451 research outputs found
Impurity in the Tomonaga-Luttinger model: a Functional Integral Approach
In this tutorial notes we review a functional bosonization approach in the
Keldysh technique to one-dimensional Luttinger liquid in the presence of an
impurity.Comment: 15 pages, 1 figure, Proceedings of LXXXI Les Houches School on
"Nanoscopic quantum transport", Les Houches, France, June 28-July 30, 200
Low temperature decoherence and relaxation in charge Josephson-junction qubits
In this lectures, we have described some essential features of loss of
coherence by a qubit coupled to the environment. We have first presented well
known semiclassical arguments that relate both decoherence and relaxation to
the environmental noise. Then we have shown that models with pure decoherence
(but no relaxation in qubit states) can be exactly solvable. As an example, we
have treated in detail the model of fluctuating background charges which is
believed to describe one of the most important channels for decoherence for the
charge Josephson junction qubit. We have shown that the decoherence rate
saturates at `high' temperatures while becoming linear in T at low temperatures
and showing in all regimes a non-monotonic behaviour as a function of the
coupling of the qubit to the fluctuating background charges. We have also
considered, albeit only perturbatively, the qubit relaxation by the background
charges and demonstrated that a quasi-linear behaviour of the spectral density
of noise deduced from the measurements of the relaxation rate can be
qualitatively explained.Comment: Lecture notes for International workshop on mesoscopic and nanoscopic
systems, Kolkata, India, February 2006, to be published by Springe
The art of algorithmic guessing in
The technique of guessing can be very fruitful when dealing with sequences
which arise in practice. This holds true especially when guessing is performed
algorithmically and efficiently. One highly useful tool for this purpose is the
package named in the software Maple. In this text we explore
and explain some of 's possibilities and illustrate them on two
examples from recent mathematical research by the author and his collaborators
Algebraicity of hypergeometric functions with arbitrary parameters
We provide a complete classification of the algebraicity of (generalized)
hypergeometric functions with no restriction on the set of their parameters.
Our characterization relies on the interlacing criteria of Christol (1987) and
Beukers-Heckman~(1989) for globally bounded and algebraic hypergeometric
functions, however in a more general setting which allows arbitrary complex
parameters with possibly integral differences. We also showcase the adapted
criterion on a variety of different examples.Comment: 21 page
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