Andrea Sacchetti

Profilo biografico

Laureato a Modena nel 1987 in Matematica.

Dal 1988 al 1991 è stato borsista presso l’Istituto Nazionale di Alta Matematica ed insegnante di Informatica Industriale presso l’I.T.I. “L. da Vinci” di Carpi.

Dal 1991 al 1999 è stato ricercatore in Fisica Matematica presso la Facoltà di Scienze MM, FF e NN dell’Università di Modena, dal 1999 al 2001 è stato Professore Associato di Meccanica Razionale presso la Facoltà di Ingegneria dell’Università di Modena, dal 2001 è Professore Ordinario di Fisica Matematica presso la Facoltà di Scienze MM, FF e NN dell’Università di Modena.

È stato Presidente del Consiglio di Corso di Laurea in Matematica e membro del Senato Accademico dell’Università di Modena e Reggio Emilia.

È membro del Comitato Scientifico del Gruppo Nazionale per la Fisica Matematica.

Pubblicazioni

Consultabili al seguente link

Research Articles

• 1. Bentosela F, Caliceti E, Grecchi V, Maioli M, Sacchetti A, Analyticity and asymptotics for the Stark-Wannier states, J. Phys. A: Math. and Gen. 21 (1988), 3321-3331.
• 2. Grecchi V, Sacchetti A, Weak-field magnetic bands in superlattices and the single-band approximation, J. Phys. A: Math. and Gen. 22 (1989), 4989-5006.
• 3. Maioli M, Sacchetti A, One-dimensional many point interactions and stability of eigenvalues, Bolettino U.M.I. (7) 5-A (1991),363-372.
• 4. Grecchi V, Maioli M, Sacchetti A, Horn of singularities for the Stark-Wannier ladders, J. Phys. A: Math. and Gen. 24 (1991), 4275-4282.
• 5. Sacchetti A, Asymptotic expansion of the Stark-Wannier states, Helv. Phys. Acta 65 (1992), 11-31.
• 6. Maioli M, Sacchetti A, Strong asymptotic expansion for the exponential anharmonic oscillator, Atti Sem. Mat. Fis. Univ. Modena XL (1992), 25-30.
• 7. Grecchi V, Maioli M, Sacchetti A, Stark resonances in disordered systems, Commun. Math. Phys. 146 (1992), 231-240.
• 8. Grecchi V, Maioli M, Sacchetti A, Wannier ladders and perturbation theory, J. Phys. A: Math. and Gen. 26 (1993), L379-L384.
• 9. Barbieri M, Maioli M, Sacchetti A, Singular continuous spectrum in a class of random Schroedinger operators, Appl. Math. Lett. 6 (1993), 23-26.
• 10. Grecchi V, Maioli M, Sacchetti A, Stark ladders of resonances: Wannier ladders and perturbation theory, Commun. Math. Phys. 159 (1994) 605-618.
• 11. Grecchi V, Sacchetti A, Asymptotics of Zener double-well splittings and magnetic gaps, J. Phys. A: Math. and Gen. 27 (1994), 1393-1399.
• 12. Maioli M, Sacchetti A, Absence of absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials, J. Phys. A: Math. and Gen. 28 (1995), 1101-1106.
• 13. Grecchi V, Sacchetti A, Crossing and anticrossing of resonances: the Wannier-Stark ladders, Annals of Physics 240 (1995),258-284.
• 14. Grecchi V, Martinez M, Sacchetti A, Double well Stark effect: crossing and anticrossing of resonances, Asympt. Anal. 13 (1996), 373-391.
• 15. Grecchi V, Martinez M, Sacchetti A, Splitting instability: the unstable double wells, J. Phys. A: Math. and Gen. 29 (1996), 4561-4587.
• 16. Grecchi V, Sacchetti A, Lifetime of the Wannier-Stark resonances and perturbation theory, Commun. Math. Phys. 185 (1997), 359-378.
• 17. Grecchi V, Sacchetti A, Metastable Bloch oscillators, Phys. Rev. Lett. 78 (1997), 4474-4477.
• 18. Sacchetti A, Band functions for the Lame’ equations, MapleTech 4 (1997), 28-33.
• 19. Grecchi V, Sacchetti A, Wannier-Bloch oscillators, Comm. Math. Phys. 197 (1998), 553-569.
• 20. Maioli M, Sacchetti A, Erratum — Absence of absolutely continuous spectrum for Stark-Bloch operators with strongly singular periodic potentials, J. Phys. A: Math. and Gen. 31 (1998), 1115-1119.
• 21. Losi A, Sacchetti A, First-kind Fredholm integral equations with kernel of Hankel type, Inverse Problems 15 (1999), 281-290.
• 22. Grecchi V, Sacchetti A, Molecular localization induced by collisions, Phys. Rev. A 61 (2000), 2106-2109.
• 23. Grecchi V, Sacchetti A, Critical metastability and destruction of the splitting in non-autonomous systems, J. Stat. Phys. 103 (2001), 339-368.
• 24. Grecchi V, Sacchetti A, The acceleration theorem for Bloch oscillators, Phys. Rev. B 21 (2001), 2303-2307.
• 25. Sacchetti A, Dynamical localization criterion for driver two-level systems, J. Phys. A: Math. And Gen. 34 (2001), 10293-10306.
• 26. Grecchi V, Martinez A, Sacchetti A, Destruction of the beating effect for a non-linear Schroedinger equation, Comm. Math. Phys. 227 (2002), 191-209.
• 27. Sacchetti A, Instability of the tunnelling distruction effect in a quasi-periodically driven two-level system, Europ. Phys. J. D 21 (2002), 229-232.
• 28. Sacchetti A, Nonlinear time-dependent one-dimensional Schrodinger equation with double-well potential, SIAM J. Math. Anal. 35 (2003), 1160-1176.
• 29. Maioli M, Sacchetti A, Gevrey formal power series of Wannier-Stark ladders, J. Phys. A: Math. And Gen. 37 (2004), 2371-2383.
• 30. Grecchi V, Sacchetti A, Critical conditions for a stable molecular structure, J. Phys. A: Math. and Gen. 37 (2004), 3527-3534.
• 31. Sacchetti A, Nonlinear time-dependent Schroedinger equations: the Gross-Pitaevskii equation with double-well potential, J. Evol. Eq. 4, (2004), 345-369.
• 32. Sacchetti A., Nonlinear double-well Schrodinger equations in the semiclassical limit, J. Stat. Phys. 119, (2005) 1347-1382.
• 33. Maioli M, Sacchetti A., Two level systems driven by a stochastic perturbation, J. Stat. Phys. 119, (2005) 1383-1396.
• 34. Lodi D., Maioli M., Sacchetti A., Dynamical localization for two-level systems periodically driven, J. Phys. A: Math. And Gen. 38, (2005). L23-L30.
• 35. Adami R., Sacchetti A., The transition from diffusion to blow-up for a nonlinear Schrodinger equation in dimension 1, J. Phys. A: Math. And Gen. 38, (2005). 8379-8392.
• 36. Della Casa F.F.G, Sacchetti A.. Stationary states for non linear one-dimensional Schrodinger equations with singular potential, Physica D, 219, (2006), 60-68.
• 37. Bambusi D., Sacchetti A., Exponential times in the one-dimensional gross-pitaevskii equation with multiple well potential, Comm. Math. Phys. 275, (2007), 1-36.
• 38. Bambusi D., Sacchetti A., Stability of spectral eigenspaces in nonlinear Schrodinger equations, Dynamics of PDE 4, (2007), 129-141.
• 39. Kovarik H., Sacchetti A., Resonances in twisted quantum waveguides, J. Phys. A: Math. and Gen. 40, (2007), 8371-8384.
• 40. Sacchetti A., Spectral splitting method for nonlinear Schroedinger equations with singular potential, J. Comp. Phys. 227, (2007), 1483-1499.
• 41. Sacchetti A., Effective mass approximation with non-parabolic bands, J. Phys. Soc. Japan 77, (2008).
• 42. Sacchetti A., Bloch oscillators in a slowly perturbed external field, J. Phys. A: Math. and Gen. 41, (2008), 265304.
• 43. Sacchetti A., Universal Critical Power for Nonlinear Schroedinger Equations with a Symmetric Double Well Potential, Phys. Rev. Lett. 103 (2009), 194101.
• 44. Kovarik H., Sacchetti A., A nonlinear Schrodinger equation with two symmetric point interactions in one dimension, J. Phys. A: Math. and Gen. 43 (2010), 155205
• 45. Sacchetti A., Hysteresis effects in Bose-Einstein condensates, Phys. Rev. A 82 (2010) 013636.
• 46. Sacchetti A., Electrical current in nanoelectronic devices, Phys. Lett. A 374, (2010), 4057-4060.
• 47. Cuoghi G., Bertoni A. and Sacchetti A., Effect of quasibound states on coherent electron transport in twisted nanowires Phys Rev B 83 (2011) 245439
• 48. Grecchi V., Kovarik H., Martinez A., Sacchetti A., Sordoni V., Resonant states for a three-body problem under an external field, Asympt. Anal. (2011) – in press
• 49. Fukuizumi R., Sacchetti A., Bifurcation and stability for nonlinear Schrodinger equation with double well potential in the semiclassical limit, arxiv:1104.1511v1, submitted (2011).
  
  Conference Proceedings 
• 1. Grecchi V, Maioli M, Sacchetti A, Stark ladders and perturbation theory in Mathematical Results in Quantum Mechanics (ed. Demuth M), Operator Theory: Advances and Applications 70, Birkhauser Verlag (Berlin) (1994) 33-36.
• 2. Sacchetti A, Destruction of the beating effect in a periodically driven double well, Proceedings of the International Conference APTEX, Bologna 13–17.9.1999 (ed. Graffi S and Martinez A).
• 3. Sacchetti A, Tunneling destruction for a non-linear Schroedinger equation, Proceedings of the International Conference Q-Math 8: Mathematical results in Quantum Mechanics, Taxco (Mex) 10-14.12.2001 (ed. Exner P and Weder R).Contribution to Books

   

• 1. Sacchetti A., Perturbation Theory, semiclassical, Chapter of the Encyclopedia of Complexity and Systems Science (Ed. Springer Verlag: 2008).
• 2. Adami R.,Noja D., Sacchetti A., On the mathematical description of the effective behaviour of one-dimensional Bose-Einstein condensates with defects, chapter in the book Bose-Einstein Condensates: Theory, Characteristics, and Current Research, (ed. Nova Publisher: 2010).

Interessi di ricerca

Metodi Matematici della Meccanica Quantistica