5,814 research outputs found
Slowly decaying classical fields, unitarity, and gauge invariance
In classical external gauge fields that fall off less fast than the inverse
of the evolution parameter (time) of the system the implementability of a
unitary perturbative scattering operator (-matrix) is not guaranteed,
although the field goes to zero. The importance of this point is exposed for
the counter-example of low-dimensionally expanding systems. The issues of gauge
invariance and of the interpretation of the evolution at intermediate times are
also intricately linked to that point.Comment: 8 pages, no figure
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
Kink stability, propagation, and length scale competition in the periodically modulated sine-Gordon equation
We have examined the dynamical behavior of the kink solutions of the
one-dimensional sine-Gordon equation in the presence of a spatially periodic
parametric perturbation. Our study clarifies and extends the currently
available knowledge on this and related nonlinear problems in four directions.
First, we present the results of a numerical simulation program which are not
compatible with the existence of a radiative threshold, predicted by earlier
calculations. Second, we carry out a perturbative calculation which helps
interpret those previous predictions, enabling us to understand in depth our
numerical results. Third, we apply the collective coordinate formalism to this
system and demonstrate numerically that it accurately reproduces the observed
kink dynamics. Fourth, we report on a novel occurrence of length scale
competition in this system and show how it can be understood by means of linear
stability analysis. Finally, we conclude by summarizing the general physical
framework that arises from our study.Comment: 19 pages, REVTeX 3.0, 24 figures available from A S o
The Interaction of Quantum Gravity with Matter
The interaction of (linearized) gravitation with matter is studied in the
causal approach up to the second order of perturbation theory. We consider the
generic case and prove that gravitation is universal in the sense that the
existence of the interaction with gravitation does not put new constraints on
the Lagrangian for lower spin fields. We use the formalism of quantum off-shell
fields which makes our computation more straightforward and simpler.Comment: 25 page
A super-Ohmic energy absorption in driven quantum chaotic systems
We consider energy absorption by driven chaotic systems of the symplectic
symmetry class. According to our analytical perturbative calculation, at the
initial stage of evolution the energy growth with time can be faster than
linear. This appears to be an analog of weak anti-localization in disordered
systems with spin-orbit interaction. Our analytical result is also confirmed by
numerical calculations for the symplectic quantum kicked rotor.Comment: 4 pages, 2 figure
Does the Chapman--Enskog expansion for sheared granular gases converge?
The fundamental question addressed in this paper is whether the partial
Chapman--Enskog expansion of the shear stress converges or not for a gas of
inelastic hard spheres. By using a simple kinetic model it is shown that, in
contrast to the elastic case, the above series does converge, the radius of
convergence increasing with inelasticity. It is argued that this paradoxical
conclusion is not an artifact of the kinetic model and can be understood in
terms of the time evolution of the scaled shear rate in the uniform shear flow.Comment: 4 pages, 1 table, 2 figures; v2: minor changes,Fig. 2 redon
The Epstein-Glaser approach to pQFT: graphs and Hopf algebras
The paper aims at investigating perturbative quantum field theory (pQFT) in
the approach of Epstein and Glaser (EG) and, in particular, its formulation in
the language of graphs and Hopf algebras (HAs). Various HAs are encountered,
each one associated with a special combination of physical concepts such as
normalization, localization, pseudo-unitarity, causality and an associated
regularization, and renormalization. The algebraic structures, representing the
perturbative expansion of the S-matrix, are imposed on the operator-valued
distributions which are equipped with appropriate graph indices. Translation
invariance ensures the algebras to be analytically well-defined and graded
total symmetry allows to formulate bialgebras. The algebraic results are given
embedded in the physical framework, which covers the two recent EG versions by
Fredenhagen and Scharf that differ with respect to the concrete recursive
implementation of causality. Besides, the ultraviolet divergences occuring in
Feynman's representation are mathematically reasoned. As a final result, the
change of the renormalization scheme in the EG framework is modeled via a HA
which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure
Perturbative Gravity in the Causal Approach
Quantum theory of the gravitation in the causal approach is studied up to the
second order of perturbation theory. We prove gauge invariance and
renormalizability in the second order of perturbation theory for the pure
gravity system (massless and massive). Then we investigate the interaction of
massless gravity with matter (described by scalars and spinors) and massless
Yang-Mills fields. We obtain a difference with respect to the classical field
theory due to the fact that in quantum field theory one cannot enforce the
divergenceless property on the vector potential and this spoils the
divergenceless property of the usual energy-momentum tensor. To correct this
one needs a supplementary ghost term in the interaction Lagrangian.Comment: 50 pages, no figures, some changes in the last sectio
Optical lattice quantum simulator for QED in strong external fields: spontaneous pair creation and the Sauter-Schwinger effect
Spontaneous creation of electron-positron pairs out of the vacuum due to a
strong electric field is a spectacular manifestation of the relativistic
energy-momentum relation for the Dirac fermions. This fundamental prediction of
Quantum Electrodynamics (QED) has not yet been confirmed experimentally as the
generation of a sufficiently strong electric field extending over a large
enough space-time volume still presents a challenge. Surprisingly, distant
areas of physics may help us to circumvent this difficulty. In condensed matter
and solid state physics (areas commonly considered as low energy physics), one
usually deals with quasi-particles instead of real electrons and positrons.
Since their mass gap can often be freely tuned, it is much easier to create
these light quasi-particles by an analogue of the Sauter-Schwinger effect. This
motivates our proposal of a quantum simulator in which excitations of
ultra-cold atoms moving in a bichromatic optical lattice represent particles
and antiparticles (holes) satisfying a discretized version of the Dirac
equation together with fermionic anti-commutation relations. Using the language
of second quantization, we are able to construct an analogue of the spontaneous
pair creation which can be realized in an (almost) table-top experiment.Comment: 21 pages, 10 figure
The Topological Unitarity Identities in Chern-Simons Theories
Starting from the generating functional of the theory of relativistic spinors
in 2+1 dimensions interacting through the pure Chern-Simons gauge field, the
S-matrix is constructed and seen to be formally the same as that of spinor
quantum electrodynamics in 2+1 dimensions with Feynman diagrams having external
photon lines excluded, and with the propagator of the topological Chern-Simons
photon substituted for the Maxwell photon propagator. It is shown that the
absence of real topological photons in the complete set of vector states of the
total Hilbert space leads in a given order of perturbation theory to
topological unitarity identities that demand the vanishing of the
gauge-invariant sum of the imaginary parts of Feynman diagrams with a given
number of internal on-shell free topological photon lines. It is also shown,
that these identities can be derived outside the framework of perturbation
theory. The identities are verified explicitly for the scattering of a
fermion-antifermion pair in one-loop order.Comment: 13 pages, LaTex file, one figure (not included
- …