Far from equilibrium steady states of 1D-Schrödinger–Poisson systems with quantum wells I
Faster than Hermitian time evolution.
Fermi Golden Rule, Feshbach Method and embedded point spectrum
A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jakić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.
Fermionic basis in conformal field theory and thermodynamic Bethe ansatz for excited states.
Ferromagnetic integrals, correlations and maximum principles
For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.
Feynman et les mathématiques
Feynman path integral as spectral decomposition
Finite difference approximation of control via the potential in a 1-D Schrödinger equation.
First-order semidefinite programming for the two-electron treatment of many-electron atoms and molecules
The ground-state energy and properties of any many-electron atom or molecule may be rigorously computed by variationally computing the two-electron reduced density matrix rather than the many-electron wavefunction. While early attempts fifty years ago to compute the ground-state 2-RDM directly were stymied because the 2-RDM must be constrained to represent an N-electron wavefunction, recent advances in theory and optimization have made direct computation of the 2-RDM possible. The constraints in...
Flatland position-dependent-mass: polar coordinates, separability and exact solvability.
Form perturbations of the second quantized Dirac field.
From multi-instantons to exact results
In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...
From random telegraph to Gaussian stochastic noises: decoherence and spectral diffusion in a semiconductor quantum dot.
Functional integral approaches to the bosonization of effective multi-quark interactions with breaking.
Fundamental solutions for Dirac-type operators
We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces and . Further, we consider the Cauchy problem for this operator.