26,580 research outputs found
Determinants of Block Tridiagonal Matrices
An identity is proven that evaluates the determinant of a block tridiagonal
matrix with (or without) corners as the determinant of the associated transfer
matrix (or a submatrix of it).Comment: 8 pages, final form. To appear on Linear Algebra and its Application
Hedin's equations and enumeration of Feynman's diagrams
Hedin's equations are solved perturbatively in zero dimension to count
Feynman graphs for self-energy, polarization, propagator, effective potential
and vertex function in a many-body theory of fermions with two-body
interaction. Counting numbers are also obtained in the GW approximation.Comment: Revised published version, 3 pages, no figure
Trihamiltonian extensions of separable systems in the plane
A method to construct trihamiltonian extensions of a separable system is
presented. The procedure is tested for systems, with a natural Hamiltonian,
separable in classical sense in one of the four orthogonal separable coordinate
systems of the Euclidean plane, and some explicit examples are constructed.
Finally a conjecture on possible generalizations to other classes of systems is
discussed: in particular, the method can be easily adapted to the eleven
orthogonal separable coordinate sets of the Euclidean three-space.Comment: 20 page
Optimal efficiency of quantum transport in a disordered trimer
Disordered quantum networks, as those describing light-harvesting complexes,
are often characterized by the presence of peripheral ring-like structures,
where the excitation is initialized, and inner reaction centers (RC), where the
excitation is trapped. The peripheral rings display coherent features: their
eigenstates can be separated in the two classes of superradiant and subradiant
states. Both are important to optimize transfer efficiency. In the absence of
disorder, superradiant states have an enhanced coupling strength to the RC,
while the subradiant ones are basically decoupled from it. Static on-site
disorder induces a coupling between subradiant and superradiant states,
creating an indirect coupling to the RC. The problem of finding the optimal
transfer conditions, as a function of both the RC energy and the disorder
strength, is very complex even in the simplest network, namely a three-level
system. In this paper we analyze such trimeric structure choosing as initial
condition a subradiant state, rather than the more common choice of an
excitation localized on a site. We show that, while the optimal disorder is of
the order of the superradiant coupling, the optimal detuning between the
initial state and the RC energy strongly depends on system parameters: when the
superradiant coupling is much larger than the energy gap between the
superradiant and the subradiant levels, optimal transfer occurs if the RC
energy is at resonance with the subradiant initial state, whereas we find an
optimal RC energy at resonance with a virtual dressed state when the
superradiant coupling is smaller than or comparable with the gap. The presence
of dynamical noise, which induces dephasing and decoherence, affects the
resonance structure of energy transfer producing an additional 'incoherent'
resonance peak, which corresponds to the RC energy being equal to the energy of
the superradiant state.Comment: This article shares part of the introduction and most of Section II
with arXiv:1508.01613, the remaining parts of the two articles treat
different problem
A size criterion for macroscopic superposition states
An operational measure to quantify the sizes of some ``macroscopic quantum
superpositions'', realized in recent experiments, is proposed. The measure is
based on the fact that a superposition presents greater sensitivity in
interferometric applications than its superposed constituent states. This
enhanced sensitivity, or ``interference utility'', may then be used as a size
criterion among superpositions.Comment: LaTeX2e-REVTeX4, 9 pages, 3 figures. V2: introduction and discussion
slightly altere
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