Counting statistics and detector properties of quantum point contacts

Quantum detector properties of the quantum point contact (QPC) are analyzed for an arbitrary electron transparency and coupling strength to the measured system and are shown to be determined by the electron counting statistics. Conditions of the quantum-limited operation of the QPC detector, which prevent information loss through the scattering time and scattering phases, are found for arbitrary coupling. We show that the phase information can be restored and used for the quantum-limited detection by inclusion of the QPC detector in the electronic Mach-Zehnder interferometer.     

A new ac electrospray mechanism by Maxwell-Wagner polarization and capillary resonance

We report a new high-frequency (>10 kHz) ac electrospray that is capable of generating micron-sized electroneutral drops. Unlike its dc counterpart, the drops are not ejected continuously from a sharp Taylor cone but intermittently from a resonating meniscus at the orifice. We attribute the resonant frequency to the capillary-inertia vibration time of the meniscus and the drop ejection to the Maxwell-Wagner electric stress at the drop tip, which is observed to reverse its direction across a crossover frequency. Above this frequency, the oppositely directed Maxwell-Wagner force causes the liquid to recede up the microneedle as an apparent electrowetting effect.     

Weight Multiplicity Free Representations, g-Endomorphism Algebras, and Dynkin Polynomials

Throughout this paper, G is a connected semisimple algebraicgroup defined over an algebraically closed field k of characteristiczero, and g is its Lie algebra.     

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid-fluid interface.     

An Inverse Problem for an Harmonic Oscillator Perturbed by Potential: Uniqueness

Consider the perturbed harmonic oscillator Ty = -y" + x²y + q(x)y on L²(R) where the real potential q satisfy some assumption on infinity (the case q L²(R), (t+1)^-rdt), r < 1 is covered).     

Formation,structure, and structural properties of a new filamentary tubular form: hollow conical-helix of graphitic boron nitride

A novel tubular form of graphitic boron nitride (BN) displaying a hollow conical-helix was discovered. It was generated via wrapping a single beltlike filament according to the geometry of an Archimedes spiral. Cone apex angles of helical-conical nanotubes (HCNTs) were found to exhibit specific values, each of which refers to a certain coincidence site lattice. A unique structural property of HCNTs was observed, displaying the transformation of apex angles during the annealing process. The observed apex angles were reduced with decreasing annealing temperature, which is in accordance with an estimated HCNT strain energy decrease for a given tubular radius. It is suggested that the curvature and apex angle of a HCNT are determined by a sole dynamic element, that is, enthalpy (DeltaH), whereas the HCNT disclination configuration changes through helical sliding of the filament.     

Torus Actions, Equivariant Moment-Angle Complexes, and Coordinate Subspace Arrangements

We show that the cohomology algebra of the complement of a coordinate subspace arrangement in the m-dimensional complex space is isomorphic to the cohomology algebra of the StanleyReisner face ring of a certain simplicial complex on m vertices. (The face ring is regarded as a module over the polynomial ring on m generators.) After that we calculate the latter cohomology algebra by means of the standard Koszul resolution of a polynomial ring. To prove these facts, we construct a homotopy equivalence (equivariant with respect to the torus action) between the complement of a coordinate subspace arrangement and the moment-angle complex defined by a simplicial complex. The moment-angle complex is a certain subset of the unit polydisk in the m-dimensional complex space invariant with respect to the action of the m-dimensional torus. This complex is a smooth manifold provided that the simplicial complex is a simplicial sphere; otherwise, the complex has a more complicated structure. Then we investigate the equivariant topology of the moment-angle complex and apply the EilenbergMoore spectral sequence. We also relate our results with well-known facts in the theory of toric varieties and symplectic geometry. Bibliography: 23 titles.     

Isotropy Representations, Eigenvalues of a Casimir Element, and Commutative Lie Subalgebras

Let h be a reductive subalgebra of a semisimple Lie algebrag and C_h U(h) be the Casimir element determined by the restrictionof the Killing form on g to h. The paper studies eigenvaluesof C_h on the isotropy representation mg/h. Some general estimatesconnecting the eigenvalues and the Dynkin indices of m are given.If h is a symmetric subalgebra, it is shown that describingthe maximal eigenvalue of C_h on exterior powers of m is connectedwith possible dimensions of commutative Lie subalgebras in m,thereby extending a result of Kostant. In this situation, aformula is also given for the maximal eigenvalue of C_h on m.More generally, a similar picture arises if h = g, where isan automorphism of finite order m and m is replaced by the eigenspaceof corresponding to a primitive mth root of unity.     

Special Points of Surfaces in the Three-Dimensional Projective Space

In the paper, 3-jets of two-dimensional surfaces in the three-dimensional affine space are classified. It is shown that there are exactly 22 types of co-oriented 3-jets of surfaces. The action of the group of affine transformations on the space of 3-jets is studied. We calculate a universal complex of singularities that is related to the orbits of the group action. Two linear homology relations for the numbers of special elliptic, hyperbolic, and parabolic points of a compact two-dimensional surface embedded in ³ are indicated. The stratification of some real cubic surfaces with respect to the types of 3-jets is described.