César R. de Oliveira

October/2023

Position	Mathematics Department - Universidade Federal de São Carlos (UFSCar).
E-mail	oliveira (at) dm.ufscar.br
Phone	+55 16 3351 9153
Address	Department of Mathematics (room 253)
	Universidade Federal de São Carlos - UFSCar
	Cx. P. 676 São Carlos, SP
	13560-970 BRAZIL

» Research Interests

The Aharonov-Bohm effect.
Quantum Mechanics: Schrödinger and Dirac operators.
Dimensional reduction.
Graphene: mathematical models.
Nonperiodicities and their influences in physical models.

»Latin American Mathematical Series

One of the editors of a new book series published by Springer and entitled Latin American Mathematical Series: UFSCar Subseries.

Details, including the editor names, can be found in the series web page.

Main Publications

» Books

Moacir Aloicio, Silas L. Carvalho, César R. de Oliveira
2023 - Spectral Measures and Dynamics: Typical Behaviors

In English
Published by Springer Nature, in the Latin American Mathematical Series: UFSCar Subseries (230 pages; ISBN 978-3-031-38288-8 hardcover).

This monograph discusses many relations between properties of fractal measures and dynamical consequences of some quantum systems and evolution semigroups, as well as in ergodic theory.
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 an introduction to the spectral theory of (unbounded) self-adjoint operators and some application to 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) on Classical Mechanics with animations, graphics, hypertexts, theoretical text, exercises, advanced questions, etc.
It is intended to high school and first year undergraduate students.

» Refereed Articles
1. César R. de Oliveira and Mariane Pigossi
  "Exact solvable family of discrete Schrödinger operators with long-range hoppings"
  Submitted for publication.
2. César R. de Oliveira and Renan G. Romano
  "Dynamical confinement for Schrödinger operators with magnetic potential and Aharonov-Bohm effect"
  Submitted for publication.
3. M. Aloisio, S. L. de Carvalho, C. R. de Oliveira and E. Souza
  "On spectral measures and convergence rates in von Neumann's Ergodic Theorem"
  Submitted for publication.
4. César R. de Oliveira, Vinícius L. Rocha and Osmar N. Souza
  "Boron nitride and graphene heterostructures modeled by quantum graphs"
  Submitted for publication.
5. M. Aloisio, S. L. Carvalho, C. R. de Oliveira and G. Santana
  "Slow dynamics for self-adjoint semigroups and unitary evolution groups"
  Submitted for publication.
6. M. Aloisio, S. L. de Carvalho, C. R. de Oliveira and E. Souza
  "On the Fourier asymptotics of absolutely continuous measures with power-law singularities"
  Submitted for publication.
7. V. Bazao, C. R. de Oliveira and P. A. Diaz
  "On the Birman-Krein Theorem"
  Comptes Rendus. Mathématique 361 (2023) 1081-1086
8. César R. de Oliveira and Vinícius L. Rocha
  "Effective quantum graph models of some nonequilateral graphyne materials"
  C - Journal of Carbon Research 9 (2023) 76 (19 pages)
9. C. R. de Oliveira and A. F. Rossini
  "Effective operators for changing sign Robin Laplacian in thin two- and three-dimensional curved waveguides"
  Communications in Analysis and Geometry 30 (2022) 1227-1268
10. César R. de Oliveira and Vinícius L. Rocha
  "Bidimensional honeycomb materials: a graph model through Dirac operator"
  Reports on Mathematical Physics 89 (2022) 231-252
11. Moacir Aloisio, Silas L. Carvalho and César R. de Oliveira
  "Positive fractal dimensions of bound states spectral measures: application to the Hydrogen atom"
  Brazilian Journal of Physics 52 (2022) 35 (8 pages)
12. R. A. Prado, C. R. de Oliveira and E. C. de Oliveira
  "Density of states and Lifshitz tails for discrete 1D random Dirac operators"
  Mathematical Physics, Analysis and Geometry 24 (2021) 30 (29 pages)
13. Moacir Aloisio, Silas L. Carvalho and César R. de Oliveira
  "Some generic fractal properties of bounded self-adjoint operators"
  Letters in Mathematical Physics 111 (2021) 114 (19 pages)
14. César R. de Oliveira and Wagner Monteiro
  "All self-adjoint extensions of the magnetic Laplacian in nonsmooth domains and gauge transformations"
  Annali della Scuola Normale Superiore di Pisa. Classe di Scenze XXII (2021) 1805-1841
15. V. Bazao, T. O. Carvalho and C. R. de Oliveira
  "Spectral Hausdorff dimensions for a class of Schrödinger operators in bounded intervals"
  Letters in Mathematical Physics 111 (2021) 65 (21 pages)
16. César R. de Oliveira and Vinícius L. Rocha
  " Dirac cones for graph models of multilayer AA-stacked graphene sheets"
  Zeitschrift für Naturforschung A 76 (2021) 371-384
17. Silas L. Carvalho and César R. de Oliveira
  "Generic zero-Hausdorff and one-upper packing spectral measures"
  Journal of Mathematical Physics 62 (2021) 013502 (8 pp.)
18. C. R. de Oliveira and M. Pigossi
  "Persistence of point spectrum for perturbations of one-dimensional operators with discrete spectra"
  In: Miranda P., Popoff N., Raikov G. (eds) Spectral Theory and Mathematical Physics. Latin American Mathematics Series (Springer-Verlag) (2020) 121-151. Cham. https://doi.org/10.1007/978-3-030-55556-6_7
19. Silas L. Carvalho and César R. de Oliveira
  "Refined scales of weak-mixing dynamical systems: typical behaviour"
  Ergodic Theory and Dynamical Systems 40 (2020) 3296-3309
20. César R. de Oliveira and Vinícius L. Rocha
  "Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model"
  J. Phys. A: Math. Theor. 53 (2020) 505201 (21 pages)
21. Moacir Aloisio, Silas L. Carvalho and César R. de Oliveira
  "Category theorems for Schrödinger semigroups"
  Zeitschrift für Analysis und ihre Anwendungen 39 (2020) 421-431
22. César R. de Oliveira and Renan G. Romano
  "A new version of the Aharonov-Bohm effect"
  Foundations of Physics 50 (2020) 137-146
23. Moacir Aloisio, Silas L. Carvalho and César R. de Oliveira
  "Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour"
  Proceedings of the American Mathematical Society 148 (2020) 2509-2523
24. V. R. Bazao, S. L. Carvalho and C. R. de Oliveira
  "Packing subordinacy with application to spectral continuity"
  Journal of the Australian Mathematical Society 108 (2020) 226-244
25. C. R. de Oliveira and A. A. Verri
  "On the Neumann Laplacian in nonuniformly collapsing strips"
  Communications in Contemporary Mathematics 22 (2020) 1950021 (18 pages)
26. Moacir Aloisio, Silas L. Carvalho and César R. de Oliveira
  "Quantum quasiballistic dynamics and thick point spectrum"
  Letters in Mathematical Physics 109 (2019) 1891-1906
27. C. R. de Oliveira and M. Pigossi
  "Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields"
  Mathematische Zeitschrift 291 (2019) 1525-1541
28. C. R. de Oliveira, L. Hartmann and A. A. Verri
  "Effective Hamiltonians in surfaces of thin quantum waveguides"
  Journal of Mathematical Physics 60 (2019) 022101 (9 pp.)
29. C. R. de Oliveira and M. Pigossi
  "Point spectrum and SULE for time-periodic perturbations of discrete 1D Schrödinger operators with electric fields"
  Journal of Statistical Physics 173 (2018) 140-162
30. César R. de Oliveira and Renan G. Romano
  "Aharonov-Bohm effect without contact with the solenoid"
  Journal of Mathematical Physics 58 (2017) 102102 (11 pp.)
31. C. R. de Oliveira and W. Monteiro
  "Generalized Kotani's trick for unitary operators"
  Reports on Mathematical Physics 79 (2017) 151-163
32. V. R. Bazao, S. L. Carvalho and C. R. de Oliveira
  "On the spectral Hausdorff dimension of 1D discrete Schrödinger operators under power decaying perturbations"
  Osaka Journal of Mathematics 54 (2017) 273-285
33. C. R. de Oliveira and A. A. Verri
  "Asymptotic approximation of thin homogeneous tubes by heterogeneous ones"
  Communications in Contemporary Mathematics (2017) 1650060 (15 pp.)
34. R. A. Prado, C. R. de Oliveira and S. L. Carvalho
  "Dynamical localization for discrete Anderson Dirac operators"
  Journal of Statistical Physics 167 (2017) 260-296
35. César R. de Oliveira and Alessandra A. Verri
  Mild singular potentials as effective Laplacian in narrow strips
  Mathematica Scandinavica 120 (2017) 145-160
36. Silas L. Carvalho and César R. de Oliveira
  "A characterization of singular packing subspaces with an application to limit-periodic operators"
  Forum Mathematicum 29 (2017) 31-40
37. Silas L. Carvalho and César R. de Oliveira
  "Correlation dimension wonderland theorems"
  Journal of Mathematical Physics 57 (2016) 063501 (19 pp.)
38. C. R. de Oliveira and A. A. Verri
  Convergence of solutions to stationary reaction-diffusion equations in some Neumann thin domains
  Journal of the Australian Mathematical Society 100 (2016) 252-271
39. Silas L. Carvalho and César R. de Oliveira
  Generic quasilocalized and quasiballistic discrete Schrödinger operators
  Proceedings of the American Mathematical Society 144 (2016) 129-141
40. C. R. de Oliveira and A. A. Verri
  Norm resolvent convergence of Dirichlet Laplacian in unbounded thin waveguides
  Bulletin of the Brazilian Mathematical Society, New Series, 46 (2015) 139-158
41. R. Bedoya, C. R. de Oliveira and A. A. Verri
  Complex Γ-convergence and magnetic Dirichlet Laplacian in bounded thin tubes
  Journal of Spectral Theory 4 (2014) 621-642
42. Silas L. Carvalho and César R. de Oliveira
  Spectral packing dimensions through power-law subordinacy
  Annales Henri Poincaré 14 (2013) 775-792
43. Silas L. Carvalho and César R. de Oliveira
  Spectral and dynamical properties of sparse one-dimensional continuous Schrödinger and Dirac operators
  Proceedings of the Edinburgh Mathematical Society 56 (2013) 1-34
44. César R. de Oliveira and Alessandra A. Verri
  Asymptotic spectrum for Dirichlet Laplacian in thin deformed tubes with scaled geometry
  Journal of Physics A: Math. Theor. 45 (2012) 435201 (22 pages)
45. 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)
46. C. R. de Oliveira and A. A. Verri
  On norm resolvent and quadratic form convergences in asymptotic thin spatial waveguides
  Proceedings of Spectral Days, Santiago, Chile, in the book series "Operator Theory: Advances and Applications'' 224 (2012) 253-276 (Birkhäuser, Basel)
47. 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
48. 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
49. 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
50. 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
51. César R. de Oliveira
  Quantum singular operator limits of thin Dirichlet tubes via Γ-convergence
  Reports on Mathematical Physics 67 (2011) 1-32
52. 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)
53. César R. de Oliveira
  Is Dirichlet the physical boundary condition for the one-dimensional hydrogen atom?
  Physics Letters A 374 (2010) 2805-2808
54. 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)
55. 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
56. César R. de Oliveira and Marciano Pereira
  Mathematical justification of the Aharonov-Bohm hamiltonian.
  Journal of Statistical Physics 133 (2008) 1175-1184
57. Milton Cobo, Carlos Gutierrez and César R. de Oliveira
  Cantor singular continuous spectrum for operators along interval exchange transformations.
  Proceedings of the American Mathematical Society 136 (2008) 923-930
58. Roberto A. Prado and César R. de Oliveira
  Dynamical lower bounds for 1D Dirac operators.
  Mathematische Zeitschrift 259 (2008) 45-60
59. 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
60. 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
61. 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
62. César R. de Oliveira and Mariza S. Simsen
  Almost periodic orbits and stability for quantum time-dependent hamiltonians.
  Reports on Mathematical Physics 60 (2007) 349-366
63. César R. de Oliveira and Thiago Werlang
  Ergodic hypothesis in classical statistical mechanics
  Rev. Bras. Ens. Fis. 29 (2) (2007) 189-201
64. 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
65. 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
66. 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
67. A. López-Castillo and César R. de Oliveira
  "classical electronic autoionization under molecular oscillations"
  Chaos, Solitons and Fractals 20 (5) (2004) 937-946
68. A. López-Castillo and César R. de Oliveira
  "Classical autoionization for the aperiodic driven hydrogen atom"
  Chaos, Solitons and Fractals 15 (2003) 859-869
69. 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
70. 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
71. 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
72. Túlio O. Carvalho and César R. de Oliveira
  "Critical energies in random palindrome models"
  Journal of Mathematical Physics 44 (3) (2003) 945-961
73. 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
74. César R. de Oliveira
  "Eigenfunction entropy as a criterion of localization"
  Physics Letters A 296 (2002) 165-170
75. 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
76. César R. de Oliveira and Marcus V. Lima
  "Singular Continuous Spectrum for a class of nonprimitive substitution Schrödinger Operators"
  Proceedings of the American Mathematical Society 130 (1) (2002) 145-156
77. 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
78. 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
79. A. López-Castillo and César R. de Oliveira
  "Chaotic versus random ionization"
  Physical Review E 63 (4), (2001) 47202 (1-3)
80. César R. de Oliveira
  "Autocorrelation scaling and fourier transform of non-autonomous systems"
  Annales Henri Poincaré 1 (5) (2000) 885-894
81. 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
82. César R. de Oliveira and Giancarlo Q. Pellegrino
  "A remark on propagation in almost periodic potentials"
  Physics Letters A 259 (5) (1999) 399-402
83. César R. de Oliveira
  "(In)Stability in classical mechanics"
  Rev. Bras. Ens. Fis. 21 (1) (1999) 22-32
84. César R. de Oliveira and Giancarlo Q. Pellegrino
  "Quantum return probability for substitution potentials"
  Journal of Physics A: Math. Gen. 32 (1999) L285-L292
85. 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
86. César R. de Oliveira and Paulo S. Goncalves
  "Correlation dimension and spectrum for the almost periodic bouncing ball"
  Physica A 265 (1999) 473-485
87. César R. de Oliveira
  "A proof of the dynamical version of the Bombieri-Taylor conjecture"
  Journal of Mathematical Physics 39 (9) (1998) 4335-4342
88. César R. de Oliveira and Maria C. de Toledo
  "Equivalence of some quantum stability concepts"
  Reports on Mathematical Physics 41 (2) (1998) 145-153
89. César R. de Oliveira and Giancarlo Q. Pellegrino
  "Identical particles and strong dynamical localization on the Möbius strip"
  Physica A 235 (1998) 188-198
90. César R. de Oliveira and Paulo S. Goncalves
  "Bifurcations and chaos for the quasiperiodic bouncing ball"
  Physical Review E 56 (4) (1997) 4868-4871
91. César R. de Oliveira
  "Classical and quantum transitions to chaos for a family of periodically driven hamiltonians"
  Annals of Physics 246 (1996) 369-380
92. 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
93. César R. de Oliveira
  "Dynamical localization for nonperiodic systems"
  Physics Letters A 201 (1995) 419-424
94. César R. de Oliveira
  "Some remarks concerning stability for nonstationary quantum systems"
  Journal of Statistical Physics 78 (1995) 1055-1066
95. 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
96. César R. de Oliveira
  "On kicked systems modulated along the Thue-Morse sequence"
  Journal of Physics A: Math. Gen. 27 (1994) L847-L851
97. 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
98. 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))
99. César R. de Oliveira
  "Spectral properties of a simple hamiltonian model"
  Journal of Mathematical Physics 34 (9) (1993) 3878-3886
100. César R. de Oliveira
  "Instability for a class of randomly kicked systems"
  Brazilian Journal of Physics 21 (3) (1993) 318-325
101. César R. de Oliveira
  "On the complete system of observables in quantum mechanics"
  Journal of Mathematical Physics 31 (10) (1990) 2406-2409
102. César R. de Oliveira
  "Attractors and characteristic exponents"
  Journal of Statistical Physics 53 (3/4) (1988) 603-612
103. César R. de Oliveira and Coraci P. Malta
  "Bifurcations in a class of time delay equations"
  Physical Review A 36 (8) (1987) 3997-4001
104. 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:

César R. de Oliveira

Position

» Research Interests

»Latin American Mathematical Series

Main Publications

» Books

» Refereed Articles