We model a nanoMOSFET by a mesoscopic, time-dependent, coupled quantumclassical system based on a sub-band decomposition and a simple scattering operator. We first compute the sub-band decomposition and electrostatic force field described by a Schrödinger-Poisson coupled system solved by a Newton-Raphson iteration using the eigenvalue/eigenfunction decomposition. The transport in the classical ...

We propose a simple level set method for the Dirichlet k-partition problem which aims to partition an open domain into K different subdomains as minimize sum of smallest eigenvalue Laplace operator in each subdomain. first formulate nested minimization functional function and eigenfunction defined As approximation, we simply replace by so that can then be converted single problem. apply standar...

Monte Carlo calculations of the irreducible particle-particle interaction on a two-leg Hubbard ladder doped near half-filling are reported. As the temperature is lowered, this interaction develops structure in momentum space similar to the magnetic susceptibility χ(q) and reflects the development of strong short-range antiferromagnetic correlations. Using this interaction, the eigenfunction of ...

We show that the finite difference Bäcklund formula for the Schrödinger Hamiltonians is a particular element of the transformation group on the set of Riccati equations considered by two of us in a previous paper. Then, we give a group theoretical explanation to the problem of Hamiltonians related by a first order differential operator. A generalization of the finite difference algorithm relati...

This paper resolves a question proposed in Kardaras and Robertson [Ann. Appl. Probab. 22 (2012) 1576–1610]: how to invest in a robust growthoptimal way in a market where precise knowledge of the covariance structure of the underlying assets is unavailable. Among an appropriate class of admissible covariance structures, we characterize the optimal trading strategy in terms of a generalized versi...

γ uLγ u where Lγ u = u ′′ +K u, the Morse index is the number of negative eigenvalues of Lγ. (By convention, an eigenfunction φ with eigenvalue λ of Lγ is a solution of Lγ φ+ λφ = 0.) Note that if λ = 0, then φ (or φn) is a (normal) Jacobi field. γ is stable if the index is zero. The index of a noncompact geodesic is the dimension of a maximal vector space of compactly supported variations for ...

In recent years several high quality Sturm-Liouville software packages have been written (e.g., SLEDGE, SLEIGN, the NAG routine SL02FM). All excel at providing eigenfunction estimates at a nite set of points but only the NAG routine provides interpolation capability, and this by a fairly crude method (especially when compared with the sophistication of its eigenvalue solver). We describe an acc...

We study the conformable fractional (CF) Dirac system with separated boundary conditions on an arbitrary time scale [Formula: see text]. Then we extend some basic spectral properties of the classical Dirac system to the CF case. Eventually, some asymptotic estimates for the eigenfunction of the CF Dirac eigenvalue problem are obtained on [Formula: see text]. So, we provide a constructive proced...

Abstract This paper studies the J -method of [ E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput. 36-4:A1978-A2001, 2014 ] for nonlinear eigenvector problems in a general Hilbert space framework. is basis variational discretization techniques and mesh-independent numerical analysis. A simple modification method mimics an energy-decreasing discrete gradient flow. In case Gross–Pitaevskii...

We study the long-time behaviour of growth-fragmentation equation, a nonlocal linear evolution equation describing wide range phenomena in structured population dynamics. show existence spectral gap under conditions that generalise those literature by using method based on Harris's theorem, result coming from equilibration Markov processes. The difficulty posed non-conservativeness is overcome ...