Bond-located phases driven by exchange interaction in the one-dimensional t-U-V-J model

The one-dimensional half-filled extended Hubbard model with on-site repulsion (U) and nearest-neighbor interactions including Coulomb repulsion (V) and exchange (J) is studied in the weak-coupling regime. We present a theoretical argument for the occurrence of bond-located phases. The bond-charge-density-wave (BCDW) is realized for J>0 and bond-spin-density-wave (BSDW) occurs for J<0.     

An open problem on the optimality of an asymptotic solution to Duffing’s nonlinear oscillation problem

Based on the renormalization group method, Kirkinis (2012) [8] obtained an asymptotic solution to Duffing’s nonlinear oscillation problem. Kirkinis then asked if the asymptotic solution is optimal. In this paper, an affirmative answer to the open problem is given by means of the homotopy analysis method.     

Renormalization group study of quantum fluctuations near classical critical points of Hamiltonian systems

A general framework is considered for treating quantum corrections to the classical limit in the Wigner function formalism. We discuss the quantal effect on the classical phenomena such as period doubling and the breakup of KAM tori. By using an exact renormalization group method, the scaling factor for Planck's constant is derived as an eigenvalue of the linearized renormalization transformation.     

Renormalization by continuous unitary transformations: one-dimensional spinless fermions

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the Hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension favorable results are obtained which agree well with the exact findings based on Bethe ansatz. Received 21 August 2002 / Received in final form 29 October 2002 Published online 31 December 2002     

Fluctuation-dissipation theorem and the dynamical renormalization group

The relation between a recently introduced dynamical real-space renormalization group and the fluctuation-dissipation theorem is discussed. An apparent incompatibility is pointed out and resolved.     

Nonequilibrium quasi-classical effective meson gas: Thermalization

We consider a gas of interacting relativistic effective mesons (qualitatively, like those produced in a heavy-ion collision), regarded as an out-of-equilibrium statistical system. We suppose large occupation numbers, temperature somewhat below typical critical temperatures and the quasi-classical regime. At some initial time t₀, let the gas be in a nonequilibrium state, with spatial inhomogeneities. The time evolution of the gas for t > t ₀ is studied by a moment method, and appropriate long-time approximations, which could yield the approach to global thermal equilibrium, are discussed.     

On analytic perturbations of a family of Feigenbaum-like equations

We prove existence of solutions (?,λ) of a family of Feigenbaum-like equations

(0.1)     

Calculation of the pressure of a hot scalar theory within the Non-Perturbative Renormalization Group

We apply to the calculation of the pressure of a hot scalar field theory a method that has been recently developed to solve the Non-Perturbative Renormalization Group. This method yields an accurate determination of the momentum dependence of n  -point functions over the entire momentum range, from the low momentum, possibly critical, region up to the perturbative, high momentum region. It has therefore the potential to account well for the contributions of modes of all wavelengths to the thermodynamical functions, as well as for the effects of the mixing of quasiparticles with multi-particle states. We compare the thermodynamical functions obtained with this method to those of the so-called Local Potential Approximation, and we find extremely small corrections. This result points to the robustness of the quasiparticle picture in this system. It also demonstrates the stability of the overall approximation scheme, and this up to the largest values of the coupling constant that can be used in a scalar theory in 3+1$3+1$ dimensions. This is in sharp contrast to perturbation theory which shows no sign of convergence, up to the highest orders that have been recently calculated.