1,718 research outputs found
Evaluating Feynman integrals by the hypergeometry
The hypergeometric function method naturally provides the analytic
expressions of scalar integrals from concerned Feynman diagrams in some
connected regions of independent kinematic variables, also presents the systems
of homogeneous linear partial differential equations satisfied by the
corresponding scalar integrals. Taking examples of the one-loop and
massless functions, as well as the scalar integrals of two-loop vacuum
and sunset diagrams, we verify our expressions coinciding with the well-known
results of literatures. Based on the multiple hypergeometric functions of
independent kinematic variables, the systems of homogeneous linear partial
differential equations satisfied by the mentioned scalar integrals are
established. Using the calculus of variations, one recognizes the system of
linear partial differential equations as stationary conditions of a functional
under some given restrictions, which is the cornerstone to perform the
continuation of the scalar integrals to whole kinematic domains numerically
with the finite element methods. In principle this method can be used to
evaluate the scalar integrals of any Feynman diagrams.Comment: 39 pages, including 2 ps figure
Cooperative Label-Free Moving Target Fencing for Second-Order Multi-Agent Systems with Rigid Formation
This paper proposes a label-free controller for a second-order multi-agent
system to cooperatively fence a moving target of variational velocity into a
convex hull formed by the agents whereas maintaining a rigid formation.
Therein, no label is predetermined for a specified agent. To attain a rigid
formation with guaranteed collision avoidance, each controller consists of two
terms: a dynamic regulator with an internal model to drive agents towards the
moving target merely by position information feedback, and a repulsive force
between each pair of adjacent agents. Significantly, sufficient conditions are
derived to guarantee the asymptotic stability of the closed-loop systems
governed by the proposed fencing controller. Rigorous analysis is provided to
eliminate the strong nonlinear couplings induced by the label-free property.
Finally, the effectiveness of the controller is substantiated by numerical
simulations
Theory of magnetoelectric photocurrent generated by direct interband transitions in semiconductor quantum well
A linearly polarized light normally incident on a semiconductor quantum well
with spin-orbit coupling may generate pure spin current via direct interband
optical transition. An electric photocurrent can be extracted from the pure
spin current when an in-plane magnetic field is applied, which has been
recently observed in the InGaAs/InAlAs quantum well [Dai et al., Phys. Rev.
Lett. 104, 246601 (2010)]. Here we present a theoretical study of this
magnetoelectric photocurrent effect associated with the interband transition.
By employing the density matrix formalism, we show that the photoexcited
carrier density has an anisotropic distribution in k space, strongly dependent
on the orientation of the electron wavevector and the polarization of the
light. This anisotropy provides an intuitive picture of the observed dependence
of the photocurrent on the magnetic field and the polarization of the light. We
also show that the ratio of the pure spin photocurrent to the magnetoelectric
photocurrent is approximately equal to the ratio of the kinetic energy to the
Zeeman energy, which enables us to estimate the magnitude of the pure spin
photocurrent. The photocurrent density calculated with the help of an
anisotropic Rashba model and the Kohn-Luttinger model can produce all three
terms in the fitting formula for measured current, with comparable order of
magnitude, but discrepancies are still present and further investigation is
needed.Comment: 13 pages, 9 figures, 2 table
GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
We present the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of
the Feynman integrals of the three-loop vacuum diagrams with arbitrary masses,
basing on Mellin-Barnes representations and Miller's transformation. The
codimension of derived GKZ hypergeometric systems equals the number of
independent dimensionless ratios among the virtual masses squared. Through GKZ
hypergeometric systems, the analytical hypergeometric series solutions can be
obtained in neighborhoods of origin including infinity. The linear independent
hypergeometric series solutions whose convergent regions have non-empty
intersection can constitute a fundamental solution system in a proper subset of
the whole parameter space. The analytical expression of the vacuum integral can
be formulated as a linear combination of the corresponding fundamental solution
system in certain convergent region.Comment: 47 pages, 2 figures. arXiv admin note: text overlap with
arXiv:2209.1519
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