Browsing by Author "Benguria, R. D."

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    A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields
    (AMER INST PHYSICS, 2015) Benguria, R. D.; Van Den Bosch, H.
    We consider the Pauli operator in R-3 for magnetic fields in L-3/2 that decay at infinity as vertical bar x vertical bar(-2-beta) with beta > 0. In this case, we are able to prove that the existence of a zero mode for this operator is equivalent to a quantity delta(B), defined below, being equal to zero. Complementing a result from Balinsky et al. [J. Phys. A: Math. Gen. 34, L19-L23 (2001)], this implies that for the class of magnetic fields considered, Sobolev, Hardy, and Cwikel, Lieb, Rosenblum (CLR) inequalities hold whenever the magnetic field has no zero mode. (C) 2015 AIP Publishing LLC.
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    Upper and lower bounds for the speed of fronts of the reaction diffusion equation with Stefan boundary conditions
    (2023) Benguria, R. D.; Depassier, M. C.
    We establish two integral variational principles for the spreading speed of the one dimensional reaction diffusion equation with Stefan boundary conditions. The first principle is valid for monostable reaction terms and the second principle is valid for arbitrary reaction terms. These principles allow to obtain several upper and lower bounds for the speed. In particular, we construct a generalized Zeldovich-Frank-Kamenetskii type lower bound for the speed and upper bounds in terms of the speed of the standard reaction diffusion problem. We construct asymptotically exact lower bounds previously obtained by perturbation theory.