Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

Quiescent X-ray emission from an evolved brown dwarf ?

I report on the X-ray detection of Gl569Bab. During a 25ksec Chandra observation the binary brown dwarf is for the first time spatially separated in X-rays from the flare star primary Gl569A. Companionship to Gl569A constrains the age of the brown dwarf pair to ~300-800 Myr. The observation presented here is only the second X-ray detection of an evolved brown dwarf. About half of the observing time is dominated by a large flare on Gl569Bab, the remainder is characterized by weak and non-variable emission just above the detection limit. This emission -- if not related to the afterglow of the flare -- represents the first detection of a quiescent corona on a brown dwarf, representing an important piece in the puzzle of dynamos in the sub-stellar regime.Comment: to appear in ApJ

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

Modeling the power flow in normal conductor-insulator-superconductor junctions

Normal conductor-insulator-superconductor (NIS) junctions promise to be interesting for x-ray and phonon sensing applications, in particular due to the expected self-cooling of the N electrode by the tunneling current. Such cooling would enable the operation of the active element of the sensor below the cryostat temperature and at a correspondingly higher sensitivity. It would also allow the use of MS junctions as microcoolers. At present, this cooling has not been realized in large area junctions (suitable for a number of detector applications). In this article, we discuss a detailed modeling of the heat flow in such junctions; we show how the heat flow into the normal electrode by quasiparticle back-tunneling and phonon absorption from quasiparticle pair recombination can overcompensate the cooling power. This provides a microscopic explanation of the self-heating effects we observe in our large area NIS junctions. The model suggests a number of possible solutions

Self-affine surface morphology of plastically deformed metals

We analyze the surface morphology of metals after plastic deformation over a range of scales from 10 nm to 2 mm, using a combination of atomic force microscopy and scanning white-light interferometry. We demonstrate that an initially smooth surface during deformation develops self-affine roughness over almost four orders of magnitude in scale. The Hurst exponent $H$ of one-dimensional surface profiles is initially found to decrease with increasing strain and then stabilizes at $H \approx 0.75$. By analyzing their statistical properties we show that the one-dimensional surface profiles can be mathematically modelled as graphs of a fractional Brownian motion. Our findings can be understood in terms of a fractal distribution of plastic strain within the deformed samples

Raman cooling and heating of two trapped Ba+ ions

We study cooling of the collective vibrational motion of two 138Ba+ ions confined in an electrodynamic trap and irradiated with laser light close to the resonances S_1/2-P_1/2 (493 nm) and P_1/2-D_3/2 (650 nm). The motional state of the ions is monitored by a spatially resolving photo multiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split S_1/2-D_3/2 Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.Comment: 8 pages, 5 figure

Hudson's Theorem for finite-dimensional quantum systems

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match published version. See also quant-ph/070200