Smilansky’s Model of Irreversible Quantum Graphs, Ii: the Point Spectrum
نویسندگان
چکیده
In the model suggested by Smilansky [6] one studies an operator describing the interaction between a quantum graph and a system of K one-dimensional oscillators attached at different points of the graph. This paper is a continuation of [3] in which we started an investigation of the case K > 1. For the sake of simplicity we consider K = 2, but our argument applies to the general situation. In this second part of the paper we apply the variational approach to the study of the point spectrum.
منابع مشابه
Smilansky’s Model of Irreversible Quantum Graphs, I: the Absolutely Continuous Spectrum
In the model suggested by Smilansky [7] one studies an operator describing the interaction between a quantum graph and a system of K one-dimensional oscillators attached at several different points in the graph. The present paper is the first one in which the case K > 1 is investigated. For the sake of simplicity we consider K = 2, but our argument is of a general character. In this first of tw...
متن کاملOn a Mathematical Model of Irreversible Quantum Graphs
The “irreversible quantum graph” model, suggested by U. Smilansky, is considered. Mathematically, the problem is in the investigation of the spectrum of the operator Aα determined by an infinite system of ordinary differential equations on a graph and by a system of boundary conditions, such as conditions on the jumps of derivatives. The operator depends on a parameter α ≥ 0 involved in the bou...
متن کاملQuantum Graphs II: Some spectral properties of quantum and combinatorial graphs
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and other areas. A Schnol type theorem is proven that allows one to detect that a point λ belongs to the spectrum when a generalized eigenfunction with an subexpo...
متن کاملIrreversible quantum graphs
Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a single harmonic oscillator is couple...
متن کاملModulation Response and Relative Intensity Noise Spectra in Quantum Cascade Lasers
Static properties, relatively intensity noise and intensity modulation response in quantum cascade lasers (QCLs) studied theoretically in this paper. The present rate equations model consists of three equations for the electrons density in the conduction band and one equation for photons density in cavity length. Two equations were derived to calculate the noise and modulation response. Calcula...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005