1,358,875 research outputs found
Klein Tunnelling and the Klein Paradox
The Klein paradox is reassessed by considering the properties of a finite
square well or barrier in the Dirac equation. It is shown that spontaneous
positron emission occurs for a well if the potential is strong enough. The
vacuum charge and lifetime of the well are estimated. If the well is wide
enough, a seemingly constant current is emitted. These phenomena are transient
whereas the tunnelling first calculated by Klein is time-independent. Klein
tunnelling is a property of relativistic wave equations, not necessarily
connected to particle emission. The Coulomb potential is investigated in this
context: it is shown that a heavy nucleus of sufficiently large will bind
positrons. Correspondingly, it is expected that as increases the Coulomb
barrier will become increasingly transparent to positrons. This is an example
of Klein tunnelling.Comment: 17 page
Klein-Gordon Oscillator in Kaluza-Klein Theory
In this contribution we study the Klein-Gordon oscillator on the curved
background within the Kaluza-Klein theory. The problem of interaction between
particles coupled harmonically with a topological defects in Kaluza-Klein
theory is studied. We consider a series of topological defects, that treat the
Klein-Gordon oscillator coupled to this background and find the energy levels
and corresponding eigenfunctions in these cases. We show that the energy levels
depend on the global parameters characterizing these spacetimes. We also
investigate a quantum particle described by the Klein-Gordon oscillator
interacting with a cosmic dislocation in Som-Raychaudhuri spacetime in the
presence of homogeneous magnetic field in a Kaluza-Klein theory. In this case,
the spectrum of energy is determined, and we observe that these energy levels
are the sum of the term related with Aharonov-Bohm flux and of the parameter
associated to the rotation of the spacetime.Comment: 15 pages, no figur
The double of the doubles of Klein surfaces
A Klein surface is a surface with a dianalytic structure. A double of a Klein
surface is a Klein surface such that there is a degree two morphism (of
Klein surfaces) . There are many doubles of a given Klein
surface and among them the so-called natural doubles which are: the complex
double, the Schottky double and the orienting double. We prove that if is a
non-orientable Klein surface with non-empty boundary, the three natural
doubles, although distinct Klein surfaces, share a common double: "the double
of doubles" denoted by . We describe how to use the double of doubles in
the study of both moduli spaces and automorphisms of Klein surfaces.
Furthermore, we show that the morphism from to is not given by the
action of an isometry group on classical surfaces.Comment: 14 pages; more details in the proof of theorem
Universal Boundary Entropies in Conformal Field Theory: A Quantum Monte Carlo Study
Recently, entropy corrections on nonorientable manifolds such as the Klein
bottle are proposed as a universal characterization of critical systems with an
emergent conformal field theory (CFT). We show that entropy correction on the
Klein bottle can be interpreted as a boundary effect via transforming the Klein
bottle into an orientable manifold with nonlocal boundary interactions. The
interpretation reveals the conceptual connection of the Klein bottle entropy
with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a
generic scheme to extract these universal boundary entropies from quantum Monte
Carlo calculation of partition function ratios in lattice models. Our numerical
results on the Affleck-Ludwig entropy and Klein bottle entropy for the
-state quantum Potts chains with show excellent agreement with the
CFT predictions. For the quantum Potts chain with , the Klein bottle
entropy slightly deviates from the CFT prediction, which is possibly due to
marginally irrelevant terms in the low-energy effective theory.Comment: 10 pages, 4 figures. Published versio
Excitation of Kaluza-Klein gravitational mode
We investigate excitation of Kaluza-Klein modes due to the parametric
resonance caused by oscillation of radius of compactification. We consider a
gravitational perturbation around a D-dimensional spacetime, which we
compactify on a (D-4)-sphere to obtain a 4-dimensional theory. The perturbation
includes the so-called Kaluza-Klein modes, which are massive in 4-dimension, as
well as zero modes, which is massless in 4-dimension. These modes appear as
scalar, vector and second-rank symmetric tensor fields in the 4-dimensional
theory. Since Kaluza-Klein modes are troublesome in cosmology, quanta of these
Kaluza-Klein modes should not be excited abundantly. However, if radius of
compactification oscillates, then masses of Kaluza-Klein modes also oscillate
and, thus, parametric resonance of Kaluza-Klein modes may occur to excite their
quanta. In this paper we consider part of Kaluza-Klein modes which correspond
to massive scalar fields in 4-dimension and investigate whether quanta of these
modes are excited or not in the so called narrow resonance regime of the
parametric resonance. We conclude that at least in the narrow resonance regime
quanta of these modes are not excited so catastrophically.Comment: 15 pages LaTeX, submitted to Phys.Rev.
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