Parametric resonances in electrostatically interacting carbon nanotube arrays

We study, numerically and analytically, a model of a one-dimensional array of carbon nanotube resonators in a two-terminal configuration. The system is brought into resonance upon application of an AC-signal superimposed on a DC-bias voltage. When the tubes in the array are close to each other, electrostatic interactions between tubes become important for the array dynamics. We show that both transverse and longitudinal parametric resonances can be excited in addition to primary resonances. The intertube electrostatic interactions couple modes in orthogonal directions and affect the mode stability.Comment: 11 pages, 12 figures, RevTeX

Breakdown of Conformal Invariance at Strongly Random Critical Points

We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a strongly random critical point. The average correlation functions of this system demonstrate a breakdown of conformal invariance, while the typical correlation functions demonstrate a breakdown of scale invariance. The breakdown of conformal invariance is due to the vanishing of the correlation functions at the infinite disorder fixed point, causing the critical correlation functions to be controlled by a dangerously irrelevant operator describing the approach to the fixed point. We relate the computation of average correlation functions to a problem of persistence in the RG flow.Comment: 9 page

Importance of an Astrophysical Perspective for Textbook Relativity

The importance of a teaching a clear definition of the ``observer'' in special relativity is highlighted using a simple astrophysical example from the exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example shows that a source moving relativistically toward a single observer at rest exhibits a time ``contraction'' rather than a ``dilation'' because the light travel time between the source and observer decreases with time. Astrophysical applications of special relativity complement idealized examples with real applications and very effectively exemplify the role of a finite light travel time.Comment: 5 pages TeX, European Journal of Physics, in pres

Quasienergy description of the driven Jaynes-Cummings model

We analyze the driven resonantly coupled Jaynes-Cummings model in terms of a quasienergy approach by switching to a frame rotating with the external modulation frequency and by using the dressed atom picture. A quasienergy surface in phase space emerges whose level spacing is governed by a rescaled effective Planck constant. Moreover, the well-known multiphoton transitions can be reinterpreted as resonant tunneling transitions from the local maximum of the quasienergy surface. Most importantly, the driving defines a quasienergy well which is nonperturbative in nature. The quantum mechanical quasienergy state localized at its bottom is squeezed. In the Purcell limited regime, the potential well is metastable and the effective local temperature close to its minimum is uniquely determined by the squeezing factor. The activation occurs in this case via dressed spin flip transitions rather than via quantum activation as in other driven nonlinear quantum systems such as the quantum Duffing oscillator. The local maximum is in general stable. However, in presence of resonant coherent or dissipative tunneling transitions the system can escape from it and a stationary state arises as a statistical mixture of quasienergy states being localized in the two basins of attraction. This gives rise to a resonant or an antiresonant nonlinear response of the cavity at multiphoton transitions. The model finds direct application in recent experiments with a driven superconducting circuit QED setup.Comment: 13 pages, 8 fi

Superconducting Nanowires as Nonlinear Inductive Elements for Qubits

We report microwave transmission measurements of superconducting Fabry-Perot resonators (SFPR), having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship (CPR) of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low quality factor sample exhibits a "crater" at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.Comment: 28 pages, 7 figure

Spatially incoherent modulational instability in a non local medium

We investigate one-dimensional transverse modulational instability in a non local medium excited with a spatially incoherent source. Employing undoped nematic liquid crystals in a planar pre-tilted configuration, we investigate the role of the spectral broadening induced by incoherence in conjunction with the spatially non local molecular reorientation. The phenomenon is modeled using the Wigner transform.Comment: 13 pages with 4 figures included. To be published in Laser Physics Letter

Electron-phonon relaxation and excited electron distribution in gallium nitride

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates of inter-band recombination and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy 'tail' covers largely the conduction band. The shape of the high-energy 'tail' strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi 'tail' is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can affect essentially the charge transport in the irradiated and highly doped semiconductors.Comment: 15 pages, 6 figure

Noise-enabled precision measurements of a Duffing nanomechanical resonator

We report quantitative experimental measurements of the nonlinear response of a radiofrequency mechanical resonator, with very high quality factor, driven by a large swept-frequency force. We directly measure the noise-free transition dynamics between the two basins of attraction that appear in the nonlinear regime, and find good agreement with those predicted by the one-dimensional Duffing equation of motion. We then measure the response of the transition rates to controlled levels of white noise, and extract the activation energy from each basin. The measurements of the noise-induced transitions allow us to obtain precise values for the critical frequencies, the natural resonance frequency, and the cubic nonlinear parameter in the Duffing oscillator, with direct applications to high sensitivity parametric sensors based on these resonators.Comment: 5 pages, 5 figure