Non-equilibrium properties of the S=1/2 Heisenberg model in a time-dependent magnetic field

The time-dependent behavior of the Heisenberg model in contact with a phonon heat bath and in an external time-dependent magnetic field is studied by means of a path integral approach. The action of the phonon heat bath is taken into account up to the second order in the coupling to the heath bath. It is shown that there is a minimal value of the magnetic field below which the average magnetization of the system does not relax to equilibrium when the external magnetic field is flipped. This result is in qualitative agreement with the mean field results obtained within $\phi^{4}$-theory.Comment: To be published in Physica

Quasi-classical Lie algebras and their contractions

After classifying indecomposable quasi-classical Lie algebras in low dimension, and showing the existence of non-reductive stable quasi-classical Lie algebras, we focus on the problem of obtaining sufficient conditions for a quasi-classical Lie algebras to be the contraction of another quasi-classical algebra. It is illustrated how this allows to recover the Yang-Mills equations of a contraction by a limiting process, and how the contractions of an algebra may generate a parameterized families of Lagrangians for pairwise non-isomorphic Lie algebras.Comment: 17 pages, 2 Table

On the theory of pseudogap anisotropy in the cuprate superconductors

We show by means of the theory of the order parameter phase fluctuations that the temperature of "closing" (or "opening") of the gap (and pseudogap) in the electron spectra of superconductors with anisotropic order parameter takes place within a finite temperature range. Every Fourier-component of the order parameter has its own critical temperature

A class of solvable Lie algebras and their Casimir Invariants

A nilpotent Lie algebra n_{n,1} with an (n-1) dimensional Abelian ideal is studied. All indecomposable solvable Lie algebras with n_{n,1} as their nilradical are obtained. Their dimension is at most n+2. The generalized Casimir invariants of n_{n,1} and of its solvable extensions are calculated. For n=4 these algebras figure in the Petrov classification of Einstein spaces. For larger values of n they can be used in a more general classification of Riemannian manifolds.Comment: 16 page

Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.Comment: 53 page

Classification of classical and non-local symmetries of fourth-order nonlinear evolution equations

In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent evolution equations belonging to the class under study which admit either semi-simple Lie groups or solvable Lie groups. The obtained lists of invariant equations (up to a local change of variables) contain both the well-known equations and a variety of new ones possessing rich symmetry. Based on the results on the group classification for local symmetries, the group classification for quasi-local symmetries of the equations is also given.Comment: LaTeX, 60 page

Realizations of Real Low-Dimensional Lie Algebras

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of variables. Our classification amends and essentially generalizes earlier works on the subject. Known results on classification of low-dimensional real Lie algebras, their automorphisms, differentiations, ideals, subalgebras and realizations are reviewed.Comment: LaTeX2e, 39 pages. Essentially exetended version. Misprints in Appendix are correcte

Bosonic sector of the two-dimensional Hubbard model studied within a two-pole approximation

The charge and spin dynamics of the two-dimensional Hubbard model in the paramagnetic phase is first studied by means of the two-pole approximation within the framework of the Composite Operator Method. The fully self-consistent scheme requires: no decoupling, the fulfillment of both Pauli principle and hydrodynamics constraints, the simultaneous solution of fermionic and bosonic sectors and a very rich momentum dependence of the response functions. The temperature and momentum dependencies, as well as the dependency on the Coulomb repulsion strength and the filling, of the calculated charge and spin susceptibilities and correlation functions are in very good agreement with the numerical calculations present in the literature

Temperature-doping phase diagram of layered superconductors

The superconducting properties of a layered system are analyzed for the cases of zero- and non-zero angular momentum of the pairs. The effective thermodynamic potential for the quasi-2D XY-model for the gradients of the phase of the order parameter is derived from the microscopic superconducting Hamiltonian. The dependence of the superconducting critical temperature T_c on doping, or carrier density, is studied at different values of coupling and inter-layer hopping. It is shown that the critical temperature T_c of the layered system can be lower than the critical temperature of the two-dimensional Berezinskii-Kosterlitz-Thouless transition T_BKT at some values of the model parameters, contrary to the case when the parameters of the XY-model do not depend on the microscopic Hamiltonian parameters.Comment: To be published in Phys. Rev.

The kinetic spherical model in a magnetic field

The long-time kinetics of the spherical model in an external magnetic field and below the equilibrium critical temperature is studied. The solution of the associated stochastic Langevin equation is reduced exactly to a single non-linear Volterra equation. For a sufficiently small external field, the kinetics of the magnetization-reversal transition from the metastable to the ground state is compared to the ageing behaviour of coarsening systems quenched into the low-temperature phase. For an oscillating magnetic field and below the critical temperature, we find evidence for the absence of the frequency-dependent dynamic phase transition, which was observed previously to occur in Ising-like systems.Comment: 26 pages, 12 figure