New PDF release: A semilinear Schrödinger equation in the presence of a

By Arioli G., Szulkin A.

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V. Skobelev: Izv. Vyssh. Uchebn. , Fiz. No. 10, 142 (1975) 36 5. E. Shabad: In: Polarization of the Vacuum and a Quantum Relativistic Gas in an External Field, ed. L. Ginzburg (Nova Science Publishers, New York, 1992) 36 40 4 Two-Point Loop Amplitude 6. B. M. P. Pitaevskii: Quantum Electrodynamics. 2nd ed. (Pergamon, Oxford 1982) 36 7. L. Adler: Ann. Phys. ) 67, 599 (1971) 37 8. J. Stoneham: J. Phys. A12, 2187 (1979) 37 9. N. G. Raffelt: Phys. Rev. D55, 7038 (1997) 37 10. N. I. Zh. Shaisultanov: Phys.

The function has the asymptotics: H(z) H(z) 8 2 16 3 2 z+ z + z , 3 15 35 1 ln 4|z|, −1 − 2z |z| |z| 1, 1. 44) for the photon O and E modes are depicted in Fig. 3. References 39 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Õ¾ ¡ ¡ ¡ ¡ Ç ¹Ô ÓØÓÒ ¡ ¹Ô ÓØÓÒ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Ѿ ¡ ¡ ¡ ¹Ô ÓØÓÒ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¼ ¡ Õ¾ Fig. 3. The dispersion law for the O and E photon modes in a strong magnetic field. 44) is taken. The dotted line corresponds to the vacuum dispersion at q 2 = 0. Above the line of the vacuum dispersion, q 2 = 0, the “photon mass” squared for the E-mode photon, Re Π (2) has the positive sign, and the sign is negative below the line.

43) can be represented in the form W (1,2) e2 m2 χ1/3 = 1/3 3 2 π ω + 1 0 du (1 − u2 )2/3 2/3 2 χ(1 − u2 ) ∞ 1 − u2 1 + u2 ∓ 2 2 dτ −∞ 1 + τ2 1 − u2 1 + u2 ± 2 2 2 [Φ (y)] 2 . 56) This result coincides, to the notations, with the result of [22], where the polarizations and ⊥ correspond to our 1 and 2. 59) ∞ 2 dttσ−1 [Φ(t + a)] , σ > 0.

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A semilinear Schrödinger equation in the presence of a magnetic field by Arioli G., Szulkin A.


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