Sandro Graffi

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All published works

Action	Title	Year	Authors
+ PDF Chat	A remark on eigenvalue perturbation theory at vanishing isolation distance	2016	F. E. Barone Sandro Graffi
+	Criteria for the reality of the spectrum of PT-symmetric Schroedinger operators and for the existence of PT-symmetric phase transitions	2015	Emanuela Caliceti Sandro Graffi
+	Corrigendum to “Convergence of a quantum normal form and an exact quantization formula” [J. Funct. Anal. 262 (2012) 3340–3393]	2014	Sandro Graffi Thierry Paul
+ PDF Chat	An existence criterion for the $\mathcal{PT}$-symmetric phase transition	2014	Emanuela Caliceti Sandro Graffi
+	A quantum Cherry theorem for perturbations of the plane rotator	2013	F. E. Barone Sandro Graffi
+ PDF Chat	Quadratic ${\mathcal P}{\mathcal T}$-symmetric operators with real spectrum and similarity to self-adjoint operators	2012	Emanuela Caliceti Sandro Graffi Michael Hitrik Johannes Sjöstrand
+	Convergence of a quantum normal form and an exact quantization formula	2012	Sandro Graffi Thierry Paul
+	Convergent Quantum Normal Forms, ${\mathcal P}{\mathcal T}$-symmetry and reality of the spectrum	2012	Emanuela Caliceti Sandro Graffi
+	Convergence of a quantum normal form and a generalization of Cherry’s theorem	2011	Fiorella Barone Sandro Graffi
+	Pietro Burgatti and His Studies on Mechanics	2011	Paolo Freguglia Sandro Graffi
+ PDF Chat	GEOMETRIC APPROACH TO THE HAMILTON–JACOBI EQUATION AND GLOBAL PARAMETRICES FOR THE SCHRÖDINGER PROPAGATOR	2011	Sandro Graffi Lorenzo Zanelli
+ PDF Chat	Global parametrices for the Schrödinger propagator and geometric approach to the Hamilton-Jacobi equation	2011	Sandro Graffi Lorenzo Zanelli
+	Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schr\"odinger propagator	2010	Sandro Graffi Lorenzo Zanelli
+ PDF Chat	PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues	2010	Emanuela Caliceti F. Cannata Sandro Graffi
+	Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator	2010	Sandro Graffi Lorenzo Zanelli
+ PDF Chat	The classical limit of the quantum Zeno effect	2009	Paolo Facchi Sandro Graffi Marilena Ligabò
+ PDF Chat	On the notion of ergodicity for finite quantum systems	2008	Mirko Degli Espositi Sandro Graffi Stefano Isola
+ PDF Chat	A criterion for the reality of the spectrum of PT-symmetric Schrödinger operators with complex-valued periodic potentials	2008	Emanuela Caliceti Sandro Graffi
+ PDF Chat	Spectral analysis of transfer operators associated to Farey fractions	2008	Claudio Bonanno Sandro Graffi Stefano Isola
+ PDF Chat	A Uniform Quantum Version of the Cherry Theorem	2007	Sandro Graffi Carlos Villegas‐Blas
+ PDF Chat	symmetric non-self-adjoint operators, diagonalizable and non-diagonalizable, with a real discrete spectrum	2007	Emanuela Caliceti Sandro Graffi Johannes Sjöstrand
+	Mathematical Aspects of Quantum Maps	2007	Mirko Degli Esposti Sandro Graffi
+ PDF Chat	Uniform convergence of the Lie–Dyson expansion with respect to the Planck constant	2007	Dario Bambusi Mirko Degli Espositi Sandro Graffi
+ PDF Chat	Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons	2007	Jürg Fröhlich Sandro Graffi Simon Schwarz
+	Spectral analysis of transfer operators associated to Farey fractions	2007	Claudio Bonanno Sandro Graffi Stefano Isola
+	A uniform quantum version of the Cherry theorem	2007	Carlos Villegas Blas Sandro Graffi
+ PDF Chat	A Local Quantum Version of the Kolmogorov Theorem	2005	David Borthwick Sandro Graffi
+	THERMODYNAMIC LIMIT FOR SPIN GLASSES	2005	Sandro Graffi
+ PDF Chat	Spectra of<i>PT</i>-symmetric operators and perturbation theory	2004	Emanuela Caliceti Sandro Graffi Johannes Sjöstrand
+ PDF Chat	Localization in Infinite Billiards: A Comparison Between Quantum and Classical Ergodicity	2004	Sandro Graffi Marco Lenci
+ PDF Chat	On the Surface Pressure for the Edwards-Anderson Model	2004	Pierluigi Contucci Sandro Graffi
+ PDF Chat	Monotonicity and Thermodynamic Limit for Short Range Disordered Models	2004	Pierluigi Contucci Sandro Graffi
+ PDF Chat	CONVEX REPLICA SYMMETRY BREAKING FROM POSITIVITY AND THERMODYNAMIC LIMIT	2004	Pierluigi Contucci Sandro Graffi
+	None	2002	Pierluigi Contucci Sandro Graffi Stefano Isola
+	Mean-Field Approximation of Quantum Systems and Classical Limit	2002	Sandro Graffi André Martínez Mario Pulvirenti
+	Méthodes KAM pour les opérateurs de Schrödinger non autonomes	2002	Sandro Graffi
+ PDF Chat	Time Quasi-Periodic Unbounded Perturbations¶of Schrödinger Operators and KAM Methods	2001	Dario Bambusi Sandro Graffi
+	Mean field behaviour of spin systems with orthogonal interaction matrix	2001	Pierluigi Contucci Sandro Graffi Stefano Isola
+ PDF Chat	Absolute Continuity of the Floquet Spectrum¶for a Nonlinearly Forced Harmonic Oscillator	2000	Sandro Graffi Kenji Yajima
+	Normal Forms and Quantization Formulae	1999	Dario Bambusi Sandro Graffi Thierry Paul
+	Long time semiclassical approximation of quantum flows: a proof of the Ehrenfest time	1998	Dario Bambusi Sandro Graffi Thierry Paul
+ PDF Chat	Ergodic properties of infinite quantum harmonic crystals: An analytic approach	1996	Sandro Graffi André Martínez
+ PDF Chat	Classical limit of the quantized hyperbolic toral automorphisms	1995	Mirko Degli Esposti Sandro Graffi Stefano Isola
+	Transition to chaos in classical and quantum mechanics	1994	Jean Bellissard Mirko Degli Esposti Giovanni Forni Sandro Graffi Stefano Isola John N. Mather
+	Quantization of the classical Lie algorithm in the Bargmann representation	1991	Mirko Degli Esposti Sandro Graffi Jan Herczyński
+	Teoria classica delle perturbazioni in meccanica quantistica	1990	Sandro Graffi
+	1/R Expansion for H2+: Analyticity, Summability, Asymptotics, and Calculation of Exponentially Small Terms	1990	R J Damburg R. Kh. Propin Sandro Graffi V. Grecchi Evans M. Harrell Jiřı́ Čı́žek Josef Paldus Harris J. Silverstone
+	The Schr�dinger equation and canonical perturbation theory	1987	Sandro Graffi Thierry Paul
+ PDF Chat	Schrödinger Operators	1985	Sandro Graffi
+	Schrödinger operators : lectures given at the 2nd 1984 session of the Centro internationale [sic] matematico estivo (C.I.M.E.) held at Como, Italy, Aug. 26-Sept. 4, 1984	1985	Sandro Graffi C.I.M.E. Session on Schrödinger Operators Centro internazionale matematico estivo
+	Operatori di Schroedinger con campi elettrici	1980	Sandro Graffi
+ PDF Chat	Resonances in Stark effect and perturbation theory	1978	Sandro Graffi V. Grecchi

Common Coauthors

Coauthor	Papers Together
Emanuela Caliceti	8
Stefano Isola	7
Pierluigi Contucci	5
Thierry Paul	4
Lorenzo Zanelli	4
Mirko Degli Esposti	4
Dario Bambusi	4
F. E. Barone	3
Johannes Sjöstrand	3
Claudio Bonanno	2
André Martínez	2
V. Grecchi	2
Josef Paldus	1
Jan Herczyński	1
Centro internazionale matematico estivo	1
C.I.M.E. Session on Schrödinger Operators	1
Giovanni Forni	1
R. Kh. Propin	1
Harris J. Silverstone	1
R J Damburg	1
Carlos Villegas‐Blas	1
Marco Lenci	1
Mario Pulvirenti	1
Jiřı́ Čı́žek	1
Jürg Fröhlich	1
Kenji Yajima	1
Mirko Degli Espositi	1
Thierry Paul	1
Mirko Degli Espositi	1
Michael Hitrik	1
F. Cannata	1
Simon Schwarz	1
Carlos Villegas Blas	1
David Borthwick	1
Marilena Ligabò	1
John N. Mather	1
Jean Bellissard	1
Evans M. Harrell	1
Paolo Freguglia	1
Paolo Facchi	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Methods of Modern Mathematical Physics	1972	Michael C. Reed Barry Simon	11
+ PDF Chat	Perturbation Theory for Linear Operators	1995	Tosio Kato	9
+	Autour de l'approximation semi-classique	1987	Didier Robert	8
+	Normal Forms and Quantization Formulae	1999	Dario Bambusi Sandro Graffi Thierry Paul	7
+	On a Hilbert space of analytic functions and an associated integral transform part I	1961	V. Bargmann	6
+	Uniform distribution of eigenfunctions on compact hyperbolic surfaces	1987	Steven Zelditch	5
+ PDF Chat	𝓟𝓣-symmetric quantum mechanics	1999	Carl M. Bender Stefan Boettcher Peter N. Meisinger	5
+ PDF Chat	Must a Hamiltonian be Hermitian?	2003	Carl M. Bender Dorje C. Brody H. F. Jones	4
+	Ergodicit� et fonctions propres du laplacien	1985	Yves Colin de Verdìère	4
+ PDF Chat	Supersymmetry and the spontaneous breakdown of 𝒫𝒯 symmetry	2001	Patrick Dorey Clare Dunning Roberto Tateo	4
+	The Schr�dinger equation and canonical perturbation theory	1987	Sandro Graffi Thierry Paul	4
+	Harmonic Analysis in Phase Space. (AM-122)	1989	Gerald B. Folland	4
+	Ergodicit� et limite semi-classique	1987	Bernard Helffer A. Martinez Didier Robert	4
+	Spectre D'Un hamiltonien quantique et mecanique classique	1980	Jacques Chazarain	4
+ PDF Chat	Fourier integral operators. I	1971	Lars Hörmander	4
+ PDF Chat	On the reality of the eigenvalues for a class of PT-symmetric oscillators	2002	K. C. Shin	4
+	The analysis of linear partial differential operators	1990	Lars Hörmander	4
+ PDF Chat	Spectral equivalences, Bethe ansatz equations, and reality properties in 𝒫𝒯-symmetric quantum mechanics	2001	Patrick Dorey Clare Dunning Roberto Tateo	3
+ PDF Chat	Two-dimensional SUSY-pseudo-Hermiticity without separation of variables	2003	F. Cannata M. V. Ioffe D. N. Nishnianidze	3
+ PDF Chat	Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations	1996	Kenji Yajima	3
+	Über die Normalform analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung	1967	Helmut Rüßmann	3
+	The Schrödinger Equation	1991	F. A. Berezin Mikhail Shubin	3
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol	3
+ PDF Chat	Borel summability: Application to the anharmonic oscillator	1970	S. Graffi V. Grecchi Barry Simon	3
+ PDF Chat	Spectra of<i>PT</i>-symmetric operators and perturbation theory	2004	Emanuela Caliceti Sandro Graffi Johannes Sjöstrand	3
+ PDF Chat	Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian	2002	Alí Mostafazadeh	3
+ PDF Chat	The Thermodynamic Limit in Mean Field Spin Glass Models	2002	Francesco Guerra Fabio Lucio Toninelli	3
+	Spectral Asymptotics in the Semi-Classical Limit	1999	Mouez Dimassi Johannes Sjöstrand	3
+	Quantization of the orientation preserving automorphisms of the torus	1993	Mirko Degli Esposti	3
+ PDF Chat	Classical limit of the quantized hyperbolic toral automorphisms	1995	Mirko Degli Esposti Sandro Graffi Stefano Isola	3
+ PDF Chat	Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries	2002	Alí Mostafazadeh	3
+ PDF Chat	Schrödinger operators with complex potential but real spectrum	1998	F. Cannata Georg Junker Johannes Trost	3
+	Symplectic topology as the geometry of generating functions	1992	Claude Viterbo	3
+	Periodic solutions of asymptotically linear Hamiltonian systems	1980	Herbert Amann Eduard Zehnder	3
+ PDF Chat	Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry	1998	Carl M. Bender Stefan Boettcher	3
+ PDF Chat	Resonances in Stark effect and perturbation theory	1978	Sandro Graffi V. Grecchi	3
+	Arithmetical properties of strongly chaotic motions	1987	I C Percival Franco Vivaldi	3
+ PDF Chat	A Uniform Quantum Version of the Cherry Theorem	2007	Sandro Graffi Carlos Villegas‐Blas	3
+ PDF Chat	Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum	2002	Alí Mostafazadeh	3
+	Lie transform perturbation theory for Hamiltonian systems	1981	John R. Cary	3
+	Theory of general perturbations with unspecified canonical variables	1966	Gen-Ichiro Hori	3
+	Ergodic problems of classical mechanics	1968	Владимир Игоревич Арнольд André Avez	2
+ PDF Chat	Supersymmetry without hermiticity within symmetric quantum mechanics	2000	Miloslav Znojil F. Cannata Bijan Bagchi Rajkumar Roychoudhury	2
+ PDF Chat	Stability of Schrödinger eigenvalue problems	1982	E. Vock Walter Hunziker	2
+ PDF Chat	On the thermodynamic formalism for the gauss map	1990	Dieter Mayer	2
+	Positive Transfer Operators and Decay of Correlations	2000	Viviane Baladi	2
+	Modular Functions and Dirichlet Series in Number Theory	1990	Tom M. Apostol	2
+	Towards a complete determination of the spectrum of a transfer operator associated with intermittency	2003	Thomas Prellberg	2
+	Statistical Mechanics: Rigorous Results	1969	David Ruelle	2
+ PDF Chat	GLOBAL FOURIER INTEGRAL OPERATORS AND SEMICLASSICAL ASYMPTOTICS	2000	Ари Лаптев Israel Michael Sigal	2