Gheorghe Nenciu

Address:

Institute of Mathematics of the Romanian Academy,
Bucuresti, P.O. Box 1-764, RO-70700, ROMANIA
fax: (401)-222.98.26

Dept. of Theoretical Physics,
University of Bucharest,
P.O. Box MG 11, 76900-Bucharest, Romania

Academic Degree:

Ph.D. in Physics (1974)

Current Position:

• Professor of Theoretical Physics, University of Bucharest
• Senior Researcher at the i Institute of Mathematics of the Romanian Academy, Bucharest

Workgroup:

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

Field of Activity:

Mathematical Physics - quantum mechanics, statistical mechanics.

Research activity:

• Theory of strong interactions
• Rigorous results in quantum theory of solids
• Spectral theory for Schrodinger and Dirac operators
• Adiabatic invariants in classical and quantum mechanics
• Statistical mechanics

Current interest in:

• Rigorous results in quantum theory of solids
• Spectral theory for Schrodinger and Dirac operators
• Adiabatic theorem of quantum mechanics

Publications:

• About the Best Stability in Weighted Dispersion Relations Nuovo Cim. Letters 4, 96-100 (1970)
• Absence of Spontaneous Magnetization in Isotropic Partially Finite Systems Phys. Letters 33A, 422-423 (1971) (with G. Costache)
• On Non-existence of Spontaneous Magnetization in a One-dimensional Heisenberg Ferromagnet Phys. Letters 34A, 422-423 (1971)
• The Asymptotic Expantion of the Displacement Field of Localised Defects in Cubic Crystals Crystal Lattice Defects 2, 175-179 (1971) (with N. Angelescu and D. Grecu)
• On Stable Potentials Commun. Math. Phys. 22, 162-165 (1971) (with N. Angelescu and V. Protopopescu)
• A Rigorous Lower Bound for the Maximum of Amplitude from Error-affected Data Nuovo Cim. 8, 75-85 (1972) (with S. Ciulli)
• Molecular Field Theory and Phase Transitions in Partially Finite Systems Phys. Stat. Solidi 51, 205-214 (1972) (with N. Angelescu and G. Costache)
• Weighted Dispersion Relations and Cut to Cut Extrapolations Commun. Math. Phys. 26, 237-246 (1972) (with S. Ciulli)
• Optimal Lower Bounds on the Hadronic Contribution to the Muon Anomalous Magnetic Moment Nuovo Cim. 11A, 319-332 (1972) (with I. Raszillier)
• On the Ground state of Ising Chains with Finite Range Interactions Phys. Lett. A43, 5,6 (1973) (with N. Angelescu and M. Bundaru)
• On the Independence of the Thermodynamic Limit on the Boundary Condition in Quantum Statistical Mechanics Comm. Math. Phys. 29, 15-30 (1972) (with N. Angelescu)
• On the Surface Contribution to the Grand Canonical Pressure of Free Quantum Gases J. Stat. Phys. 7, 119-130 (1973)
• The Schur-Pick-Nevanlinna Interpolation -an Alternative to N/D Equations Nucl. Phys. B53, 584-596 (1973)
• On Determinations of the KN Effective Coupling Constant from forward Amplitude Nucl. Phys. B59, 93-105 (1973) (with N. Sznajder Hald and J. L. Petersen)
• Optimal Information for the Pion Form Factor from Analiticity and Experimental Data Nucl. Phys. B63, 285-300 (1973) (with I. Raszillier, W. Schmidt and H. Schneider)
• On the L2 Improperly Posed Problems J. Math. Anal. App. 42, 132-137 (1973)
• Optimal Analytic Extrapolation for the Scattering Amplitude from Cuts to Interior Points J. Math. Phys. 14, 1675-1691 (1973) (with S. Ciulli)
• A New Method for the General Solution of Partial Wave Dispersion Relations Helv. Phys. Acta 47, 137-162 (1974) (with G. Rasche and W. S. Woolcock)
• Eigenfunction Expantions for Schrodinger and Dirac Operators with Singular Potentials Commun. Math. Phys. 42, 221-229 (1975)
• On the Landau Diamagnetism Commun. Math. Phys. 42, 9-28 (1975) (with N. Angelescu and M. Bundaru)
• On the Perturbations of Gibbs Semigroups Commun. Math. Phys. 42, 29-30 (1975) (with N. Angelescu and M. Bundaru)
• Self-adjointness and Invariance of the Essential Spectrum for Dirac Operators Defined as Quadratic Forms Commun. Math. Phys. 48, 235-247 (1976)
• Self-adjointness and Invariance of the Essential Spectrum for Dirac Operators Defined as Quadratic Forms Helv. Phys. Acta 50, 1-4 (1977)
• On Regular External Fields in Quantum Electrodynamics Helv. Phys. Acta 51, 412-424 (1978) (with G. Scharf)
• General Solution of Multichannel Partial Wave Dispersion Relations. I. Coincident Thresholds, Pole Approximations Helv. Phys. Acta 51, 608 (1978) (with G. Rasche, M. Stihi and W. S. Woolcock)
• On the Adiabatic Limit for Dirac Particles in External Fields Commun. Math. Phys. 76, 117-128 (1980)
• On the Adiabatic Theorem in Quantum Mechanics J. Phys. A: Math. Gen. 13, L15 (1980)
• General Solution of Multichannel Partial Wave Dispersion Relations. II. Noncoincident Thresholds, One Pole approximation Helv. Phys. Acta 53, 134-158 (1980) (with G. Rasche and W. S. Woolcock)
• On the Dynamics of Bloch Electrons in External Electric Fields Phys. Lett. 78A, 101 (1980) (with A. Nenciu)
• The critical Behaviour of the Kac Type Models for Semi-infinite Systems J. Stat. Phys. 24, 529-552 (1981) (with N. Angelescu, M. Bundaru and G. Costache)
• Adiabatic Theorem and Spectral Concentration. I. Arbitrary Order Spectral Concentration for the Stark Effect in Atomic Physics Commun. Math. Phys. 82, 121-136 (1981)
• Dynamics of Bloch Electrons in External Electric Fields: I. Bounds for Interband Transitions and Effective Wannier Hamiltonians J. Phys. A: Math. Gen. 14, 2817, (1981) (with A. Nenciu)
• On the Order of Excitonic Phase Transition Phys. Lett. A93, 201-204 (1983) (with N. Angelescu and N. S. Tonchev)
• Dynamics of Bloch Electrons in External Electric Fields: II. Existence of Strak-Wannier resonances J. Phys. A: Math. Gen. 15, 3313 (1982) (with A. Nenciu)
• The Existence of Energy gaps for Three Dimensional Systems without Long Range Order J. Phys. A Math. Gen.14, L109 (1981) (with A. Nenciu)
• A Lowner Type Interpolation Problem Applied to Partial Wave Dispersion Relations Helv. Phys. Acta 56, 1046 (1983) (with G. Rasche)
• Removing Cut-offs Singular Perturbations: an Abstract Result Lett. Math. Phys. 7, 301 (1983)
• Applications of the Krein Resolvent Formula to the Theory of Self-adjoint Extensions of Positive Symmetric Operators J. Operator Theory 10, 209 (1983)
• Existence of the Exponentially Localised Wannier Functions Commun. Math. Phys. 91, 81-85 (1983)
• On the Influence of the Reservoir and of the Shape of the Fermi Surface on the Phase Diagram of Two-band Models for Cr Alloys J. Phys. F: Met. Phys. 14, 2155-2166 (1984) (with N. Angelescu and N. S. Tonchev)
• Stability of Energy Gaps under Variations of the Magnetic Field Lett. Math. Phys. 11, 127-132 (1986)
• Existence of Spontaneous Pair Creation in the External Field Approximation of Q.E.D. Commun. Math. Phys. 109, 303-312 (1987)
• Bloch Electrons in a Magnetic Field: Rigorous Justification of Peierls-Onsager Effective Hamiltonian Lett. Math. Phys. 17, 247-252 (1989)
• On the Nonrelativistic Limit if the Dirac Hamiltonian Ann. Inst. Henri Poincare 51, 231-263 (1989) (with D. R. Grigore, and R. Purice)
• Existence of Stark-Wannier Resonances for Nonperiodic One-dimensional Systems Phys. Rev. B40, 3622-3624 (1989) (with A. Nenciu)
• Adiabatic Theorems and Gell-Mann-Low Formula Helv. Phys Acta 62, 372-388 (1989) (with G. Rasche)
• On the Theory of Adiabatic Invariants for Linear Hamiltonian Systems Comptes Rendus Acad. Sci. Paris, A310, 807-810 (1990) (with A. Boutet de Monvel)
• Dynamics of Band Electrons in Electric and Magnetic Fields: Rigorous Justification of Effective Hamiltonians Rev. Mod. Phys. 63, 91-127 (1991)
• Asymptotic Invariant Subspaces, adiabatic theorems and block diagonalisation in: Recent Developments in Quantum Mechanics. Kluver, Dordrecht, 1991, p. 133-149
• Perturbation Theory for Time Dependent Hamiltonians: Rigorous Justification of the Effective Hamiltonians Helv. Phys. Acta 65, 529-559 (1992) (with Ph-A. Martin)
• Adiabatic Theorem for Non-Selfadjoint Operators J. Phys A: Math. Gen. 25, 5741-5751 (1992) (with G. Rasche)
• Existence of Exponentially Localised Wannier Functions for Nonperiodic Systems Phys. Rev. B47, 10112-10115 (1993) (with A. Nenciu)
• Linear Adiabatic Theory. Exponential Estimates Commun. Math. Phys. 152, 479-496 (1993)
• Floquet Operators without Absolutely Continous Spectrum Ann. Inst. Henri Poincare 59, 91-97 (1993)
• Adiabatic Reduction Theory. Semiclassical S-Matrix for N-State One-dimensional Systems Op. Theor.: Advances and Applications, 70, 307-319, (Birkhauser Verlag Basel) (1994)
• Semiclassical Inelastic S Matrix for One-dimensional N- States Systems in: On Three Levels. NATO ASI Series B Physics, 234, 149-154. Ed: M. Fannes et all, Plenum, New-York (1994). (with Ph-A. Martin)
• On Adiabatic Reduction Theory Op. Theory.: Adv. and Appl.78, 243-252, Birkhauser, Basel (1995). (with A. Martinez)
• Semi-classical Inelastic S-Matrix for One-dimensional N-States Systems Rev. Math. Phys. 7, 193-242 (1995) (with Ph. A. Martin)
• Perturbed Periodic Hamiltonians: Essential Spectrum and Exponential Decay of Eigenfunctions Lett. Math. Phys. 34, 119-133 (1995). (with A. Boutet de Monvel and A. Nenciu)
• One-dimensional Dirac Hamiltonian: Semiclassical and High-energy Asymptotics for Gaps J. Math. Phys. 37, 3153-3167 (1996) (with R. Purice)
• Adiabatic Theory: Stability of Systems with Increasing Gaps Ann. Inst. Henri Poincare
• Existence of generalised Wannier functions for one dimensional systems Commun. Math. Phys. 190, 541-548 (1998) (with A. Nenciu)
• On Eigenfunction Decay for two Dimensional Magnetic Schrodinger Operators Commun. Math. Phys. 192, 671-685 (1998) (with H. Cornean)