César R. de Oliveira

November/2012

Some (low resolution) pictures:

Research Interests

1. The Aharonov-Bohm effect.
2. Quantum Mechanics: Schroedinger and Dirac operators.
3. Dimensional reduction.
4. Spectral Theory and time-dependent quantum systems.
5. Nonperiodicities and their influence in physical models.
6. Nonlinear dynamics and chaos.

Main Publications

» Books

• César R. de Oliveira 2009 - Intermediate Spectral Theory and Quantum Dynamics
  In English (Go to ISTQD book page).
  Published by Birkhäuser, Basel, Switzerland, volume 54 in the series Progress in Mathematical Physics (410 pages; ISBN 978-3-7643-8794-5).
  
  This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics.
  
  
• César R. de Oliveira 2010 - Introduction to Functional Analysis - Projeto Euclides (257 pages)
  In Portuguese (Go to IFA book page)
  2001 - Introduction to Functional Analysis - 1st Edition
  In Portuguese (English Contents).
  Published by IMPA, Rio de Janeiro (ISBN 85-244-0186-9 and 978-85-244-0311-8).
  
  It is an introduction to the subject for graduate (or advanced undergraduate) students. There are 30 chapters; each one was dimensioned to be covered in one lecture. Most chapters present Notes and proposed exercises (there are about 430 of them in the text); at the end there are solutions to selected exercises.
  
  
• César R. de Oliveira

  2000 - CD-ROM: Physics in Action - Mechanics (2nd ''printing'' 2010)
  
  In Portuguese (FAMecanica 1.0 - contents).
  Published by EdUFSCar, São Carlos (ISBN 978-85-85173-44-9).
  
  It is an electronic book in CD-ROM (Windows(R) 95/98/NT and Macintosh(R)) on Classical Mechanics with animations, graphics, hypertexts, numerical procedures (ready to use) related to the subject, theoretical text, exercises, advanced questions, examinations, etc.
  It is intended to high school and first year undergraduate students.
  
  
  
  

  » Refereed Articles

• César R. de Oliveira and Alessandra A. Verri
  Asymptotic spectrum for Dirichlet Laplacian in thin deformed tubes with scaled geometry
  J. Phys. A: Math. Theor. 45 435201 (2012) (22 pages)
  
  
• Silas L. Carvalho and César R. de Oliveira
  Spectral packing dimensions through power-law subordinacy
  To appear in Annales Henri Poincaré (2012)
  
  
• César R. de Oliveira and Alessandra A. Verri
  Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential
  Journal of Mathematical Physics 53, (2012) 052104 (20 pages)
  
  
• Silas L. Carvalho and César R. de Oliveira
  Spectral and dynamical properties of sparse one-dimensional continuous Schrödinger and Dirac operators
  To appear in Proceedings of the Edinburgh Mathematical Society.
  
  
• C. R. de Oliveira and A. A. Verri
  On norm resolvent and quadratic form convergences in asymptotic thin spatial waveguides
  Proceedings of Spectral Days 2010, Santiago, Chile, in the book series "Operator Theory: Advances and Applications'' 224, (2012) 253-276 (Birkhäuser, Basel)
  
  
• Roberto A. Prado and César R. de Oliveira
  Sparse 1D discrete Dirac operators I: Quantum transport
  Journal of Mathematical Analysis and Applications 385, (2012) 947-960
  
  
• Silas L. Carvalho, César R. de Oliveira and Roberto A. Prado
  Sparse 1D discrete Dirac operators II: Spectral properties
  Journal of Mathematical Physics 52, (2011) 073501
  
  
• César R. de Oliveira and Alessandra A. Verri
  On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
  Journal of Mathematical Analysis and Applications 381, (2011) 454-468
  
  
• César R. de Oliveira and Marciano Pereira
  Impenetrability of Aharonov-Bohm solenoids: proof of norm resolvent convergence
  Letters in Mathematical Physics 95, (2011) 41-51
  
  
• César R. de Oliveira
  Quantum singular operator limits of thin Dirichlet tubes via Gamma-convergence
  Reports on Mathematical Physics 67, (2011) 1-32
  
  
• César R. de Oliveira and Marciano Pereira
  Scattering and self-adjoint extensions of the Aharonov-Bohm hamiltonian
  Journal of Physics A: Math. Theor., 45, (2010) 354011, 29 pages
  
  
• César R. de Oliveira
  Is Dirichlet the physical boundary condition for the one-dimensional hydrogen atom?
  Physics Letters A 374, (2010) 2805-2808
  
  
• César R. de Oliveira and Mariza S. Simsen
  Quantum energy expectation in periodic time-dependent hamiltonians via Green functions
  Mathematical Problems in Engineering 2009, (2009) Article ID 902506, 30 pages
  
  
• César R. de Oliveira and Alessandra A. Verri
  Self-adjoint extensions of Coulomb systems in 1,2 and 3 dimensions.
  Annals of Physics 324, (2009) 251-266
  
  
• César R. de Oliveira and Marciano Pereira
  Mathematical justification of the Aharonov-Bohm hamiltonian.
  Journal of Statistical Physics 133, (2008) 1175-1184
  
  
• Milton Cobo, Carlos Gutierrez and César R. de Oliveira
  Cantor singular continuous spectrum for operators along interval exchange transformations.
  Proceedings of the American Math. Soc. 136, (2008) 923-930
  
  
• Roberto A. Prado and César R. de Oliveira
  Dynamical lower bounds for 1D Dirac operators.
  Mathematische Zeitschrift 259, (2008) 45-60
  
  
• César R. de Oliveira and Roberto A. Prado
  Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum.
  Journal of Differential Equations 235, (2007) 85-100
  
  
• César R. de Oliveira and Mariza S. Simsen
  A Floquet Operator with Pure Point Spectrum and Dynamical Instability.
  Annales Henri Poincaré 8, (2007) 1255-1277
  
  
• Túlio O. Carvalho and César R. de Oliveira
  Hybrid Quasicrystals, Transport and Localization in Products of Minimal Sets.
  Journal of Statistical Physics 127 (6), (2007) 1221-1235
  
  
• César R. de Oliveira and Mariza S. Simsen
  Almost periodic orbits and stability for quantum time-dependent hamiltonians.
  Reports on Math. Phys. 60, (2007) 349-366
  
  
• César R. de Oliveira and Thiago Werlang
  Ergodic Hypothesis in Classical Statistical Mechanics.
  Rev. Bras. Ens. Fis. 29 (2), (2007) 189-201
  
  
• Alejandro Lopez-Castillo and César R. de Oliveira
  "Dimensionalities of Weak Solutions in Hydrogenic Systems"
  Journal of Physics A: Math. Gen. 39, (2006) 3447-3454
  
  
• César R. de Oliveira and Roberto A. Prado
  "Spectral and Localization Properties for the One-Dimensional Bernoulli Discrete Dirac Operator"
  Journal of Mathematical Physics 46, (2005) 072105 1-17
  
  
• César R. de Oliveira and Roberto A. Prado
  "Dynamical Delocalization for the 1D Bernoulli Discrete Dirac Operator"
  Journal of Physics A: Math. Gen. 38, (2005) L115-L119
  
  
• A. López-Castillo and César R. de Oliveira
  "Classical Electronic Autoionization under Molecular Oscillations"
  Chaos, Solitons and Fractals 20 (5), (2004) 937-946
  
  
• A. López-Castillo and César R. de Oliveira
  "Classical autoionization for the aperiodic driven hydrogen atom"
  Chaos, Solitons and Fractals 15, (2003) 859-869
  
  
• César R. de Oliveira and Carlos Gutierrez
  "Almost Periodic Schrödinger Operators Along Interval Exchange Transformations"
  Journal of Mathematical Analysis and Applications 283, (2003) 570-581
  
  
• César R. de Oliveira, C. Miguel Arizmendi and Juan Sanchez
  "Multifractal Analysis and Randomness of Almost Periodic Forced Two-Level Systems"
  Physica A 330 (3/4), (2003) 400-408
  
  
• Marcus V. Lima and César R. de Oliveira
  "Uniform Cantor Singular Continuous Spectrum for Nonprimitive Schrödinger Operators"
  Journal of Statistical Physics 112 (1/2), (2003) 357-374
  
  
• Túlio O. Carvalho and César R. de Oliveira
  "Critical Energies in Random Palindrome Models"
  Journal of Mathematical Physics 44 (3), (2003) 945-961
  
  
• A. López-Castillo and César R. de Oliveira
  "Classical Ionization for the Aperiodic Driven Hydrogen Atom"
  Chaos, Solitons and Fractals 15 (5), (2003) 859-869
  
  
• César R. de Oliveira
  "Eigenfunction Entropy as a Criterion of Localization"
  Physics Letters A 296, (2002) 165-170
  
  
• Túlio O. Carvalho and César R. de Oliveira
  "Spectra and Transport in Almost Periodic Dimers"
  Journal of Statistical Physics 107 (5/6), (2002) 1015-1030
  
  
• César R. de Oliveira and Marcus V. Lima
  "Singular Continuous Spectrum for a Class of Nonprimitive Substitution Schrödinger Operators"
  Proceedings of the Americam Mathematical Society 130 (1), (2002) 145-156
  
  
• César R. de Oliveira and Giancarlo Q. Pellegrino
  "Spin Manifestation and the Spin-Statistics Conexion" (In Portuguese)
  In: Fundamentos da Física, vol. 2, Osvaldo Pessoa Jr. (org.), Ed. Liv. Física, São Paulo, 2001, 61-66
  
  
• César R. de Oliveira and Giancarlo Q. Pellegrino
  "(De)Localization In The Prime Schrödinger Operator"
  Journal of Physics A: Math. Gen. 34, (2001) L239-L243
  
  
• A. López-Castillo and César R. de Oliveira
  "Chaotic Versus Random Ionization"
  Physical Review E 63 (4), (2001) 47202-1 -- 47202-3
  
  
• César R. de Oliveira
  "Autocorrelation Scaling and Fourier Transform of Non-Autonomous Systems"
  Annales Henri Poincaré 1 (5), (2000) 885-894
  
  
• César R. de Oliveira and Marcus V. Lima
  "A Nonprimitive Substitution Schrödinger Operator with Generic Singular Continuous Spectrum"
  Reports on Mathematical Physics 45 (3), (2000) 431-436
  
  
• César R. de Oliveira and Giancarlo Q. Pellegrino
  "A Remark On Propagation in Almost Periodic Potentials"
  Physics Letters A 259 (5), (1999) 399-402
  
  
• César R. de Oliveira
  "(In)Stability in Classical Mechanics"
  Rev. Bras. Ens. Fis. 21 (1), (1999) 22-32
  
  
• César R. de Oliveira and Giancarlo Q. Pellegrino
  "Quantum Return Probability for Substitution Potentials"
  Journal of Physics A: Math. Gen. 32, (1999) L285-L292
  
  
• A. López-Castillo and César R. de Oliveira
  "Classical Stability of the Hydrogen Atom in Intense Driven Radial Electric Field"
  Journal of Physics B: Atom. Molec. 32 (12), (1999) 2951-2961
  
  
• César R. de Oliveira and Paulo S. Goncalves
  "Correlation Dimension and Spectrum for the Almost Periodic Bouncing Ball"
  Physica A 265, (1999) 473-485
  
  
• César R. de Oliveira
  "A Proof of the Dynamical Version of the Bombieri-Taylor Conjecture"
  Journal of Mathematical Physics 39 (9), (1998) 4335-4342
  
  
• César R. de Oliveira and Maria C. de Toledo
  "Equivalence of Some Quantum Stability Concepts"
  Reports on Mathematical Physics 41 (2), (1998) 145-153
  
  
• César R. de Oliveira and Giancarlo Q. Pellegrino
  "Identical Particles and Strong Dynamical Localization on the Möbius Strip"
  Physica A 235, (1998) 188-198
  
  
• César R. de Oliveira and Paulo S. Goncalves
  "Bifurcations and Chaos for the Quasiperiodic Bouncing Ball"
  Physical Review E 56 (4), (1997) 4868-4871
  
  
• César R. de Oliveira
  "Classical and Quantum Transitions to Chaos for a Family of Periodically Driven Hamiltonians"
  Annals of Physics 246, (1996) 369-380
  
  
• César R. de Oliveira
  "Numerical Study of the Long-Time Behavior of Quantum Systems Driven by Thue-Morse Forces. Application to Two-Level Systems"
  Europhysics Letters 31 (2), (1995) 63-68
  
  
• César R. de Oliveira
  "Dynamical Localization for Nonperiodic Systems"
  Physics Letters A 201, (1995) 419-424
  
  
• César R. de Oliveira
  "Some Remarks Concerning Stability for Nonstationary Quantum Systems"
  Journal of Statistical Physics 78, (1995) 1055-1066
  
  
• César R. de Oliveira, Ana T. Lombardi and Wilson F. Jardim
  "Copper Complexation by Natural Organic Matter. A Multiligand Model"
  Chemical Speciation and Bioavailability 7 (4), (1995) 125-131
  
  
• César R. de Oliveira
  "On Kicked Systems Modulated Along the Thue-Morse Sequence"
  Journal of Physics A: Math. Gen. 27, (1994) L847-L851
  
  
• C. R. de Oliveira, I. Guarneri and G. Casati,
  "From Power-Localized to Extended Quasi-Energy Eigenstates in a Quantum Periodically Driven System"
  Europhysics Letters 27 (3), (1994) 187-192
  
  
• César R. de Oliveira
  "From Dynamical Localization to the Nonstationary Quantum Stability Problem"
  In the book: Trends in Statistical Physics vol. 1 (1994) 165-178 (Research Trends, Trivandrum, India (ISBN 81 85607 61 3))
  
  
• César R. de Oliveira
  "Spectral Properties of a Simple Hamiltonian Model"
  Journal of Mathematical Physics 34 (9), (1993) 3878-3886
  
  
• César R. de Oliveira
  "Instability for a Class of Randomly Kicked Systems"
  Brazilian Journal of Physics 21 (3), (1993) 318-325
  
  
• César R. de Oliveira
  "On the Complete System of Observables in Quantum Mechanics"
  Journal of Mathematical Physics 31 (10), (1990) 2406-2409
  
  
• César R. de Oliveira
  "Attractors and Characteristic Exponents"
  Journal of Statistical Physics 53 (3/4), (1988) 603-612
  
  
• César R. de Oliveira and Coraci P. Malta
  "Bifurcations in a Class of Time Delay Equations"
  Physical Review A 36 (8), (1987) 3997-4001
  
  
• César R. de Oliveira and Coraci P. Malta
  "Action-Angle Variables for the Harmonic Oscillator: Ambiguity Spin x Duplication Spin"
  Annals of Physics 155, (1984) 447-460
  
  
  

  Since March/01/2001: