MHD α2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator
نویسندگان
چکیده
منابع مشابه
MHD α2−dynamo, Squire equation and PT −symmetric interpolation between square well and harmonic oscillator
It is shown that the α−dynamo of Magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT −symmetric Quantum Mechanics are closely related as spectral problems in Krein spaces. For the α−dynamo and the PT −symmetric model the strong similarities are demonstrated with the help of a 2 × 2 operator matrix representation, whereas the Squire equation is re-inter...
متن کاملsetups: PT −symmetric matrix toy model, MHD α 2 −dynamo, and extended Squire equation ∗)
The spectra of self-adjoint operators in Krein spaces are known to possess real sectors as well as sectors of pair-wise complex conjugate eigenvalues. Transitions from one spectral sector to the other are a rather generic feature and they usually occur at exceptional points of square root branching type. For certain parameter configurations two or more such exceptional points may happen to coal...
متن کاملPT −symmetric square well
Below a (comparatively large) measure of non-Hermiticity Z = Z (crit) 0 > 0 of a PT symmetrically complexified square well, bound states are constructed non-numerically. All their energies prove real and continuous in the (Hermitian) limit Z → 0. Beyond the threshold Z (crit) 0 (and, in general, beyond Z (crit) m at m = 0, 1, . . .) the lowest two real energies (i.e., E2m and E2m+1) are shown t...
متن کاملOvercritical PT -symmetric square well potential in the Dirac equation
We study scattering properties of a PT -symmetric square well potential with real depth larger than the threshold of particle-antiparticle pair production as the time component of a vector potential in the Dirac equation. Spontaneous pair production inside the well becomes tiny beyond the strength at which discrete bound states with real energies disappear, consistently with a spontaneous break...
متن کاملDiscrete PT −symmetric square-well oscillators
Exact solvability of the discretized N−point version of the PT −symmetric squarewell model at all N is pointed out. Its wave functions are found proportional to the classical Tshebyshev polynomials Uk cos θ) of a complex argument. A compact secular equation is derived giving the real spectrum of energies at all the non-Hermiticity strengths Z ∈ (−Zcrit(N), Zcrit(N)). In the limit Z → 0 the mode...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2005
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.1915293