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The mixed regularity of electronic wave functions multiplied by explicit correlation factors***

Harry Yserentant (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The electronic Schrödinger equation describes the motion of N electrons under Coulomb interaction forces in a field of clamped nuclei. The solutions of this equation, the electronic wave functions, depend on 3N variables, three spatial dimensions for each electron. Approximating them is thus inordinately challenging. As is shown in the author's monograph [Yserentant, Lecture Notes in Mathematics2000, Springer (2010)], the regularity of the solutions, which increases with the number of electrons,...

The monotone Poisson process

Alexander C. R. Belton (2006)

Banach Center Publications

The coefficients of the moments of the monotone Poisson law are shown to be a type of Stirling number of the first kind; certain combinatorial identities relating to these numbers are proved and a new derivation of the Cauchy transform of this law is given. An investigation is begun into the classical Azéma-type martingale which corresponds to the compensated monotone Poisson process; it is shown to have the chaotic-representation property and its sample paths are described.

The quantum 3D superparticle.

Mezincescu, Luca, Townsend, Paul K. (2011)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

The Quantum Birkhoff Normal Form and Spectral Asymptotics

San Vũ Ngọc (2006)

Journées Équations aux dérivées partielles

In this talk we explain a simple treatment of the quantum Birkhoff normal form for semiclassical pseudo-differential operators with smooth coefficients. The normal form is applied to describe the discrete spectrum in a generalised non-degenerate potential well, yielding uniform estimates in the energy E . This permits a detailed study of the spectrum in various asymptotic regions of the parameters ( E , ℏ ) , and gives improvements and new proofs for many of the results in the field. In the completely resonant...

The quantum duality principle

Fabio Gavarini (2002)

Annales de l’institut Fourier

The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors 𝒬 𝒰 ℰ 𝒜 ⟶ 𝒬 ℱ 𝒮 ℋ 𝒜 and 𝒬 ℱ 𝒮 ℋ 𝒜 ⟶ 𝒬 𝒰 ℰ 𝒜 , inverse to...

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