Search results for "Fixed point"
showing 10 items of 347 documents
Efficient adiabatic tracking of driven quantum nonlinear systems
2013
We derive a technique of robust and efficient adiabatic passage for a driven nonlinear quantum system, describing the transfer to a molecular Bose-Einstein condensate from an atomic one by external fields. The pulse ingredients are obtained by tracking the dynamics derived from a Hamiltonian formulation, in the adiabatic limit. This leads to a nonsymmetric and nonmonotonic chirp. The efficiency of the method is demonstrated in terms of classical phase space, more specifically with the underlying fixed points and separatrices. We also prove the crucial property that this nonlinear system does not have any solution leading exactly to a complete transfer. It can only be reached asymptotically …
Evidence against non-asymptotically-free theories of strong interactions
1977
Abstract It is shown that ultraviolet finite fixed point theories of strong interactions are incompatible with the pattern of scaling deviations in deep inelastic lepton-hadron processes.
Minimal technicolor on the lattice
2009
Abstract We present results from a lattice study of SU(2) gauge theory with 2 flavors of Dirac fermions in adjoint representation. This is a candidate for a minimal (simplest) walking technicolor theory, and has been predicted to possess either an IR fixed point (where the physics becomes conformal) or a coupling which evolves very slowly, so-called walking coupling. In this initial part of the study we investigate the lattice phase diagram and the excitation spectrum of the theory.
Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure
1999
In this work we consider a coupled system of Schwinger-Dyson equations for self-energy and vertex functions in QED_3. Using the concept of a semi-amputated vertex function, we manage to decouple the vertex equation and transform it in the infrared into a non-linear differential equation of Emden-Fowler type. Its solution suggests the following picture: in the absence of infrared cut-offs there is only a trivial infrared fixed-point structure in the theory. However, the presence of masses, for either fermions or photons, changes the situation drastically, leading to a mass-dependent non-trivial infrared fixed point. In this picture a dynamical mass for the fermions is found to be generated c…
Screened potential and quarkonia properties at high temperatures
2009
We perform a quark model calculation of the quarkonia b (b) over bar and c (c) over bar spectra using smooth and sudden string breaking potentials. The screening parameter is scale dependent and can be related to an effective running gluon mass that has a finite infrared fixed point. A temperature dependence for the screening mass is motivated by lattice QCD simulations at finite temperature. Qualitatively different results are obtained for quarkonia properties close to a critical value of the deconfining temperature when a smooth or a sudden string breaking potential is used. In particular, with a sudden string breaking potential quarkonia radii remain almost independent of the temperature…
Second-Order Phase Transition Induced by Deterministic Fluctuations in Aperiodic Eight-State Potts Models
1999
We investigate the influence of aperiodic modulations of the exchange interactions between nearest-neighbour rows on the phase transition of the two-dimensional eight-state Potts model. The systems are studied numerically through intensive Monte Carlo simulations using the Swendsen-Wang cluster algorithm for different aperiodic sequences. The transition point is located through duality relations, and the critical behaviour is investigated using FSS techniques at criticality. While the pure system exhibits a first-order transition, we show that the deterministic fluctuations resulting from the aperiodic coupling distribution are liable to modify drastically the physical properties in the nei…
An intrinsic characterization of 2+2 warped spacetimes
2010
We give several equivalent conditions that characterize the 2+2 warped spacetimes: imposing the existence of a Killing-Yano tensor $A$ subject to complementary algebraic restrictions; in terms of the projector $v$ (or of the canonical 2-form $U$) associated with the 2-planes of the warped product. These planes are principal planes of the Weyl and/or Ricci tensors and can be explicitly obtained from them. Therefore, we obtain the necessary and sufficient (local) conditions for a metric tensor to be a 2+2 warped product. These conditions exclusively involve explicit concomitants of the Riemann tensor. We present a similar analysis for the conformally 2+2 product spacetimes and give an invaria…
Multiplicity of positive solutions for a degenerate nonlocal problem with p-Laplacian
2021
Abstract We consider a nonlinear boundary value problem with degenerate nonlocal term depending on the L q -norm of the solution and the p-Laplace operator. We prove the multiplicity of positive solutions for the problem, where the number of solutions doubles the number of “positive bumps” of the degenerate term. The solutions are also ordered according to their L q -norms.
Renormalization-scheme ambiguity and perturbation theory near a fixed point
1984
We consider the perturbative calculation of critical exponents in massless, renormalizable theories having a nontrivial fixed point. In conventional perturbation theory, all results depend on the arbitrary renormalization scheme used. We show how to resolve this problem, following the "principle of minimal sensitivity" approach. At least three orders of perturbation theory are required for quantitative results. We give scheme-independent criteria for determining the presence or absence of a fixed point in $n\mathrm{th}$ order, and discuss the conditions under which perturbative results might be reliable. As illustrations we discuss QED with many flavors, and ${({\ensuremath{\varphi}}^{4})}_…
Low-energy fixed points of random Heisenberg models
2002
The effect of quenched disorder on the low-energy and low-temperature properties of various two- and three-dimensional Heisenberg models is studied by a numerical strong disorder renormalization group method. For strong enough disorder we have identified two relevant fixed points, in which the gap exponent, omega, describing the low-energy tail of the gap distribution, P(Delta) ~ Delta^omega is independent of disorder, the strength of couplings and the value of the spin. The dynamical behavior of non-frustrated random antiferromagnetic models is controlled by a singlet-like fixed point, whereas for frustrated models the fixed point corresponds to a large spin formation and the gap exponent …