1,696 research outputs found
Completeness of scattering states of the Dirac Hamiltonian with a step potential
The completeness, together with the orthonormality, of the eigenfunctions of
the Dirac Hamiltonian with a step potential is shown explicitly. These
eigenfunctions describe the scattering process of a relativistic fermion off
the step potential and the resolution of the identity in terms of them
(completeness) is shown by explicitly summing them up, where appropriate
treatments of the momentum integrations are crucial. The result would bring
about a basis on which a field theoretical treatment for such a system can be
developed.Comment: 16 pages, 1 figure
Resonant Scattering Can Enhance the Degree of Entanglement
Generation of entanglement between two qubits by scattering an entanglement
mediator is discussed. The mediator bounces between the two qubits and exhibits
a resonant scattering. It is clarified how the degree of the entanglement is
enhanced by the constructive interference of such bouncing processes. Maximally
entangled states are available via adjusting the incident momentum of the
mediator or the distance between the two qubits, but their fine tunings are not
necessarily required to gain highly entangled states and a robust generation of
entanglement is possible.Comment: 7 pages, 13 figure
Entanglement Purification through Zeno-like Measurements
We present a novel method to purify quantum states, i.e. purification through
Zeno-like measurements, and show an application to entanglement purification.Comment: 5 pages, 1 figure; Contribution to the Proceedings of "Mysteries,
Puzzles and Paradoxes in Quantum Mechanics", Gargnano, Italy, 2003 (to be
published in J. Mod. Opt.
Macroscopic limit of a solvable dynamical model
The interaction between an ultrarelativistic particle and a linear array made
up of two-level systems (^^ ^^ AgBr" molecules) is studied by making use of
a modified version of the Coleman-Hepp Hamiltonian. Energy-exchange processes
between the particle and the molecules are properly taken into account, and the
evolution of the total system is calculated exactly both when the array is
initially in the ground state and in a thermal state. In the macroscopic limit
(), the system remains solvable and leads to interesting
connections with the Jaynes-Cummings model, that describes the interaction of a
particle with a maser. The visibility of the interference pattern produced by
the two branch waves of the particle is computed, and the conditions under
which the spin array in the limit behaves as a ^^ ^^
detector" are investigated. The behavior of the visibility yields good insights
into the issue of quantum measurements: It is found that, in the
thermodynamical limit, a superselection-rule space appears in the description
of the (macroscopic) apparatus. In general, an initial thermal state of the ^^
^^ detector" provokes a more substantial loss of quantum coherence than an
initial ground state. It is argued that a system decoheres more as the
temperature of the detector increases. The problem of ^^ ^^ imperfect
measurements" is also shortly discussed.Comment: 30 pages, report BA-TH/93-13
Zero energy resonance and the logarithmically slow decay of unstable multilevel systems
The long time behavior of the reduced time evolution operator for unstable
multilevel systems is studied based on the N-level Friedrichs model in the
presence of a zero energy resonance.The latter means the divergence of the
resolvent at zero energy. Resorting to the technique developed by Jensen and
Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is
characterized by the zero energy eigenstate that does not belong to the Hilbert
space. It is then shown that for some kinds of the rational form factors the
logarithmically slow decay of the reduced time evolution operator can be
realized.Comment: 31 pages, no figure
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