Radu Purice

Address:

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

Academic Degree:

Habilitation in Mathematics; IMAR (2014)

Ph.D. in Physics; Bucharest University (1990)

Current Position:

Senior Researcher, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucuresti

Workgroup:

Evolution Equations and Control Theory, Partial Differential Equations and Mathematical Physics

Prizes:

"Gheorghe Titeica" Prize of the Romanian Academy 2002

Field of Activity:

Mathematical Physics - quantum mechanics.

Co-director

of the CNRS European Associated Laboratory "LEA Mathématique et Modélisation Franco-Roumain"

Member

in the IUPAP Commission C18 (on Mathematical Physics)

of the IAMP

in the Romanian Team of the RTN "Network in Noncommutative Geometry"

Coordinator of the Romanian Team on the International Research Network ECO-Math organised by CNRS, the Romanian Academy and "Simion Stoilow" Institute of Mathematics of the Romanian Academy.

Director of the Laboratoire Européen Associé MATH-MODE (CNRS - Romanian Academy)

Coordinator of the European Programme EURROMMAT

Coordinator of the Romanian team of the Euro-DGR "Mathematics and Quantum Physics"

Member in the Management Team of the POS DRU Programme of postdoctoral research: Cercetarea Stiintifica economica, suport al bunastarii si dezvoltarii umane în context european

Coordinator of the National CEx Programme Deterministic and Stochastic Differential Methods in the Study of Certain Evolution Models (MDDS)

Member of the IMAR research team on the CNCSIS PCCE Contract Nr. 8/2010 Sisteme diferentiale in analiza neliniara si aplicatii.

Coorganizer of

XIII-eme Colloque Franco-Roumain de Mathematiques Appliques, Iasi, 2016

International Conference: Mathematical aspects of solid state physics, quantum transport and spectral analysis, Bucuresti, 2014

XII-eme Colloque Franco-Roumain de Mathematiques Appliques, Lyon, 2014

XI-eme Colloque Franco-Roumain de Mathematiques Appliques, Bucuresti, 2012

The LEA Math-Mode Workshop , Bucuresti, 2011

7-th Congress of Romanian Mathematicians , Brasov, 2011

4-th annual meeting of the EU-NCG Network , Bucuresti, 2011

Workshop in Nonlinear Analysis and Mathematical Physics - Romanian - German Symposium on Mathematics and its Applications , Sibiu, May 2009

Qmath10 International Conference , Moeciu, 2007

Workshop on Aspects mathématiques du transport dans les systèmes mésoscopiques, Marseille, December 2006

Former Positions:

Deputy Director, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucuresti 2012 - 2014

Scientific Secretary, Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucuresti 1999 - 2012

Assistant doctorand, Ecole de Physique, Université de Genève, Genève 1984 - 1985

Researcher, National Institute of Physics and Nuclear engineering - Department of Fundamental Physics, Bucuresti 1979 - 1990

Research activity:

• 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

Current interest in:

• 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

Recent Papers:

• 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

Graduate Lecture Series:

• 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

Some Recent Talks:

• 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

Publications:

List of published papers

List of edited volumes

Reviewed in Mathematical Reviews

On Research Gate