We study groundstates and low-temperature phases of quantum lattice systems in statistical mechanics: quantum spin systems and fermionic or bosonic lattice gases. The Hamiltonians of such systems have the form H = H0 + tV, where H0 is a classical Hamiltonian, V is a quantum perturbation, and t is the perturbation parameter. Conventional methods to study such systems cannot be used when H0 has i...

We study the classical and quantum perturbation theory for two non–resonant oscillators coupled by a nonlinear quartic interaction. In particular we analyze the question of quantum corrections to the torus quantization of the classical perturbation theory (semiclassical mechanics). We obtain up to the second order of perturbation theory an explicit analytical formula for the quantum energy leve...

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength epsilon. In the regime of weak perturbation, the fidelity decays as exp(-c epsilon(2)t(gamma)) with gamma approximately 1.7. In the regime of strong perturbation...

These notes are a survey of the material treated in a series of lectures delivered at the Xth Summer School Jorge Andr e Swieca. They are concerned with renormalization in Quantum Field Theories. At the level of perturbation series, we review classical results as Feynman graphs, ultraviolet and infrared divergences of Feynman integrals, Weinberg's theorem and Hepp's theorem, the renormalization...

by means of he's homotopy perturbation method (hpm) an approximate solution of velocity eld is derived for the ow in straight pipes of non-newtonian uid obeying the sisko model. the nonlinear equations governing the ow in pipe are for- mulated and analyzed, using homotopy perturbation method due to he. furthermore, the obtained solutions for velocity eld is graphically sketched and compared w...

We explain the essence of perturbation problems. The key to understanding is the structure of chain homotopy equivalence – the standard one must be replaced by a finer notion which we call a strong chain homotopy equivalence. We formulate an Ideal Perturbation Lemma and show how both new and classical (including the Basic Perturbation Lemma) results follow from this ideal statement.

At high temperature the infrared modes of a weakly coupled quantum field theory can be treated nonperturbatively in real time using the classical field approximation. We use this to introduce a nonperturbative approach to the calculation of finite-temperature spectral functions, employing the classical KMS condition in real time. The method is illustrated for the one-particle spectral function ...

The divergences problem in QFT should be overcame presumably due to the unification of the fundamental interactions [1]. We evidently cannot to achieve this goal now. Together with this there are divergences in problems where the highenergy processes simply cannot be involved (say electron self-energy, Lamb’s shift, etc.). Last ones reflect the formal character of perturbation theory applied to...

An analogue of Kolmogorov’s superconvergent perturbation theory in classical mechanics is constructed for self adjoint operators. It is different from the usual Rayleigh–Schrödinger perturbation theory and yields expansions for eigenvalues and eigenvectors in terms of functions of the perturbation parameter. PACS Code: 03.65.-w, 31.15+q, 02.30.Mv, 02.90.+p

In a classical Symbolic Perturbation scheme, degeneracies are handled by substituting some polynomials in ε for the inputs of a predicate. Instead of a single perturbation, we propose to use a sequence of (simpler) perturbations. Moreover, we look at their effects geometrically instead of algebraically; this allows us to tackle cases that were not tractable with the classical algebraic approach...