Quantization of classical integrable systems. Part IV: systems of resonant oscillators

By applying methods already discussed in a previous series of papers by the same authors, we construct here classes of integrable quantum systems which correspond to n fully resonant oscillators with nonlinear couplings. The same methods are also applied to a series of nontrivial integral sets of functions, which can be constructed when additional symmetries are present due to the equality of some of the frequencies. Besides, for n=3 and resonance 1:1:2, an exceptional integrable system is obtained, in which integrability is not explicitly connected with this type of symmetry. In this exceptional case, quantum integrability can be realized by means of a modification of the symmetrization procedure.Comment: 23 page

Modern mechanisms make manless Martian mission mobile: Spin-off spells stairclimbing self-sufficiency for earthbound handicapped

Concepts were developed for three wheel chairs from progressively improving designs of a proposed unmanned roving vehicle for the surface exploration of Mars; as a spin-off, a concept for a stair-climbing wheel chair was generated. The mechanisms employed in these are described. The Mars mission is envisioned using the booster rockets and aeroshell of the Viking missions

Phase transitions and edge scaling of number variance in Gaussian random matrices

We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the probability $\mathcal{P}_{\scriptscriptstyle N,L}(N_L)$ that $N_L$ eigenvalues lie within the box $[-L,L]$. This probability scales as $\mathcal{P}_{\scriptscriptstyle N,L}(N_L=\kappa_L N)\approx\exp\left(-{\beta} N^2 \psi_L(\kappa_L)\right)$, where $\beta$ is the Dyson index of the ensemble and $\psi_L(\kappa_L)$ is a $\beta$-independent rate function that we compute exactly. We identify three regimes as $L$ is varied: (i) $\, N^{-1}\ll L<\sqrt{2}$ (bulk), (ii) $\ L\sim\sqrt{2}$ on a scale of $\mathcal{O}(N^{-{2}/{3}})$ (edge) and (iii) $\ L > \sqrt{2}$ (tail). We find a dramatic non-monotonic behavior of the number variance $V_N(L)$ as a function of $L$: after a logarithmic growth $\propto \ln (N L)$ in the bulk (when $L \sim {\cal O}(1/N)$), $V_N(L)$ decreases abruptly as $L$ approaches the edge of the semi-circle before it decays as a stretched exponential for $L > \sqrt{2}$. This "drop-off" of $V_N(L)$ at the edge is described by a scaling function $\tilde V_{\beta}$ which smoothly interpolates between the bulk (i) and the tail (iii). For $\beta = 2$ we compute $\tilde V_2$ explicitly in terms of the Airy kernel. These analytical results, verified by numerical simulations, directly provide for $\beta=2$ the full statistics of particle-number fluctuations at zero temperature of 1d spinless fermions in a harmonic trap.Comment: 5 pag., 3 fig, published versio

Acoustic black holes in a two-dimensional "photon-fluid"

Optical field fluctuations in self-defocusing media can be described in terms of sound waves in a 2D photon-fluid. It is shown that, while the background fluid couples with the usual flat metric, sound-like waves experience an effective curved spacetime determined by the physical properties of the flow. In an optical cavity configuration, the background spacetime can be suitably controlled by the driving beam allowing the formation of acoustic ergoregions and event horizons. An experiment simulating the main features of the rotating black hole geometry is proposed.Comment: revised versio

Quantized Skyrmion Fields in 2+1 Dimensions

A fully quantized field theory is developped for the skyrmion topological excitations of the O(3) symmetric CP$^1$-Nonlinear Sigma Model in 2+1D. The method allows for the obtainment of arbitrary correlation functions of quantum skyrmion fields. The two-point function is evaluated in three different situations: a) the pure theory; b) the case when it is coupled to fermions which are otherwise non-interacting and c) the case when an electromagnetic interaction among the fermions is introduced. The quantum skyrmion mass is explicitly obtained in each case from the large distance behavior of the two-point function and the skyrmion statistics is inferred from an analysis of the phase of this function. The ratio between the quantum and classical skyrmion masses is obtained, confirming the tendency, observed in semiclassical calculations, that quantum effects will decrease the skyrmion mass. A brief discussion of asymptotic skyrmion states, based on the short distance behavior of the two-point function, is also presented.Comment: Accepted for Physical Review

Inverter-converter automatic paralleling and protection

Electric control and protection circuits for parallel operation of inverter-converte