11,188 research outputs found
Multiple solutions for a self-consistent Dirac equation in two dimensions
This paper is devoted to the variational study of an effective model for the
electron transport in a graphene sample. We prove the existence of infinitely
many stationary solutions for a nonlin-ear Dirac equation which appears in the
WKB limit for the Schr{\"o}dinger equation describing the semi-classical
electron dynamics. The interaction term is given by a mean field,
self-consistent potential which is the trace of the 3D Coulomb potential.
Despite the nonlinearity being 4-homogeneous, compactness issues related to the
limiting Sobolev embedding are avoided thanks to the regular-ization property of the
operator (-\Delta)^{-\frac{1}{2}. This also allows us to prove smoothness of
the solutions. Our proof follows by direct arguments
Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity
In this paper we prove the existence of an exponentially localized stationary
solution for a two-dimensional cubic Dirac equation. It appears as an effective
equation in the description of nonlinear waves for some Condensed Matter
(Bose-Einstein condensates) and Nonlinear Optics (optical fibers) systems. The
nonlinearity is of Kerr-type, that is of the form || 2 and thus
not Lorenz-invariant. We solve compactness issues related to the critical
Sobolev embedding H 1 2 (R 2 , C 2) L 4 (R 2 , C 4) thanks to a
particular radial ansatz. Our proof is then based on elementary dynamical
systems arguments. Content
Effect of temperature on non-Markovian dynamics in Coulomb crystals
In this paper we generalize the results reported in Phys. Rev. A 88, 010101
(2013) and investigate the flow of information induced in a Coulomb crystal in
presence of thermal noise. For several temperatures we calculate the
non-Markovian character of Ramsey interferometry of a single 1/2 spin with the
motional degrees of freedom of the whole chain. These results give a more
realistic picture of the interplay between temperature, non-Markovianity and
criticality.Comment: 5 pages, 3 figures. Accepted for publication in Special Issue of the
International Journal of Quantum Information devoted to IQIS2013 conferenc
Some properties of Dirac-Einstein bubbles
We prove smoothness and provide the asymptotic behavior at infinity of
solutions of Dirac-Einstein equations on , which appear in the
bubbling analysis of conformal Dirac-Einstein equations on spin 3-manifolds.
Moreover, we classify ground state solutions, proving that the scalar part is
given by Aubin-Talenti functions, while the spinorial part is the conformal
image of -Killing spinors on the round sphere .Comment: 14 pages. J. Geom. Anal. (2020
A Novel Method of Solving Linear Programs with an Analog Circuit
We present the design of an analog circuit which solves linear programming
(LP) problems. In particular, the steady-state circuit voltages are the
components of the LP optimal solution. The paper shows how to construct the
circuit and provides a proof of equivalence between the circuit and the LP
problem. The proposed method is used to implement a LP-based Model Predictive
Controller by using an analog circuit. Simulative and experimental results show
the effectiveness of the proposed approach.Comment: 8 page
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