Finite renormalizations in the Epstein Glaser framework and renormalization of the S‐matrix of Φ4‐theory

A formula describing finite renormalizations is derived in the Epstein‐Glaser formalism and an explicit calculation of finite counterterms in Φ⁴‐theory is performed. The Zimmermann identities and the action principle for changes of parameters in the interaction are presented independent of the adiabatic limit.     

Bulk singularities at critical end points: a field-theory analysis

A class of continuum models with a critical end point is considered whose Hamiltonian [φ,ψ] involves two densities: a primary order-parameter field, φ, and a secondary (noncritical) one, ψ. Field-theoretic methods (renormalization group results in conjunction with functional methods) are used to give a systematic derivation of singularities occurring at critical end points. Specifically, the thermal singularity ∼ | t|^{2 - α} of the first-order line on which the disordered or ordered phase coexists with the noncritical spectator phase, and the coexistence singularity ∼ | t|^{1 - α} or ∼ | t|^β of the secondary density <ψ> are derived. It is clarified how the renormalization group (RG) scenario found in position-space RG calculations, in which the critical end point and the critical line are mapped onto two separate fixed points _CEP ^* and _λ ^*, translates into field theory. The critical RG eigenexponents of _CEP ^* and _λ ^* are shown to match. _CEP ^* is demonstrated to have a discontinuity eigenperturbation (with eigenvalue y = d), tangent to the unstable trajectory that emanates from _CEP ^* and leads to _λ ^*. The nature and origin of this eigenperturbation as well as the role redundant operators play are elucidated. The results validate that the critical behavior at the end point is the same as on the critical line. Received 18 January 2001     

SOME REMARKS ON SINGULAR DARBOUX TRANSFORMATIONS FOR UNITONS

61. IntroductionHarmonic maPS from memann surfaCes to Lie ~ and synUnetric spaces have re~ much attention recentlyll--6]' An imPOrtant class Of harmonic maPS called unitonsis introduced by Uhlenbedll]. In [2,3], Darboux transformation method is introduced, andthe explicit expreS8ionS for Darboux matrices are used to Obtain new ~ maPS froma knOWn one. By introduced the s~ Darboux trareforlnationS and making use of akind of renormalization Procedure, the authors PreSent a purely algebr…     

Evaluating First-Order Molecular Properties of Delocalized Ionic or Excited States in Molecular Aggregates by Renormalized Excitonic Method

In the past few years, the renormalized excitonic model (REM) approach was developed as an efficient low-scaling ab initio excited state method, which assumes the low-lying excited states of the whole system are a linear combination of various single monomer excitations and utilizes the effective Hamiltonian theory to derive their couplings. In this work, we further extend the REM calculations for the evaluations of first-order molecular properties (e.g. charge population and transition dipole moment) of delocalized ionic or excited states in molecular aggregates, through generalizing the effective Hamiltonian theory to effective operator representation. Results from the test calculations for four different kinds of one dimensional (1D) molecular aggregates (ammonia, formaldehyde, ethylene and pyrrole) indicate that our new scheme can efficiently describe not only the energies but also wavefunction properties of the low-lying delocalized electronic states in large systems.     

Flux modulated flat band engineering in square-kagomé ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagomé ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical boundary created by the site with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.     

Electronic properties of a molecular system with Platinum

The electronic properties are studied using a finite homogeneous molecule called Trans-platinum-linked oligo(tetraethenylethenes). This system is composed of individual molecules such as benzene rings, platinum, Phosphore and Sulfur. The mechanism for the study of the electron transport through this system is based on placing the molecule between metal contacts to control the current through the molecular system.We study this molecule based on the tight-binding approach for the calculation of the transport properties using the Landauer-Büttiker formalism and the Fischer-Lee relationship, based on a semi-analytic Green's function method within a real-space renormalization approach. Our results show a significant agreement with experimental measurements.     

Continuity of Julia set and its Hausdorff dimension of Yang-Lee zeros

We show the continuity of the Julia set and its Hausdorff dimension about a family of rational maps concerning 2-dimensional diamond hierarchical Potts models about anti-ferromagnetic coupling in statistical mechanics.     

Intermediate asymptotics,scaling laws and renormalization group in continuum mechanics

Scaling laws and self-similar solutions are very popular concepts in modern continuum mechanics. In the present paper these concepts are analyzed both from the viewpoint of intermediate asymptotics, known in classical mathematical physics and fluid mechanics, and from the viewpoint of the renormalization group technique, known in modern theoretical physics. The definition of the renormalization group is proposed, related to the intermediate asymptotics with incomplete similarity. The general presentation is illustrated by examples of essentially non-linear problems where all analytical properties of the solutions and their asymptotics are rigorously proved, as well by an example from turbulence, where the rigorous problem statement is missing. General lecture delivered at the 11th Italian National Congress of Theoretical and Applied Mechanics (AIMETA), Trento, Sept./Oct. 1992.     

Renormalization group symmetry method and gas dynamics

A new scenario in the renormalization group symmetry method is introduced to solve an initial value problem for a system of partial differential equations. As a specific example, we give an exact solution for the adiabatic perfect gas dynamics, which describes a contracting and expanding localized mass of gas.