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We evaluate the variance of coefficients of the characteristic polynomial of the quantum evolution operator for chaotic 4-regular quantum graphs (networks) via periodic orbits without taking the semiclassical limit. The variance of the n-th coefficient is precisely determined by the number of primitive pseudo orbits (sets of distinct primitive periodic orbits) with n bonds that fall in the following classes: those with no self-intersections, and those where all the self-intersections consist of two sections of the pseudo orbit crossing at a single vertex (2-encounters of length zero).
Let $Gamma$ be an arbitrary $mathbb{Z}^n$-periodic metric graph, which does not coincide with a line. We consider the Hamiltonian $mathcal{H}_varepsilon$ on $Gamma$ with the action $-varepsilon^{-1}{mathrm{d}^2/mathrm{d} x^2}$ on its edges; here $var
We demonstrate that the (s-wave) geometric spectrum of the Efimov energy levels in the unitary limit is generated by the radial motion of a primitive periodic orbit (and its harmonics) of the corresponding classical system. The action of the primitiv
A quantum system interacting with a dilute gas experiences irreversible dynamics. The corresponding master equation can be derived within two different approaches: The fully quantum description in the low-density limit and the semiclassical collision
The scattering amplitude in simple quantum graphs is a well-known process which may be highly complex. In this work, motivated by the Shannon entropy, we propose a methodology that associates to a graph a scattering entropy, which we call the average
Fawzi and Fawzi recently defined the sharp Renyi divergence, $D_alpha^#$, for $alpha in (1, infty)$, as an additional quantum Renyi divergence with nice mathematical properties and applications in quantum channel discrimination and quantum communicat