Andrea Sacchetti

Biographical profile

Graduated in Modena in 1987 in Mathematics.

From 1988 to 1991 he was a scholarship holder at the National Institute of Advanced Mathematics and a teacher of Industrial Informatics at the ITI “L. da Vinci” of Carpi.

From 1991 to 1999 he was a researcher in Mathematical Physics at the Faculty of MM, FF and NN Sciences of the University of Modena, from 1999 to 2001 he was Associate Professor of Rational Mechanics at the Faculty of Engineering of the University of Modena, from 2001 he is Full Professor of Mathematical Physics at the MM, FF and NN Faculty of Sciences of the University of Modena.

He was President of the Mathematics Degree Course Council and member of the Academic Senate of the University of Modena and Reggio Emilia.

He is a member of the Scientific Committee of the National Group for Mathematical Physics.

Main publications

Available for consultation below 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 Jan. 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 Jan. 22 (1989), 4989-5006.
• 3. Maioli M, Sacchetti A, One-dimensional many point interactions and stability of eigenvalues, Bolettino UMI (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 Jan. 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. Phys. 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 Jan. 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 Jan. 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 Jan. 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, Assympt. Anal. 13 (1996), 373-391 .
• 15. Grecchi V, Martinez M, Sacchetti A, Splitting instability: the unstable double wells, J. Phys. A: Math. and Jan. 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 Jan. 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 Jan. 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 tunneling 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 Jan. 37 (2004), 2371-2383.
• 30. Grecchi V, Sacchetti A, Critical conditions for a stable molecular structure, J. Phys. A: Math. and Jan. 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 Jan. 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 Jan. 38, (2005). 8379-8392.
• 36. Della Casa FFG, 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 Jan. 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 Jan. 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 Jan. 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 behavior of one-dimensional Bose-Einstein condensates with defects, chapter in the book Bose-Einstein Condensates: Theory, Characteristics, and Current Research, (ed. Nova Publisher: 2010).

Research interests

Mathematical Methods of Quantum Mechanics