Fabrication of large addition energy quantum dots in graphene

We present a simple technique to fabricate graphene quantum dots in a cryostat. It relies upon the controlled rupture of a suspended graphene sheet subjected to the application of a large electron current. This results in the in-situ formation of a clean and ultra-narrow constriction, which hosts one quantum dot, and occasionally a few quantum dots in series. Conductance spectroscopy indicates that individual quantum dots can possess an addition energy as large as 180 meV and a level spacing as large as 25 meV. Our technique has several assets: (i) the dot is suspended, thus the electrostatic influence of the substrate is reduced, and (ii) contamination is minimized, since the edges of the dot have only been exposed to the vacuum in the cryostat.Comment: Improved version. To appear in Applied Physics Letter

Spectroscopy of Rb2_{2} dimers in solid 4^{4}He

We present experimental and theoretical studies of the absorption, emission and photodissociation spectra of Rb$_{2}$ molecules in solid helium. We have identified 11 absorption bands of Rb$_{2}$. All laser-excited molecular states are quenched by the interaction with the He matrix. The quenching results in efficient population of a metastable (1)$^{3}\Pi_{u}$ state, which emits fluorescence at 1042 nm. In order to explain the fluorescence at the forbidden transition and its time dependence we propose a new molecular exciplex Rb$_{2}(^{3}\Pi_{u})$He$_{2}$. We have also found evidence for the formation of diatomic bubble states following photodissociation of Rb$_{2}$

Stochastic integration in UMD Banach spaces

In this paper we construct a theory of stochastic integration of processes with values in $\mathcal{L}(H,E)$, where $H$ is a separable Hilbert space and $E$ is a UMD Banach space (i.e., a space in which martingale differences are unconditional). The integrator is an $H$-cylindrical Brownian motion. Our approach is based on a two-sided $L^p$-decoupling inequality for UMD spaces due to Garling, which is combined with the theory of stochastic integration of $\mathcal{L}(H,E)$-valued functions introduced recently by two of the authors. We obtain various characterizations of the stochastic integral and prove versions of the It\^{o} isometry, the Burkholder--Davis--Gundy inequalities, and the representation theorem for Brownian martingales.Comment: Published at http://dx.doi.org/10.1214/009117906000001006 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Stochastic evolution equations in UMD Banach spaces

We discuss existence, uniqueness, and space-time H\"older regularity for solutions of the parabolic stochastic evolution equation dU(t) = (AU(t) + F(t,U(t))) dt + B(t,U(t)) dW_H(t), t\in [0,\Tend], U(0) = u_0, where $A$ generates an analytic $C_0$-semigroup on a UMD Banach space $E$ and $W_H$ is a cylindrical Brownian motion with values in a Hilbert space $H$. We prove that if the mappings $F:[0,T]\times E\to E$ and $B:[0,T]\times E\to \mathscr{L}(H,E)$ satisfy suitable Lipschitz conditions and $u_0$ is \F_0-measurable and bounded, then this problem has a unique mild solution, which has trajectories in C^\l([0,T];\D((-A)^\theta) provided $\lambda\ge 0$ and $\theta\ge 0$ satisfy \l+\theta<\frac12. Various extensions of this result are given and the results are applied to parabolic stochastic partial differential equations.Comment: Accepted for publication in Journal of Functional Analysi

Detection of low energy single ion impacts in micron scale transistors at room temperature

We report the detection of single ion impacts through monitoring of changes in the source-drain currents of field effect transistors (FET) at room temperature. Implant apertures are formed in the interlayer dielectrics and gate electrodes of planar, micro-scale FETs by electron beam assisted etching. FET currents increase due to the generation of positively charged defects in gate oxides when ions (121Sb12+, 14+, Xe6+; 50 to 70 keV) impinge into channel regions. Implant damage is repaired by rapid thermal annealing, enabling iterative cycles of device doping and electrical characterization for development of single atom devices and studies of dopant fluctuation effects

Ito's formula in UMD Banach spaces and regularity of solutions of the Zakai equation

Using the theory of stochastic integration for processes with values in a UMD Banach space developed recently by the authors, an Ito formula is proved which is applied to prove the existence of strong solutions for a class of stochastic evolution equations in UMD Banach spaces. The abstract results are applied to prove regularity in space and time of the solutions of the Zakai equation.Comment: Accepted for publication in Journal of Differential Equation