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On phase segregation in nonlocal two-particle Hartree systems

100%
Aschbacher W., Squassina M.
Open Mathematics
|
2009
|
tom 7
|
nr 2
230-248
EN
We prove the phase segregation phenomenon to occur in the ground state solutions of an interacting system of two self-coupled repulsive Hartree equations for large nonlinear and nonlocal interactions. A self-consistent numerical investigation visualizes the approach to this segregated regime.
2
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Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

84%
Weber H.
Open Mathematics
|
2007
|
tom 5
|
nr 2
415-427
EN
Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.
3
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Quantum optimal control using the adjoint method

53%
Borzì A.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2012
|
tom 1
93-111
EN
Control of quantum systems is central in a variety of present and perspective applications ranging from quantum optics and quantum chemistry to semiconductor nanostructures, including the emerging fields of quantum computation and quantum communication. In this paper, a review of recent developments in the field of optimal control of quantum systems is given with a focus on adjoint methods and their numerical implementation. In addition, the issues of exact controllability and optimal control are discussed for finite- and infinitedimensional quantum systems. Some insight is provided considering ’two-level’ models. This work is completed with an outlook to future developments.
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