Narrow Results

We proposed Atomic Schwinger–Dyson method (ASD method) in previous paper, which was a nonperturbative and relativistic quantum field theory for a finite baryon density. We think it is important to show the significance of renormarization in order to get real physical predictions. Moreover, the real value of physical mass, electric charge and wave function are completely different from those of the non-renormalized electron and photon in mean field theory, since there are many of the particle-antiparticle creations and annihilations, particle-hole excitation, and Pauli blocking, which give an effect on bare mass, electric charge, polarization of vacuum, and self-energy. In this paper, we shows that ASD method is renormalizable theory, and that photon condensation of ASD method gave rise to Coulomb's potential and the mass shift of electron. The interacting photon and electron fields, which have physical mass and electric charge, are expressed as generalized free field equations by using the mass shift and the self-energy of those particles. We obtain the expression of an exact solution of these particles on the basis of the Green functional method.

We evaluate the universal turbulent Prandtl numbers in the energy and enstrophy régimes of the Kraichnan-Batchelor spectra of two-dimensional turbulence using a self-consistent mode-coupling formulation coming from a renormalized perturbation expansion coupled with dynamic scaling ideas. The turbulent Prandtl number is found to be exactly unity in the (logarithmic) enstrophy régime, where the theory is infrared marginal. In the energy régime, the theory being finite, we extract singularities coming from both ultraviolet and infrared ends by means of Laurent expansions about these poles. This yields the turbulent Prandtl number σ ≈ 0.9 in the energy régime.

In this work, we present a review of the results obtained in the exploitation of percolation theory and the renormalization group method in the study of soil moisture spatial patterns.

In order to capture critical point in soil moisture spatio-temporal dynamics, we developed an algorithm consisting of three steps: (i) dichotomization, i.e., transforming the soil moisture maps into binary maps; (ii) identification of the largest wet cluster; (iii) scaling transformation, i.e., applying an ad hoc implemented coarse-graining procedure to the binary maps.

The methodology was explored by means of several applications on soil moisture data coming from field measurement, remote sensing, and hydrological modelling over a wide range of spatial scales. From the relations between the occupation probability in soil moisture spatial patterns and the normalized size of the largest cluster at different scales, as well as the scaling behaviour, it is possible to argue that also for this physical system the critical point theory applies.

The critical probability seems to be a structural feature of the catchment, being insensitive to the scale of the analysis, as well as to the parameterization of the methodology.

We compute analytically the all-loop level critical exponents for a massless thermal Lorentz-violating (LV) O(N) self-interacting $\lambda {\varphi }^4$ scalar field theory. For that, we evaluate, firstly explicitly up to next-to-leading loop order and later in a proof by induction up to any loop level, the respective $\beta$-function and anomalous dimensions in a theory renormalized in the massless BPHZ method, where a reduced set of Feynman diagrams to be calculated is needed. We investigate the effect of the Lorentz violation in the outcome for the critical exponents and present the corresponding mathematical explanation and physical interpretation.

The way to determine the renormalized energy of inhomogeneous systems of a quantum field under an external potential is established for both equilibrium and nonequilibrium scenarios based on thermo field dynamics. The key step is to find an extension of the on-shell concept valid in homogeneous case. In the nonequilibrium case, we expand the field operator by time-dependent wavefunctions that are solutions of the appropriately chosen differential equation, synchronizing with temporal change of thermal situation, and the quantum transport equation is derived from the renormalization procedure. Through numerical calculations of a triple-well model with a reservoir, we show that the number distribution and the time-dependent wavefunctions are relaxed consistently to the correct equilibrium forms at the long-term limit.