37 research outputs found
Distributional Borel Summability for Vacuum Polarization by an External Electric Field
It is proved that the divergent perturbation expansion for the vacuum
polarization by an external constant electric field in the pair production
sector is Borel summable in the distributional sense.Comment: 14 page
PT Symmetric Schr\"odinger Operators: Reality of the Perturbed Eigenvalues
We prove the reality of the perturbed eigenvalues of some PT symmetric
Hamiltonians of physical interest by means of stability methods. In particular
we study 2-dimensional generalized harmonic oscillators with polynomial
perturbation and the one-dimensional for
Distributional Borel Summability of Odd Anharmonic Oscillators
It is proved that the divergent Rayleigh-Schrodinger perturbation expansions
for the eigenvalues of any odd anharmonic oscillator are Borel summable in the
distributional sense to the resonances naturally associated with the system
Prove d'esame degli anni 2006 - 2012
Queste prove d'esame degli anni passati costituiscono parte integrante del materiale didattico su cui prepararsi per l'esame
Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
Within CPT-symmetric quantum mechanics the most elementary differential form
of the charge operator C is assumed. A closed-form integrability of the related
coupled differential self-consistency conditions and a natural embedding of the
Hamiltonians in a supersymmetric scheme is achieved. For a particular choice of
the interactions the rigorous mathematical consistency of the construction is
scrutinized suggesting that quantum systems with non-self-adjoint Hamiltonians
may admit probabilistic interpretation even in presence of a manifest breakdown
of both T symmetry (i.e., Hermiticity) and PT symmetry.Comment: 13 page
symmetric non-selfadjoint operators, diagonalizable and non-diagonalizable, with real discrete spectrum
Consider in , , the operator family . \ds
H_0= a^\ast_1a_1+... +a^\ast_da_d+d/2 is the quantum harmonic oscillator with
rational frequencies, a symmetric bounded potential, and a real
coupling constant. We show that if , being an explicitly
determined constant, the spectrum of is real and discrete. Moreover we
show that the operator \ds H(g)=a^\ast_1 a_1+a^\ast_2a_2+ig a^\ast_2a_1 has
real discrete spectrum but is not diagonalizable.Comment: 20 page
CPT-conserving Hamiltonians and their nonlinear supersymmetrization using differential charge-operators C
A brief overview is given of recent developments and fresh ideas at the
intersection of PT and/or CPT-symmetric quantum mechanics with supersymmetric
quantum mechanics (SUSY QM). We study the consequences of the assumption that
the "charge" operator C is represented in a differential-operator form. Besides
the freedom allowed by the Hermiticity constraint for the operator CP,
encouraging results are obtained in the second-order case. The integrability of
intertwining relations proves to match the closure of nonlinear SUSY algebra.
In an illustration, our CPT-symmetric SUSY QM leads to non-Hermitian polynomial
oscillators with real spectrum which turn out to be PT-asymmetric.Comment: 25 page