Institute of Mathematics of the Romanian
Academy,
Calea Grivitei 21, 010702 Bucharest, Romania
Mail
Address: P.O. Box 1-764, Bucuresti, ROMANIA
Tel.:
+4021-319.65.09
fax: +4021-319.65.05
E-mail: Radu dot
Purice at imar dot ro
Habilitation in Mathematics; IMAR (2014)
Ph.D. in Physics; Bucharest University (1990)
Senior Researcher,
Institute of Mathematics "Simion
Stoilow" of the Romanian Academy, Bucuresti
Evolution
Equations and Control Theory, Partial Differential Equations and
Mathematical Physics
Mathematical Physics - quantum mechanics.
study of
some models in field theory: Markoff property for the Free Euclidean
Electromagnetic Field; solutions to the Ghinzburg- Landau equations
in a two-dimensional bounded domain
study of the
Dirac Hamiltonian: nonrelativistic limit; time - dependent
perturbations; singular perturbations; scattering theory
the Dirac Hamiltonian with time
dependent perturbations
spectral
analysis and propagation estimations for quantum Hamiltonians
the
conjugate operator method and its applications in spectral theory
and evolution properties
weighted
estimations of Hardy type for quantum Hamiltonians
operator
algebra methods in spectral theory and dynamics of quantum systems
non-equilibrium steady states and
transport theory
functional calculus for quantum
observables in a magnetic field
Horia D. Cornean, Bernard Helffer and Radu Purice: A fresh look at the Peierls-Onsager substitution.pdf
Horia D. Cornean, Bernard Helffer and Radu Purice: The fibre operators in the Bloch-Floquet decomposition of periodic magnetic pseudo-differential operators.pdf
Horia D. Cornean, Bernard Helffer and Radu Purice: A rigorous Peierls-Onsager effective dynamics for semimetals in long-range magnetic fields.pdf
Horia D. Cornean and Radu Purice: Spectral regularity with respect to dilations for a class of pseudodifferential operators.pdf
Horia D. Cornean and Radu Purice: Sharp spectral stability for a class of singularly perturbed pseudo-differential operators.pdf
Horia D. Cornean, Bernard Helffer and Radu Purice: Matrix representation of Magnetic pseudo-differential operators via tight Gabor frames.pdf
Horia D. Cornean, Bernard Helffer and Radu Purice: Spectral analysis near a Dirac type crossing in a weak non-constant magnetic field.pdf
Horia Cornean, Bernard Helffer, Radu Purice: A Beals criterion for magnetic pseudodifferential operators proved with magnetic Gabor frames .pdf
Viorel Iftimie, Marius Mantoiu, Radu Purice: Quantum observables as magnetic pseudodifferential operators .pdf
Horia Cornean, Bernard Helffer, Radu Purice: Peierls' substitution for low lying spectral energy windows .pdf
Horia Cornean, Bernard Helffer, Radu Purice: Low lying spectral gaps induced by slowly varying magnetic fields .pdf
Nassim Athmouni and Radu Purice: A Schatten-von Neumann class criterion for the magnetic Weyl calculus .pdf
Horia D. Cornean, Viorel Iftimie, Radu Purice: Peierls substitution and magnetic pseudo-differential calculus .pdf
Marius Mantoiu, Radu Purice: On Fréchet-Hilbert Algebras .pdf
Horia D. Cornean, Radu Purice: Spectral edge regularity of magnetic Hamiltonians .pdf
Viorel Iftimie, Radu Purice: The Peierls-Onsager Effective Hamiltonian in a complete gauge covariant setting: Description of the spectrum .pdf
Horia D. Cornean, Radu Purice: On the regularity of the Hausdorff distance between spectra of perturbed magnetic Hamiltonians .pdf
Marius Mantoiu, Radu Purice, Serge Richard: Positive Quantization in the Presence of a Variable Magnetic Field .pdf
Viorel Iftimie, Radu Purice: Magnetic Fourier Integral Operators .pdf
Bernard Helffer, Radu Purice: Magnetic calculus and semiclassical trace formulas .pdf
Horia Cornean, Pierre Duclos, Radu Purice: Adiabatic non-equilibrium steady states in the partition free approach .pdf
Viorel Iftimie, Radu Purice: Eigenfunctions decay for magnetic pseudodifferential operators .pdf
Nassim Athmouni, Marius Mantoiu, Radu Purice: On the continuity of spectra for families of magnetic pseudodifferential operators .pdf
Marius Mantoiu, Radu Purice, Serge Richard: Coherent states in the presence of a variable magnetic field .pdf
Marius Mantoiu, Radu Purice: The Modulation Mapping for Magnetic Symbols and Operators .pdf
Viorel Iftimie, Marius Mantoiu, Radu Purice: Unicity of the integrated density of states for relativistic Schroedinger operators with regular fields and singular electric potentials .pdf
Viorel Iftimie, Marius Mantoiu, Radu Purice: The magnetic formalism; new results .pdf
Viorel Iftimie, Marius Mantoiu, Radu Purice: Commutator Criteria for Magnetic Pseudodifferential Operators .pdf
The first proof given at the International Conference Qmath 10, Moeciu (Romania) 2007,
A Beals type criterion for pseudidifferential operators with a magnetic field
Viorel Iftimie, Marius Mantoiu, Radu Purice: Estimating the number of negative eigenvalues of a relativistic Hamiltonian with regular magnetic field .pdf
Horia Cornean, Pierre Duclos, Gheorghe Nenciu, Radu Purice: Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula .pdf
Viorel Iftimie, Marius Mantoiu, Radu Purice: Magnetic Pseudodifferential Operators .pdf
Marius Mantoiu, Radu Purice: The Mathematical Formalism of a Particle in a Magnetic Field .pdf
Marius Mantoiu, Radu Purice, Serge Richard: Spectral and Propagation Results for Magnetic Schroedinger Operators; a C*-Algebraic Framework .pdf
Marius Mantoiu, Radu Purice: Strict Deformation Quantization for a Particle in a Variable Magnetic Field .pdf; Abstract
Marius Mantoiu, Radu Purice, Serge Richard: Twisted Crossed Products and Magnetic Pseudodifferential Operators .pdf
Marius Mantoiu, Radu Purice: The Magnetic Weyl Calculus .pdf; Abstract
Marius Mantoiu, Radu Purice: The Algebra of Observables in a Magnetic Field .pdf
W.O. Amrein, M. Mantoiu, R. Purice:Propagation Properties for Schroedinger Operators Affiliated to Certain C*-Algebras .pdf; Abstract
Floquet theory - a quantum mechanical point of view. Seminar talk at University of Illinois at Chicago; April 3, 2019 (lecture notes)
Non-equilibrium steady states and currents. Graduate lectures given in the frame of a Common Seminar organized by the University of Aalborg and the Unicersity of Århus; Denmark, May 3-15, 2013. (lecture notes)
Non-equilibrium steady states and currents. (Quantum Transport and Related Problems in Mathematical Physics - Summer School, Hammamet, Tunisia 2-7th Sepember 2012
Analyse spectrale des familles de Bloch isolés dans un champ magnétique regulier. Talk given at the 16th French Romanian Colloquium, Bucharest, 26-30th August, 2024.
Some results in the spectral analysis of quantum Hamiltonians with magnetic fields. Talk given at the Trans-Carpatian Seminar on Geometry and Physics, on-line, March 13, 2024.
Spectral regularity for a class of pseudo-differential operators with “dilation” perturbation. Talk given at the 10-th Congress of Romanian Mathematicians (CRM10), Piteşti, June 30 - July 5, 2023.
Magnetic pseudo-differential operators and Gabor frames. Talk given at the 28-th International Conference on Operator Theory (OT28), Timisoara, June 27 - July 1, 2022.
Spectral analysis near a conic point of a 2 dimensional periodic Hamiltonian in a weak magnetic field. Talk given at the International Conference: Solid-Mathematics 2021, Marne la Vallée, August 25-27, 2021, (hybrid mode).
Spectral analysis of the bottom of the spectrum of a 2 dimensional periodic magnetic Hamiltonian. Talk given at the International Conference: Mathematkical challenge of Quantum Transport in Nanosystems - Pierre Duclos Workshop, Saint Petersburg, September 14 – 16, 2020.
Peirl's substitution at the bottom of the spectrum in the absence of Wannier functions. Talk given at the University of Illinois at Chicago, on April 8, 2019. presentation.
Les hamiltoniens effectifs de Peierls-Onsager en tant que OPD magnétiques. Workshop - Transitions de phase et équations non locales, Centre Francophone de Mathématiques, IMAR Bucarest. 25 - 27 April 2018. presentation
Low lying spectral gaps induced by slowly varying magnetic fields. Workshop: Spectral Theory and Mathematical Physics. Université de Lorraine - Metz, 16 - 18 Mai 2017. presentation
Spectral gaps for periodic Hamiltonians in slowly varying magnetic fields. In the frame of the Spectral Analysis Seminar at the Pontificia Universidad Catolica de Chile, Santiago de Chile. December 1-st, 2016.
The Peierls-Onsager substitution in the framework of magnetic ΨDO. Workshop - Magnetic fields and semi-classical analysis, Centre &ldquot;Henri Lebesgue&rdquot;, Rennes France, May 19 - 22, 2015. pesentation
The Magnetic Coherent States. XXXII Workshop on Geometric Methods in Physics. Biaƚowieża, Poland, June 30 - July 6, 2013. pesentation
The Magnetic Moyal algebras. Seminar of Harmonic Analysis. Bucharest, September 21-22, 2012. pesentation
Decay of Eigenfunctions of Magnetic Hamiltonians. (7-th Workshop Mathematical Challenges of Quantum Transport in Nano-Optoelectronic Systems, WIAS Berlin, February 04-05, 2011 ).pdf
A Non Equilibrium Steady State as an Adiabatic Limit. (10-ème Colloque Franco - Roumain de Mathématiques Appliquées, Poitiers, 26 - 31 Aoû 2010).pdf
The algebra of quantum observables in a magnetic field: Spectral continuity with respect to the magnetic field. (Workshop Spectral Problems for Quantum Hamiltonians, Centre Interfacultaire Bernoulli, EPF Lausanne, February 2010).pdf