOs, covering 65 arcmin^2 to a depth of 27.9 AB with a point-spread function FWHM of 0".18. In this contribution, we use a subset of these fields to explore the evolution of the galactic stellar mass-radius relation for a magnitude-limited sample of 102 spectroscopically confirmed star-forming galaxies ((SFR) ~ 30 M_☉ yr^(–1)) with stellar mass M_* ~ 10^(10) M_☉. Although the light profile of these galaxies often has an irregular, multi-component morphology, it is typically possible to describe the brightest component with a Sersic profile of index n ~ 1. The circularized half-light radius r e of the brightest component is on average r_e = 1.66 ± 0.79 kpc (i.e., ~50%-70% the size of local late-type galaxies with similar stellar mass), consistent with recent theoretical models that incorporate strong feedback from star-forming regions. The mean half-light radius increases with stellar mass and, at fixed stellar mass, evolves with cosmic time as ~(1 + z)^(–1.42), suggesting that high-redshift star-forming galaxies may evolve onto the local stellar mass-radius relation by redshift z ~ 1.
18098456
A broad-band FT-ICR Penning trap system for KATRIN
The KArlsruhe TRItium Neutrino experiment KATRIN aims at improving the upper limit of the mass of the electron antineutrino to about 0.2 eV (90% c.l.) by investigating theβ-decay of tritium gas molecules T2→ ( 3 HeT) + + e − + ¯ νe. The experiment is currently under construction to start firs t data taking in 2012. One source of systematic uncertainties in the KATRIN experiment is the formation of ion clusters when tritium decays and decay products interact with residual tritium molecules. It is essential to monitor the a bundances of these clusters since they have different final state energies than tritium ions. For this purpose, a protot ype of a cylindrical Penning trap has been constructed and tested at the Max-Planck-Institute for Nuclear Physics in Heidelberg, which will be installed in the KATRIN beam line. This system employs the technique of Fourier-Transform Ion-Cyclotron-Resonance in order to measure the abundances of the different stored ion species.
26765894
Magic square from Yang-Mills squared.
We give a unified description of D=3 super-Yang-Mills theory with N=1, 2, 4, and 8 supersymmeties in terms of the four division algebras: reals (R), complexes (C), quaternions (H) and octonions (O). Tensoring left and right super-Yang-Mills multiplets with N=1, 2, 4, 8 we obtain a magic square RR, CR, CC, HR, HC, HH, OR, OC, OH, OO description of D=3 supergravity with N=2, 3, 4, 5, 6, 8, 9, 10, 12, 16.