Marginal distributions in (2N)(\bf 2N)-dimensional phase space and the quantum (N+1)(\bf N+1) marginal theorem

We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e. depending on a (complete) commuting set of $N$ variables, are considered. A diagrammatic or graph theoretic formulation of the problem is developed. We then exactly determine the set of ``admissible'' data, i.e. those types of data for which the problem always admits solutions. This is done in the case where the joint distributions originate from quantum mechanics as well as in the case where this constraint is not imposed. In particular, it is shown that a necessary (but not sufficient) condition for the existence of solutions is $n\leq N+1$. When the data are admissible and the quantum constraint is not imposed, the general solution for the phase space density is determined explicitly. For admissible data of a quantum origin, the general solution is given in certain (but not all) cases. In the remaining cases, only a subset of solutions is obtained.Comment: 29 pages (Work supported by the Indo-French Centre for the Promotion of Advanced Research, Project Nb 1501-02). v2 to add a report-n

Integrated atomistic process and device simulation of decananometre MOSFETs

In this paper we present a methodology for the integrated atomistic process and device simulation of decananometre MOSFETs. The atomistic process simulations were carried out using the kinetic Monte Carlo process simulator DADOS, which is now integrated into the Synopsys 3D process and device simulation suite Taurus. The device simulations were performed using the Glasgow 3D statistical atomistic simulator, which incorporates density gradient quantum corrections. The overall methodology is illustrated in the atomistic process and device simulation of a well behaved 35 nm physical gate length MOSFET reported by Toshiba

Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach

Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order linear differential operator with position depndent coefficients and the system of equations arising from the intertwining relationship is solved for the coefficients by taking an ansatz. A complete scheme for obtaining general solution is obtained which is valid for any arbitrary potential and mass function. The proposed technique allows us to generate isospectral potentials with the following spectral modifications: (i) to add new bound state(s), (ii) to remove bound state(s) and (iii) to leave the spectrum unaffected. To explain our findings with the help of an illustration, we have used point canonical transformation (PCT) to obtain the general solution of the position dependent mass Schrodinger equation corresponding to a potential and mass function. It is shown that our results are consistent with the formulation of type A N-fold supersymmetry [14,18] for the particular case N = 1 and N = 2 respectively.Comment: Some references have been adde

Secure, performance-oriented data management for nanoCMOS electronics

The EPSRC pilot project Meeting the Design Challenges of nanoCMOS Electronics (nanoCMOS) is focused upon delivering a production level e-Infrastructure to meet the challenges facing the semiconductor industry in dealing with the next generation of ‘atomic-scale’ transistor devices. This scale means that previous assumptions on the uniformity of transistor devices in electronics circuit and systems design are no longer valid, and the industry as a whole must deal with variability throughout the design process. Infrastructures to tackle this problem must provide seamless access to very large HPC resources for computationally expensive simulation of statistic ensembles of microscopically varying physical devices, and manage the many hundreds of thousands of files and meta-data associated with these simulations. A key challenge in undertaking this is in protecting the intellectual property associated with the data, simulations and design process as a whole. In this paper we present the nanoCMOS infrastructure and outline an evaluation undertaken on the Storage Resource Broker (SRB) and the Andrew File System (AFS) considering in particular the extent that they meet the performance and security requirements of the nanoCMOS domain. We also describe how metadata management is supported and linked to simulations and results in a scalable and secure manner

Two photon annihilation operators and squeezed vacuum

Inverses of the harmonic oscillator creation and annihilation operators by their actions on the number states are introduced. Three of the two photon annihilation operators, viz., a(sup +/-1)a, aa(sup +/-1), and a(sup 2), have normalizable right eigenstates with nonvanishing eigenvalues. The eigenvalue equation of these operators are discussed and their normalized eigenstates are obtained. The Fock state representation in each case separates into two sets of states, one involving only the even number states while the other involving only the odd number states. It is shown that the even set of eigenstates of the operator a(sup +/-1)a is the customary squeezed vacuum S(sigma) O greater than