Quantum field theory on a growing lattice

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.Comment: 28 pages, 2 figures; v.2: added comments on defining energy, and reference

Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur

Event horizons and ergoregions in 3He

Event horizons for fermion quasiparticles naturally arise in moving textures in superconductors and Fermi superfluids. We discuss the example of a planar soliton moving in superfluid 3He-A, which is closely analogous to a charged rotating black hole. The moving soliton will radiate quasiparticles via the Hawking effect at a temperature of about 5 \mu K, and via vacuum polarization induced by the effective `electromagnetic field' and `ergoregion'. Superfluid 3He-A thus appears to be a useful system for experimental and theoretical simulations of quantum effects related to event horizons and ergoregions.Comment: RevTex, 8 pages, 3 figures, submitted to Phys. Rev. D, corrected after referee repor

Effective spacetime and Hawking radiation from moving domain wall in thin film of 3He-A

An event horizon for "relativistic" fermionic quasiparticles can be constructed in a thin film of superfluid 3He-A. The quasiparticles see an effective "gravitational" field which is induced by a topological soliton of the order parameter. Within the soliton the "speed of light" crosses zero and changes sign. When the soliton moves, two planar event horizons (black hole and white hole) appear, with a curvature singularity between them. Aside from the singularity, the effective spacetime is incomplete at future and past boundaries, but the quasiparticles cannot escape there because the nonrelativistic corrections become important as the blueshift grows, yielding "superluminal" trajectories. The question of Hawking radiation from the moving soliton is discussed but not resolved.Comment: revtex file, 4 pages, 2 figures, submitted to JETP Let

Bases in Lie and Quantum Algebras

Applications of algebras in physics are related to the connection of measurable observables to relevant elements of the algebras, usually the generators. However, in the determination of the generators in Lie algebras there is place for some arbitrary conventions. The situation is much more involved in the context of quantum algebras, where inside the quantum universal enveloping algebra, we have not enough primitive elements that allow for a privileged set of generators and all basic sets are equivalent. In this paper we discuss how the Drinfeld double structure underlying every simple Lie bialgebra characterizes uniquely a particular basis without any freedom, completing the Cartan program on simple algebras. By means of a perturbative construction, a distinguished deformed basis (we call it the analytical basis) is obtained for every quantum group as the analytical prolongation of the above defined Lie basis of the corresponding Lie bialgebra. It turns out that the whole construction is unique, so to each quantum universal enveloping algebra is associated one and only one bialgebra. In this way the problem of the classification of quantum algebras is moved to the classification of bialgebras. In order to make this procedure more clear, we discuss in detail the simple cases of su(2) and su_q(2).Comment: 16 pages, Proceedings of the 5th International Symposium on Quantum Theory and Symmetries QTS5 (July 22-28, 2007, Valladolid (Spain)

An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications

We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series Z = \log(\e^X \e^Y) in an arbitrary generalized Hall basis of the free Lie algebra $\mathcal{L}(X,Y)$ generated by $X$ and $Y$. It is based on the close relationship of $\mathcal{L}(X,Y)$ with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in $\mathcal{L}(X,Y)$) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when $X$ and $Y$ are real or complex matrices.Comment: 30 page

Cosmological Particle Creation in the Presence of Lorentz Violation

In recent years, the effects of Lorentz symmetry breaking in cosmology has attracted considerable amount of attention. In cosmological context several topics can be affected by Lorentz violation,e.g., inflationary scenario, CMB, dark energy problem and barryogenesis. In this paper we consider the cosmological particle creation due to Lorentz violation (LV). We consider an exactly solvable model for finding the spectral properties of particle creation in an expanding space-time exhibiting Lorentz violation. In this model we calculate the spectrum and its variations with respect to the rate and the amount of space-time expansion.Comment: 6 pages, 6 figures, To appear in Physics Letters