Publications
Books and Thesis
3. N.C. Dias, J.N. Prata, Local Fractional Derivatives, Book chapter (62 pp).
Editor: J. Cresson, Nova Publishers (2014).
2. N.C. Dias, A. Mikovic, J.N. Prata (Editors), Special Issue: Quantum Gravity and Noncommutative Geometry.
Modern Physics Letters A Numbers 17 & 18 (2005), World Scientific.
1. J.N. Prata, Reflecting Boundaries and Massless Factorized Scattering in Two Dimensions. PhD Thesis (University of Durham, U.K., 1998)
Articles/Pre-Prints
71. On Wigdersons' approach to the uncertainty principle.
Available at arxiv: https://arxiv.org/pdf/2312.17438 (with N.C. Dias and F. Luef).
70. A metaplectic perspective of uncertainty principles in the Linear Canonical Transform domain.
Journal of Functional Analysis 287 (2024) 110494 (with N.C. Dias and M. de Gosson).
69. Vibration modes of the Euler-Bernoulli beam equation with singularities.
Journal of Differential Equations 381 (2024) 185-208 (with N.C. Dias and C. Jorge).
68. An existence and uniqueness result about algebras of Schwartz distributions.
Monatshefte für Mathematik 203 (2024) 43-61 (with N.C. Dias and C. Jorge).
67. On orthogonal projections of symplectic balls.
Comptes Rendus Mathématique 362 (2024) 217-227 (with N.C. Dias and M. de Gosson).
66. Gabor products and a phase space approach to nonlinear analysis.
Analysis and Applications 21 (2023) 1417-1446 (with N.C. Dias and N. Teofanov).
65. On a recent conjecture by Z. van Herstraeten and N.J. Cerf for the quantum Wigner entropy.
Annales de l'Institut Henri Poincaré 24 (2023) 2341-2362 (with N.C. Dias).
64. Uncertainty principle via variational calculus on modulation spaces.
Journal of Functional Analysis 283 (2022) 109605 (with N.C. Dias and F. Luef).
63. Partial traces and the geometry of entanglement; sufficient conditions for the separability of Gaussian states.
Reviews in Mathematical Physics 34 (3) (2022) 2250005 (with N.C. Dias and M. de Gosson).
62. Boundaries and profiles in the Wigner formalism.
Journal of Computational Electronics 20 (2021) 2020-2038 (with N.C. Dias).
61. 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 (with N.C. Dias and C. Jorge).
60. Uncertainty relations for a non-canonical phase-space noncommutative algebra.
Journal of Physics A: Mathematical and Theoretical 52 (2019) 225203 (with N.C. Dias).
59. Ordinary differential equations with point interactions: An inverse problem.
Journal of Mathematical Analysis and Applications 471 (2019) 53-72 (with N.C. Dias and C. Jorge).
58. A refinement of the Robertson-Schrodinger uncertainty principle and a Hirschman-Shannon inequality for Wigner distributions.
Journal of Fourier Analysis and Applications 25 (2019) 210-241 (with N.C. Dias and M. de Gosson).
57. Quantum mappings acting by coordinate transformations on Wigner distributions.
Revista Matemática Iberoamericana 15 (2019) 317-337 (with N.C. DIas).
56. What is the Wigner function closest to a given square integrable function?
SIAM Journal on Mathematical Analysis 50 (2018) 5161 - 5197 (with J.S. Ben-Benjamin, L. Cohen, N.C. Dias and P. Loughlin).
55. Wigner functions on non-standard symplectic vector spaces.
Journal of Mathematical Physics 59 (2018) 012108 (27 pp) (with N.C. Dias).
54. One-dimensional Schrodinger operators with singular potentials: A Schwartz distributional formulation.
Journal of Differential Equations 260 (2016) 6548-6580 (with N.C. Dias and C. Jorge).
53. Bell operator and Gaussian squeezed states in noncommutative quantum mechanics.
Physical Review D 93 (2016) 104055 (9 pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
52. Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle.
Physical Review D 91 (2015) 065036 (32 pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
51. Robertson-Schrödinger formulation of Ozawa's uncertainty principle.
Journal of Physics: Conference Series 626 (2015) 012050 (8 pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
50. Entanglement and separability in the noncommutative phase-space scenario.
Journal of Physics: Conference Series 626 (2015) 012046 (8 pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
49. Maximal covariance group of Wigner transforms and pseudo-differential operators.
Proceedings of the American Mathematical Society 142 (2014) 3183-3192 (with N.C. Dias and M. de Gosson).
48. Phase-space noncommutative formulation of Ozawa's uncertainty principle.
Physical Review D 90 (2014) 045023 (10pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
47. Robertson-Schroedinger type formulation of Ozawa's noise-disturbance uncertainty principle.
Physical Review A 89 (2014) 042112 (6pages) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
46. A Symplectic extension map and a new Shubin class of pseudo-differential operators.
Journal of Functional Analysis 266 (2014) 3772-3796 (with N.C. Dias and M. de Gosson).
45. Metaplectic formulation of the Wigner transform and applications.
Reviews in Mathematical Physics 25 (2013) 1343010 (19pp) (with N.C. Dias and M. de Gosson).
44. Entanglement due to noncommutativity in phase space.
Physical Review D 88, 085013 (2013) (6pp) (with C. Bastos, A. Bernardini, O. Bertolami and N.C. Dias).
43. Noncommutative graphene.
International Journal of Modern Physics A 28 (2013) 1350064 (13pp) (with C. Bastos, O. Bertolami and N.C. Dwas).
42. Quantum mechanics in phase space: the Schrodinger and the Moyal representations.
Journal Pseudo-Differential Operators and Applications 3 (2012) 367-398 (with N.C. Dias, M. de Gosson and F. Luef).
41. Violation of the Robertson-Schrodinger uncertainty principle and non-commutative quantum mechanics.
Physical Review D 86, 105030 (2012) (5pp) (with C. Bastos, O. Bertolami and N.C. Dias).
40. Noncanonical phase-space noncommutative black holes.
AIP Conference Proceedings 1458 (2012) 319-322 (with C. Bastos, O. Bertolami and N.C. Dias).
39. 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 (with N.C. Dias, M. de Gosson and F. Luef).
38. Noncommutative black holes and the singularity problem.
Journal of Physics: Conference Series 314 (2011) 012042 (with C. Bastos, O. Bertolami and N.C. Dias).
37. Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes.
Physical Review D 84 (2011) 024005 (9 pages). (with C. Bastos, O. Bertolami and N.C. Dias).
36. Entropic gravity, phase-space noncommutativity and the equivalence principle.
Classical and Quantum Gravity 28 (2011) 125007 (with C. Bastos, O. Bertolami and N.C. Dias).
35. Self-adjoint, globally defined Hamiltonian operators for systems with boundaries.
Communications on Pure and Applied Analysis 10 (2011) 1687-1706 (with N.C. Dias and A. Posilicano).
34. A global, dynamical formulation of quantum confined systems.
Proceedings of the Estonian Academy of Sciences (Mathematics) 59 (2010) 290-293 (with N.C. Dias).
33. Noncommutative black holes.
Journal of Physics: Conference Series 222 (2010) 012033 (with C. Bastos, O. Bertolami and N.C. Dias).
32. A deformation quantization theory for noncommutative quantum mechanics.
Journal of Mathematical Physics 51 (2010) 072101 (with N.C. Dias, M. de Gosson and F. Luef).
31. Wigner measures in noncommutative quantum mechanics.
Communications in Mathematical Physics 299 (2010) 709-740 (with C. Bastos and N.C. Dias).
30. Singularity problem and phase-space noncanonical noncommutativity.
Physical Review D 82 (Rapid Communications) (2010) 041502 (with C. Bastos, O. Bertolami and N.C. Dias).
29. Black holes and phase space noncommutativity.
Physical Review D 80 (2009) 124038 (with C. Bastos, O. Bertolami and N.C. Dias).
28. A multiplicative product of distributions and applications to linear differential equations with distributional coefficients.
Journal of Mathematical Analysis and Applications 359 (2009) 216 - 228 (with N.C. Dias).
27. The Narcowich-Wigner spectrum of a pure state.
Reports on Mathematical Physics 63 (2009) 43 - 54 (with N.C. Dias).
26. Noncommutative quantum mechanics and quantum cosmology.
International Journal of Modern Physics A 24 (2009) 2741 (with C. Bastos, O. Bertolami and N.C. Dias).
25. Noncommutative quantum cosmology.
Journal Physics: Conference Series 174 (2009) 012053 (with C. Bastos, O. Bertolami and N.C. Dias).
24. Exact master equation for a noncommutative Brownian particle.
Annals of Physics 324 (2009) 73-96 (with N.C. Dias).
23. Weyl-Wigner formulation of noncommutative quantum mechanics.
Journal of Mathematical Physics 49 (2008) 072101 (with C. Bastos, O. Bertolami and N.C. Dias).
22. A multiplicative product of distributions and a global formulation of the confined Schrodinger equation.
Journal of Generalized Lie Theory and Applications, 2 (2008) No. 3, 137 - 141 (with N.C. Dias).
21. Phase-space noncommutative quantum cosmology.
Physical Review D78 (2008) 023516 (with C. Bastos, O. Bertolami and N.C. Dias).
20. Features of Moyal trajectories.
Journal of Mathematical Physics 48 (2007) 012109 (with N.C. Dias).
19. Deformation quantization of noncommutative quantum mechanics and dissipation.
Journal of Physics: Conference Series 67 (2007) 012058 (with C. Bastos, O. Bertolami and N.C. Dias).
18. Deformation quantization of confined systems.
International Journal of Quantum Information 5 (2007) 257 (with N.C. Dias).
17. Environment-induced decoherence in noncommutative quantum mechanics.
International Journal of Quantum Information 5 (2007) 287 (with N.C. Dias).
16. Coherent states expectation values as semiclassical trajectories.
Journal of Mathematical Physics 47 (2006) 082101 (with N.C. Dias and A. Mikovic).
15. Comment on “On infinite walls in deformation quantization”.
Annals of Physics 321 (2006) 495 - 502 (with N.C. Dias).
14. Stargenfunctions, generally parametrized systems and a causal formulation of phase space quantum mechanics.
Journal of Mathematical Physics 46 (2005) 072107 (with N.C. Dias).
13. Deformation quantization and Wigner functions.
Modern Physics Letters A 20 (2005) 1371 - 1385 (with N.C. Dias).
12. Admissible states in quantum phase space.
Annals of Physics 313/1 (2004) 110 - 146 (with N.C. Dias).
11. Formal solutions of stargenvalue equations.
Annals of Physics 311/1 (2004) 120 - 151 (with N.C. Dias).
10. Time dependent transformations in deformation quantization.
Journal of Mathematical Physics 45 (2004) 887 - 901 (with N.C. Dias).
9. Bohmian trajectories and quantum phase space distributions.
Physics Letters A 302 (2002) 261 - 272 (with N.C. Dias).
8. Wigner functions with boundaries.
Journal of Mathematical Physics 43 (2002) 4602 – 4627 (with N.C. Dias).
7. Causal Interpretation and quantum phase space.
Physics Letters A 291 (2001) 355 - 366 (with N.C. Dias).
6. Generalized Weyl-Wigner Map and Vey Quantum Mechanics.
Journal of Mathematical Physics 42 (2001) 5565 - 5579 (with N.C. Dias).
5. Symmetric hybrid dynamics: A canonical formulation of coupled classical-quantum dynamics.
E-print: quant-ph/0005019 (2000) (with N.C. Dias).
4. Symmetric classical mechanics.
E-print: quant-ph/0003005 (2000) (with N.C. Dias).
3. Boundary TBA equations for a non-diagonal theory.
Nuclear Physics B 565 (2000) 641 - 652.
2. Reflection factors for the Principle Chiral Model.
Physics Letters B 438 (1998) 115 - 122.
1. The super-Liouville equation on the half-line.
Physics Letters B 405 (1997) 271 - 279.
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