Vitali Vougalter
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Research Interests
Vitali Vougalter has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Dmitry E. Pelinovsky
Department of Mathematics and Statistics, McMaster University, Hamilton, Canada
1 shared publication - Scipio Cuccagna
Department of Mathematics and Geosciences, University of Trieste, Trieste, Italy
1 shared publication - Semjon Vugalter
Mathematisches Institut, Ludwig-Maximilians-Universität München, Munich, Germany
1 shared publication - Thomas Chen
Courant Institute of Mathematical Sciences, New York University, New York, USA
1 shared publication
Latest Publications
- 22 October 2004
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 58 (1) , 1-29
Spectra of positive and negative energies in the linearized NLS problem
We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L2‐scattering theory for the linearized NLS operators and recover results of Grillakis [5] with a Fermi golden rule.
- 22 October 2004
- Published by Wiley in Communications on Pure and Applied Mathematics
- Vol. 58 (1) , 1-29
Spectra of positive and negative energies in the linearized NLS problem
We study the spectrum of the linearized NLS equation in three dimensions in association with the energy spectrum. We prove that unstable eigenvalues of the linearized NLS problem are related to negative eigenvalues of the energy spectrum, while neutrally stable eigenvalues may have both positive and negative energies. The nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum. We derive bounds on the number of unstable eigenvalues of the linearized NLS problem and study bifurcations of embedded eigenvalues of positive and negative energies. We develop the L2‐scattering theory for the linearized NLS operators and recover results of Grillakis [5] with a Fermi golden rule.
- Open Access
The increase of Binding Energy and Enhanced Binding in Non-Relativistic QED
We consider a Pauli-Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum $P = 0$.Open AccessThe increase of Binding Energy and Enhanced Binding in Non-Relativistic QED
We consider a Pauli-Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum $P = 0$.