16,270 research outputs found
Right eigenvalue equation in quaternionic quantum mechanics
We study the right eigenvalue equation for quaternionic and complex linear
matrix operators defined in n-dimensional quaternionic vector spaces. For
quaternionic linear operators the eigenvalue spectrum consists of n complex
values. For these operators we give a necessary and sufficient condition for
the diagonalization of their quaternionic matrix representations. Our
discussion is also extended to complex linear operators, whose spectrum is
characterized by 2n complex eigenvalues. We show that a consistent analysis of
the eigenvalue problem for complex linear operators requires the choice of a
complex geometry in defining inner products. Finally, we introduce some
examples of the left eigenvalue equations and highlight the main difficulties
in their solution.Comment: 24 pages, AMS-Te
Quaternionic potentials in non-relativistic quantum mechanics
We discuss the Schrodinger equation in presence of quaternionic potentials.
The study is performed analytically as long as it proves possible, when not, we
resort to numerical calculations. The results obtained could be useful to
investigate an underlying quaternionic quantum dynamics in particle physics.
Experimental tests and proposals to observe quaternionic quantum effects by
neutron interferometry are briefly reviewed.Comment: 21 pages, 16 figures (ps), AMS-Te
Symmetry-protected dissipative preparation of matrix product states
We propose and analyze a method for efficient dissipative preparation of
matrix product states that exploits their symmetry properties. Specifically, we
construct an explicit protocol that makes use of driven-dissipative dynamics to
prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) states, which features
symmetry-protected topological order and non-trivial edge excitations. We show
that the use of symmetry allows for robust experimental implementation without
fine-tuned control parameters. Numerical simulations show that the preparation
time scales polynomially in system size . Furthermore, we demonstrate that
this scaling can be improved to by using parallel
preparation of AKLT segments and fusing them via quantum feedback. A concrete
scheme using excitation of trapped neutral atoms into Rydberg state via
Electromagnetically Induced Transparency is proposed, and generalizations to a
broader class of matrix product states are discussed
Error suppression in Hamiltonian based quantum computation using energy penalties
We consider the use of quantum error detecting codes, together with energy
penalties against leaving the codespace, as a method for suppressing
environmentally induced errors in Hamiltonian based quantum computation. This
method was introduced in [1] in the context of quantum adiabatic computation,
but we consider it more generally. Specifically, we consider a computational
Hamiltonian, which has been encoded using the logical qubits of a single-qubit
error detecting code, coupled to an environment of qubits by interaction terms
that act one-locally on the system. Energy penalty terms are added that
penalize states outside of the codespace. We prove that in the limit of
infinitely large penalties, one-local errors are completely suppressed, and we
derive some bounds for the finite penalty case. Our proof technique involves
exact integration of the Schrodinger equation, making no use of master
equations or their assumptions. We perform long time numerical simulations on a
small (one logical qubit) computational system coupled to an environment and
the results suggest that the energy penalty method achieves even greater
protection than our bounds indicate.Comment: 26 pages, 7 figure
Radar multipath study for rain-on-radome experiments at the Aircraft Landing Dynamics Facility
An analytical study to determine the feasibility of a rain-on-radome experiment at the Aircraft Landing Dynamics Facility (ALDF) at the Langley Research Center is described. The experiment would measure the effects of heavy rain on the transmission of X-band weather radar signals, looking in particular for sources of anomalous attenuation. Feasibility is determined with regard to multipath signals arising from the major structural components of the ALDF. A computer program simulates the transmit and receive antennas, direct-path and multipath signals, and expected attenuation by rain. In the simulation, antenna height, signal polarization, and rainfall rate are variable parameters. The study shows that the rain-on-radome experiment is feasible with regard to multipath signals. The total received signal, taking into account multipath effects, could be measured by commercially available equipment. The study also shows that horizontally polarized signals would produce better experimental results than vertically polarized signals
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