New Discrete States in Two-Dimensional Supergravity

Two-dimensional string theory is known to contain the set of discrete states that are the SU(2) multiplets generated by the lowering operator of the SU(2) current algebra.Their structure constants are defined by the area preserving diffeomorphisms in two dimensions. We show that the interaction of $d=2$ superstrings with the superconformal ghosts enlarges the algebra of dimension 1 currents and hence the new discrete states appear. These new states are the SU(N) multiplets, if the algebra includes the currents of ghost numbers from -N to N-2, not related by the picture-changing. We compute the structure constants of these new discrete states for N=3 and express them in terms of SU(3) Clebsch-Gordan coefficients,relating their operator algebra to the volume preserving diffeomorphisms in d=3. For general N, the algebra is conjectured to be isomorphic to SDiff(N). This points at possible holographic relations between 2d superstrings and field theories in higher dimensions.Comment: 22 pages; typos corrected, 2 references adde

Variational Principle for Mixed Classical-Quantum Systems

An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical variables are expressed in the form of a quantum state vector which includes the action of the classical subsystem in its phase factor. It is shown that the statistical ensemble of Brownian state vectors for a quantum particle in a classical thermal environment can be described by a density matrix evolving according to a nonlinear quantum Fokker-Planck equation. Exact solutions of this equation are obtained for a two-level system in the limit of high temperatures, considering both stationary and nonstationary initial states. A treatment of the common time shared by the quantum system and its classical environment, as a collective variable rather than as a parameter, is presented in the Appendix.Comment: 16 pages, LaTex; added Figure 2 and Figure

Design and fabrication of densely integrated silicon quantum dots using a VLSI compatible hydrogen silsesquioxane electron beam lithography process

Hydrogen silsesquioxane (HSQ) is a high resolution negative-tone electron beam resist allowing for direct transfer of nanostructures into silicon-on-insulator. Using this resist for electron beam lithography, we fabricate high density lithographically defined Silicon double quantum dot (QD) transistors. We show that our approach is compatible with very large scale integration, allowing for parallel fabrication of up to 144 scalable devices. HSQ process optimisation allowed for realisation of reproducible QD dimensions of 50 nm and tunnel junction down to 25 nm. We observed that 80% of the fabricated devices had dimensional variations of less than 5 nm. These are the smallest high density double QD transistors achieved to date. Single electron simulations combined with preliminary electrical characterisations justify the reliability of our device and process

AC0(MOD2) lower bounds for the Boolean inner product

AC0 ◦MOD2 circuits are AC0 circuits augmented with a layer of parity gates just above the input layer. We study AC0 ◦ MOD2 circuit lower bounds for computing the Boolean Inner Product functions. Recent works by Servedio and Viola (ECCC TR12-144) and Akavia et al. (ITCS 2014) have highlighted this problem as a frontier problem in circuit complexity that arose both as a first step towards solving natural special cases of the matrix rigidity problem and as a candidate for constructing pseudorandom generators of minimal complexity. We give the first superlinear lower bound for the Boolean Inner Product function against AC0 ◦ MOD2 of depth four or greater. Specifically, we prove a superlinear lower bound for circuits of arbitrary constant depth, and an Ω( ˜ n 2 ) lower bound for the special case of depth-4 AC0 ◦ MOD2. Our proof of the depth-4 lower bound employs a new “moment-matching” inequality for bounded, nonnegative integer-valued random variables that may be of independent interest: we prove an optimal bound on the maximum difference between two discrete distributions’ values at 0, given that their first d moments match

The non-conventional use of 99mTc-Tetrofosmine for dynamic hepatobiliary scintigraphy

BACKGROUND: Classic dynamic hepatobiliary scintigraphy (DHBS) is commonly performed with 99mTc-Iminodiacetic Acid (IDA) derivatives and represents a non-invasive diagnosis method for biliary dyskinesia, fistulas, surgical anastomosis, etc (1). This study assesses the possibility of performing DHBS with 99mTc-Tetrofosmine (TF), a radiopharmaceutical (RF) dedicated to myocardial perfusion scintigraphy (MPS), but being excreted through the liver. The possibility to use 99mTc-TF for DHBS may be important in situations when the standardized RF for this procedure (IDA derivatives) is not available. MATERIAL AND METHODS: We performed DHBS for 30 patients referred for investigation by internal medicine and surgery departments. The patients had been fasting for12 hours. The dynamic investigation started simultaneously with the intravenous (IV) administration of 37–110 MBq (1–3 mCi) 99mTc-TF. Dynamic images were recorded for 30–45 minutes, one image per minute, followed by static scintigraphy at 1 h, 1.5 h, 2 h, and 3 h after IV injection. RESULTS: The quality of scintigraphic images of the liver and biliary tree obtained at DHBS with 99mTc-TF ensured the correct diagnosis of biliary dyskinesia, stasis, stenosis, and fistulas. CONCLUSIONS: DHBS using 99mTc-TF is justified by the image quality and by the good cost/benefits ratio. Because the IDA derivatives are not always available, this finding may be important for medical practice. 99mTc-TF evacuated through the bile duct allows DHBS interpretation, while the necessary dose is approximately 8 to 20 times smaller than that used for myocardial perfusion scintigraphy. Nuclear Med Rev 2011; 14, 2: 79–8