Short distance QCD contribution to the electroweak mass difference of pions

It is known that the short distance QCD contribution to the mass difference of pions is quadratic on the quark masses, and irrelevant with respect to the long distance part. It is also considered in the literature that its calculation contains infinities, which should be absorbed by the quark mass renormalization. Following a prescription by Craigie, Narison, and Riazuddin of a renormalization-group-improved perturbation theory to deal with the electromagnetic mass shift problem in QCD, we show that the short distance QCD contribution to the electroweak pion mass difference (with mu=md≠0) is finite and, of course, its value is negligible compared to other contributions.

Eletrodinâmica de ordem superior em (2+1)D

Pós-graduação em Física - IFT

Fluxo do grupo de renormalização dos modelos-'alfa' e as álgebras de Lie contínuas

Pós-graduação em Física - IFT

Dynamics of doublon-holon pairs in Hubbard two-leg ladders

The dynamics of holon-doublon pairs is studied in Hubbard two-leg ladders using the time-dependent density matrix renormalization group method. We find that the geometry of the two-leg ladder, which is qualitatively different from a one-dimensional chain due to the presence of a spin gap, strongly affects the propagation of a doublon-holon pair. Two distinct regimes are identified. For weak interleg coupling, the results are qualitatively similar to the case of the propagation previously reported in Hubbard chains, with only a renormalization of parameters. More interesting is the case of strong interleg coupling where substantial differences arise, particularly regarding the double occupancy and properties of the excitations such as the doublon speed. Our results suggest a connection between the presence of a spin gap and qualitative changes in the doublon speed, indicating a weak coupling between the doublon and the magnetic excitations.

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

Charge dynamics in half-filled Hubbard chains with finite on-site interaction

We study the charge dynamic structure factor of the one-dimensional Hubbard model with finite on-site repulsion U at half-filling. Numerical results from the time-dependent density matrix renormalization group are analyzed by comparison with the exact spectrum of the model. The evolution of the line shape as a function of U is explained in terms of a relative transfer of spectral weight between the two-holon continuum that dominates in the limit U -> infinity and a subset of the two-holon-two-spinon continuum that reconstructs the electron-hole continuum in the limit U -> 0. Power-law singularities along boundary lines of the spectrum are described by effective impurity models that are explicitly invariant under spin and eta-spin SU(2) rotations. The Mott-Hubbard metal-insulator transition is reflected in a discontinuous change of the exponents of edge singularities at U = 0. The sharp feature observed in the spectrum for momenta near the zone boundary is attributed to a van Hove singularity that persists as a consequence of integrability.

Rounding of a first-order quantum phase transition to a strong-coupling critical point

We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the N-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme. DOI: 10.1103/PhysRevB.86.214204

Signatures of quantum phase transitions in parallel quantum dots: Crossover from local moment to underscreened spin-1 Kondo physics

We study a strongly interacting "quantum dot 1" and a weakly interacting "dot 2" connected in parallel to metallic leads. Gate voltages can drive the system between Kondo-quenched and non-Kondo free-moment phases separated by Kosterlitz-Thouless quantum phase transitions. Away from the immediate vicinity of the quantum phase transitions, the physical properties retain signatures of first-order transitions found previously to arise when dot 2 is strictly noninteracting. As interactions in dot 2 become stronger relative to the dot-lead coupling, the free moment in the non-Kondo phase evolves smoothly from an isolated spin-one-half in dot 1 to a many-body doublet arising from the incomplete Kondo compensation by the leads of a combined dot spin-one. These limits, which feature very different spin correlations between dot and lead electrons, can be distinguished by weak-bias conductance measurements performed at finite temperatures.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Higher spatial derivative field theories

In this work, we employ renormalization group methods to study the general behavior of field theories possessing anisotropic scaling in the spacetime variables. The Lorentz symmetry breaking that accompanies these models are either soft, if no higher spatial derivative is present, or it may have a more complex structure if higher spatial derivatives are also included. Both situations are discussed in models with only scalar fields and also in models with fermions as a Yukawa-like model.

Running coupling and pomeron loop effects on inclusive and diffractive DIS cross sections

Within the framework of a (1 + 1)-dimensional model which mimics high-energy QCD, we study the behavior of the cross sections for inclusive and diffractive deep inelastic gamma*h scattering cross sections. We analyze the cases of both fixed and running coupling within the mean-field approximation, in which the evolution of the scattering amplitude is described by the Balitsky-Kovchegov equation, and also through the pomeron loop equations, which include in the evolution the gluon number fluctuations. In the diffractive case, similarly to the inclusive one, suppression of the diffusive scaling, as a consequence of the inclusion of the running of the coupling, is observed.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

Black hole formation with an interacting vacuum energy density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological beta parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time, but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the value of beta. In the radiation case, a trapped surface is formed for beta <= 1/2, whereas for beta >= 1/2, a naked singularity is developed. In general, the critical value is beta = 1-2/3(1 + omega) where omega is the parameter describing the equation of state of the fluid component.

Untersuchungen zum nichtstörungstheoretischen Renormierungsverhalten der Quanten-Einstein-Gravitation

Deutsche Version: Zunächst wird eine verallgemeinerte Renormierungsgruppengleichung für die effektiveMittelwertwirkung der EuklidischenQuanten-Einstein-Gravitation konstruiert und dann auf zwei unterschiedliche Trunkierungen, dieEinstein-Hilbert-Trunkierung und die$R^2$-Trunkierung, angewendet. Aus den resultierendenDifferentialgleichungen wird jeweils die Fixpunktstrukturbestimmt. Die Einstein-Hilbert-Trunkierung liefert nebeneinem Gaußschen auch einen nicht-Gaußschen Fixpunkt. Diesernicht-Gaußsche Fixpunkt und auch der Fluß in seinemEinzugsbereich werden mit hoher Genauigkeit durch die$R^2$-Trunkierung reproduziert. Weiterhin erweist sichdie Cutoffschema-Abhängigkeit der analysierten universellenGrößen als äußerst schwach. Diese Ergebnisse deuten daraufhin, daß dieser Fixpunkt wahrscheinlich auch in der exaktenTheorie existiert und die vierdimensionaleQuanten-Einstein-Gravitation somit nichtperturbativ renormierbar sein könnte. Anschließend wird gezeigt, daß der ultraviolette Bereich der$R^2$-Trunkierung und somit auch die Analyse des zugehörigenFixpunkts nicht von den Stabilitätsproblemen betroffen sind,die normalerweise durch den konformen Faktor der Metrikverursacht werden. Dadurch motiviert, wird daraufhin einskalares Spielzeugmodell, das den konformen Sektor einer``$-R+R^2$''-Theorie simuliert, hinsichtlich seinerStabilitätseigenschaften im infraroten (IR) Bereichstudiert. Dabei stellt sich heraus, daß sich die Theorieunter Ausbildung einer nichttrivialen Vakuumstruktur auf dynamische Weise stabilisiert. In der Gravitation könnteneventuell nichtlokale Invarianten des Typs $intd^dx,sqrt{g}R (D^2)^{-1} R$ dafür sorgen, daß der konformeSektor auf ähnliche Weise IR-stabil wird.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.