9,140 research outputs found
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
are considered
according to their Lie point symmetry groups. The set represents the
point 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 generated by and . It is based
on the close relationship of 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 ) 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 and 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
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