Publications


4. N.C. Dias, J.N. Prata, Local Fractional Derivatives, Book chapter (62 pp).Editor: J. Cresson, Nova Publishers (2014). 
3. N.C. Dias, A. Mikovic, J.N. Prata (Editores), Special Issue: Quantum Gravity and Noncommutative Geometry.Modern Physics Letters A Numbers 17 & 18 (2005), World Scientific.
2. N.C. Dias, The Dynamics of Quantum Gravity - A Proposal.Ph.D Thesis, Pennsylvania State University (1997, USA). 1. N.C. Dias, Variáveis não locais em teorias de Yang-Mills e de gravitação.Tese de Licenciatura, Instituto Superior Técnico (1993). (In Portuguese).

68. N.C. Dias, C. Jorge e J.N Prata: Vibration modes of the Euler-Bernoulli beam equation with singularities.
Journal of Differential Equations 381 (2024) 185-208.67. N.C. Dias, C. Jorge e J.N Prata: An existence and uniqueness result about algebras of Schwartz distributions.
To appear in Monatshefte für Mathematik (2023).66. N.C. Dias, J.N. Prata and N. Teofanov: Short-time Fourier transform of the pointwise product of two functions with application to the nonlinear Schroedinger equation.Analysis and Applications 21 n.6 (2023) 1417-1446.
65. N.C. Dias and J.N. Prata: On a recent conjecture by Z. van Herstraeten and N.J. Cerf for the quantum Wigner entropy. Annales Henri Poincaré 24 (2023) 2341-2362.
64. N.C. Dias, M. de Gosson and J.N. Prata: On orthogonal projections of symplectic balls.To appear in Comptes Rendus Mathematique (2023).
63. N.C. Dias, M. de Gosson and J.N. Prata: Partial traces and the geometry  of entanglement; sufficient conditions for the separability of Gaussian states.Reviews in Mathematical Physics 34 (3) (2022) 2250005 (36 pages).
62. N.C. Dias, F. Luef and J.N. Prata: Uncertainty Principle Via Variational Calculus on Modulation Spaces.Journal of Functional Analysis 283 (2022) 109605 (30 pages).
61. N.C. Dias and J.N. Prata: Boundaries and profiles in the Wigner formalism.Journal of Computational Electronics 20 (2021) 2020-2038.60. N.C. Dias, C. Jorge and J.N. Prata: Ordinary Differential Equations With Singular Coefficients: An Intrinsic Formulation with Applications to the Euler-Bernoulli Beam Equation.
Journal of Dynamics and Differential Equations 33 (2021) 593-619.59. N.C. Dias and J.N. Prata: Quantum mappings acting by coordinate transformations on Wigner distributions.
Revista Matemática Iberoamericana 35 n.2 (2019) 317-337.58. N.C. Dias and J.N. Prata: Uncertainty relations for a non-canonical phase-space noncommutative algebra.
Journal of Physics A: Mathematical and Theoretical 52 (2019) 225203 (32 pp).57. N.C. Dias, C. Jorge and J.N. Prata: Ordinary differential equations with point interactions: An inverse problem. Journal of Mathematical Analysis and Applications 471 (2019) 53-72. 
56. N.C. Dias, M. de Gosson and J.N. Prata: A refinement of the Robertson-Schroedinger uncertainty principle and a Hirschman–Shannon Inequality for Wigner Distributions. Journal of Fourier Analysis and Applications 25 (2019) 210-241. 
55. J.S. Ben-Benjamin, L. Cohen, N.C. Dias, P. Loughlin and J.N. Prata: What is the Wigner function closest to a given square integrable function?SIAM Journal on Mathematical Analysis 50(5) (2018) 5161-5197.
54. N.C. Dias and J.N. Prata: Wigner functions on non-standard symplectic vector spaces. Journal of Mathematical Physics 59 (2018) 012118 (27 pp).
53. N.C. Dias, C. Jorge and J.N. Prata: One-dimensional Schroedinger operators with singular potentials: A Schwartz distributional formulation.Journal of Differential Equations 260 (2016) 6548-6580.
52. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata: Bell operator and Gaussian squeezed states in noncommutative quantum mechanics.Physical Review D 93 (2016) 104055 (9 pp).
51. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata: Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle. Physical Review D 91 (2015) 065036 (32 pp).
50. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata:   Robertson-Schrödinger formulation of Ozawa's uncertainty principle.Journal of Physics: Conference Series 626 (2015) 012050 (8 pages).
49. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata:  Entanglement and separability in the noncommutative phase-space scenario.Journal of Physics: Conference Series 626 (2015) 012046 (8 pages).
48. N.C. Dias, M. de Gosson, and J.N. Prata: A Symplectic extension map and a new Shubin class of pseudo-differential operators.Journal of Functional Analysis 266 (2014) 3772-3796. 
47. N.C. Dias, M. de Gosson, and J.N. Prata: Maximal covariance group of Wigner transforms and pseudo-differential operators.Proceedings of the American Mathematical Society 142 n.9 (2014) 3183-3192.
46. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata: Phase-space noncommutative formulation of Ozawa's uncertainty principle.Physical Review D 90 (2014) 045023 (10pp).
45. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata: Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle.Physical Review A 89 (2014) 042112 (6pp).
44. N.C. Dias, M. de Gosson, and J.N. Prata: Metaplectic formulation of the Wigner transform and applications.Reviews in Mathematical Physics 25 n.10 (2013) 1343010 (19pp).
43. C. Bastos, A. Bernardini, O. Bertolami, N.C. Dias and J.N.Prata: Entanglement due to Noncommutative in the Phase space. Physical Review D 88 (2013) 085013 (6pp).
42. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Noncommutative Graphene.International Journal of Modern Physics A 28 n.16 (2013) 1350064 (13pp).
41. N.C. Dias, M. de Gosson, F. Luef and J.N. Prata: Quantum mechanics in phase space: the Schrodinger and the Moyal representations.Journal Pseudo-Differential Operators and Applications 3 n.4 (2012) 367-398.
40. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Violation of the Robertson-Schrodinger uncertainty principle and non-commutative quantum mechanics.Physical Review D 86 (2012) 105030 (5pp).
39. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata:  Noncanonical phase-space noncommutative black holes.AIP Conference Proceedings 1458 (2012) 319-322.
38. N.C. Dias, M. De Gosson, F. Luef and J.N. Prata: A pseudo differential calculus on non standard symplectic space; spectral and regularity results in modulation spaces. Journal de Mathématiques Pures et Appliquées 96 (2011) 423-445.
37. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes.Physical Review D 84 (2011) 024005 (9 pp).
36. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Entropic Gravity, Phase-Space Noncommutativity and the Equivalence Principle.Classical and Quantum Gravity 28 (2011) 125007 (8pp).
35. N.C. Dias, A. Posilicano and J.N. Prata: Self-Adjoint, globally defined Hamiltonian operators for systems with boundaries.Communications on Pure and Applied Analysis 10 n.6 (2011) 1687-1706.
34. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata:  Noncommutative black holes and the singularity problem.Journal of Physics: Conference Series 314 (2011) 012042.
33. N.C. Dias and J.N. Prata: A Global, Dynamical Formulation of Quantum Confined Systems. Proceedings of the Estonian Academy of Sciences (Mathematics) 59 n.4 (2010) 290-293.
32. N.C. Dias, M. de Gosson, F. Luef and J.N. Prata: A Deformation Quantization Theory for Noncommutative Quantum Mechanics.Journal of Mathematical Physics 51 (2010) 072101. 
31. C. Bastos, N.C. Dias and J.N.Prata: Wigner Measures in Noncommutative Quantum Mechanics.Communications in Mathematical Physics 299 n.3 (2010) 709-740.
30. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Singularity problem and phase-space noncanonical noncommutativity.Physical Review D 82 (2010) 041502.
29. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata:  Noncommutative black holes.Journal of Physics: Conference Series 222 (2010) 012033.
28. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Black holes and phase space noncommutativity.Physical Review D 80 (2009) 124038.
27. N.C. Dias and J.N. Prata: A multiplicative product of distributions and applications to linear differential equations with distributional coefficients.Journal of Mathematical Analysis and Applications 359 (2009) 216 - 228.
26. N.C. Dias and J.N. Prata: The Narcowich-Wigner spectrum of a pure state.Reports Mathematical Physics 63 n.1 (2009) 43 - 52.
25. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Noncommutative quantum mechanics and quantum cosmology.International Journal of Modern Physics A 24 (2009) 2741.
24. N.C. Dias and J.N. Prata: Exact master equation for a noncommutative Brownian particle.      
Annals of Physics 324 (2009) 73-96.
23.   C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Noncommutative quantum cosmology.Journal Physics: Conference Series 174 (2009) 012053.
22. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Weyl-Wigner Formulation of Noncommutative Quantum Mechanics. Journal of Mathematical Physics 49 (2008) 072101.
21. C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Phase-Space Noncommutative Quantum Cosmology.Physical Review D 78 (2008) 023516.
20.   N.C. Dias and J.N. Prata: A multiplicative product of distributions and a global formulation of the confined Schroedinger equation.Journal of Generalized Lie Theory and Applications, 2 (2008) No. 3, 137 - 141.
19. N.C. Dias and J.N. Prata: Features of Moyal Trajectories. Journal of Mathematical Physics 48 (2007) 012109.
18. N.C. Dias and J.N. Prata: Deformation Quantization of Confined Systems. International Journal of Quantum Information 5 (2007) 257.
17. N.C. Dias and J.N. Prata: Environment-Induced Decoherence in Noncommutative Quantum Mechanics. International Journal of Quantum Information 5 (2007) 287.
16.   C. Bastos, O. Bertolami, N.C. Dias and J.N.Prata: Deformation quantization of noncommutative quantum mechanics and dissipation. Journal of Physics: Conference Series 67 (2007) 012058.
15. N.C. Dias, A. Mikovic and J.N. Prata: Coherent States Expectation Values as Semiclassical Trajectories.Journal of Mathematical Physics 47 (2006) 082101.
14. N.C. Dias and J.N. Prata: Comment on “On infinite walls in deformation quantization”.  Annals of Physics 321 (2006) 495 - 502.
13. N.C. Dias and J.N. Prata: Stargenfunctions, generally covariant systems and a causal formulation of phase space quantum mechanics. Journal of Mathematical Physics 46 (2005) 072107.
12. N.C. Dias and J.N. Prata:  Deformation quantization and Wigner functions.Modern Physics Letters A 20 (2005) 1371 - 1385.
11. N.C. Dias and J.N. Prata: Admissible States in Quantum Phase Space. Annals of Physics 313/1 (2004) 110 - 146.
10. N.C. Dias and J.N. Prata: Formal Solutions of Stargenvalue Equations. Annals of Physics 311/1 (2004) 120 - 151.
9. N.C. Dias and J.N. Prata: Time Dependent Transformations in Deformation Quantization. Journal of Mathematical Physics 45 (2004) 887 - 901. 
8. N.C. Dias and J.N. Prata: Bohmian Trajectories and Quantum Phase Space Distributions. Physics Letters A 302 (2002) 261 - 272. 7. N.C. Dias: Classicality Criteria. Journal of Mathematical Physics 43 (2002) 5882 - 5901.
6. N.C. Dias and J.N. Prata: Wigner Functions with Boundaries. Journal of Mathematical Physics 43 (2002) 4602 - 4627.
5. N.C. Dias and J.N. Prata: Causal Interpretation and Quantum Phase Space. Physics Letters A 291 (2001) 355 - 366. 4. N.C. Dias and J.N. Prata: Generalized Weyl-Wigner Map and Vey Quantum Mechanics. Journal of Mathematical Physics 42 (2001) 5565 - 5579.
3. N.C. Dias: Half Quantization.Journal of Physics A: Mathematical and General 34 (2001) 771 - 791.
Papers in the Archives:
2. N.C. Dias and J.N. Prata: Symmetric Hybrid Dynamics: A canonical formulation of coupled classical-quantum dynamics. E-print: quant-ph/0005019 (2000).
1. N.C. Dias and J.N. Prata: Symmetric Classical Mechanics. E-print: quant-ph/0003005 (2000).