April 2012
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Day April 6, 2012

Coulomb potential and the paradoxes of PT-symmetrization

Miloslav Znojil

Besides the standard quantum version of the Coulomb/Kepler problem, an alternative quantum model with not too dissimilar phenomenological (i.e., spectral and scattering) as well as mathematical (i.e., exact-solvability) properties may be formulated and solved. Several aspects of this model are described. The paper is made self-contained by explaining the underlying innovative quantization strategy which assigns an entirely new role to symmetries.

Quantum Physics (quant-ph)

Non-Hermitian approach for modeling of noise-assisted quantum electron transfer in photosynthetic complexes

Alexander I. Nesterov, Gennady P. Berman, Alan R. Bishop

We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). Each fluctuator has two independent parameters, an amplitude and a switching rate. We represent the noise by a set of fluctuators with fitting parameters (boundaries of switching rates), which allows us to build a desired spectral density of noise in a wide range of frequencies. We analyze the quantum dynamics and the efficiency of the ET as a function of (i) the energy gap between the donor and acceptor, (ii) the strength of the interaction with the continuum, and (iii) noise parameters. As an example, numerical results are presented for the ET through the active pathway in a quinone-type photosystem II RC.

Quantum Physics (quant-ph); Biological Physics (physics.bio-ph)

Finding room for antilinear terms in the Hamiltonian

Michael Eisele

Although the Hamiltonian in quantum physics has to be a linear operator, it is possible to make quantum systems behave as if their Hamiltonians contained antilinear (i.e., semilinear or conjugate-linear) terms. For any given quantum system, another system can be constructed that is physically equivalent to the original one. It can be designed, despite the Wightman reconstruction theorem, so that antilinear operators in the original system become linear operators in the new system. Under certain conditions, these operators can then be added to the new Hamiltonian. The new quantum system has some unconventional features, a hidden degeneracy of the vacuum and a subtle distinction between the Hamiltonian and the observable of energy, but the physical equivalence guarantees that its states evolve like those in the original system and that corresponding measurements produce the same results. The same construction can be used to make time-reversal linear.

Mathematical Physics (math-ph); Quantum Physics (quant-ph)