Instability of solitary waves on Euler's elastica

Stability of solitary waves in a thin inextensible and unshearable rod of infinite length is studied. Solitary-wave profile ofthe elastica of such a rod without torsion has the form of a planar loop and its speed depends on a tension in the rod. The linear instability of a solitary-wave profile subject to perturbations escaping from the plane of the loop is established for a certain range of solitary-wave speeds. It is done using the properties of the Evans function, an analytic function on the right complex half-plane, that has zeroes if and only if there exist the unstable modes of the linearization around a solitary-wave solution. The result follows from comparison of the behaviour of the Evans function in some neighbourhood of the origin with its asymptotic at infinity. The explicit computation of the leading coefficient of the Taylor series of the Evans function near the origin is performed by means of the symbolic computer language.Comment: 19 pages, 2 figure

Heat cost of parametric generation of microwave squeezed states

In parametric systems, squeezed states of radiation can be generated via extra work done by external sources. This eventually increases the entropy of the system despite the fact that squeezing is reversible. We investigate the entropy increase due to squeezing and show that it is quadratic in the squeezing rate and may become important in the repeated operation of tunable oscillators (quantum buses) used to connect qubits in various proposed schemes for quantum computing.Comment: 11 pages, 1 figur

Resonance at the Rabi frequency in a superconducting flux qubit

We analyze a system composed of a superconducting flux qubit coupled to a transmission-line resonator driven by two signals with frequencies close to the resonator's harmonics. The first strong signal is used for exciting the system to a high energetic state while a second weak signal is applied for probing effective eigenstates of the system. In the framework of doubly dressed states we showed the possibility of amplification and attenuation of the probe signal by direct transitions at the Rabi frequency. We present a brief review of theoretical and experimental works where a direct resonance at Rabi frequency have been investigated in superconducting flux qubits. The interaction of the qubit with photons of two harmonics has prospects to be used as a quantum amplifier (microwave laser) or an attenuator.Comment: This paper is the extended version of the talk given by one of the authors at the Conference On Nuclei And Mesoscopic Physics, 5-9 May 2014, Michigan State University, East Lansing, US