Prof. Itzhack Dana

Prof.
Prof. Itzhack Dana
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Research

  • Quantum Chaos and Transport, Topological Quantum Numbers, Related Topics in Mathematical Physics and Phase-Space Quantum Mechanics, and Experimental Realizations of Quantum-Chaos Phenomena.

  • Nonintegrable Hamiltonian Dynamics, Quasiregularity, Pseudochaos, and Chaotic/Pseudochaotic Transport.

Publications

Google Scholar

[2017] I. Dana, Topological Properties of Adiabatically Varied Floquet Systems, Phys. Rev. E 96, 022216 (http://arxiv.org/abs/1701.05057). [pdf file]

[2016] M. Ben-Harush and I. Dana, Generic Superweak Chaos Induced by Hall Effect, Phys. Rev. E 93052207 (http://arxiv.org/abs/1605.03198). [pdf file]

[2015] I. Dana, Quantum Properties of Double Kicked Systems with Classical Translational Invariance in Momentum, Phys. Rev. E 91, 012914 (http://arxiv.org/abs/1410.7362). [pdf file]

[2014] I. Dana, Topologically Universal Spectral Hierarchies of Quasiperiodic Systems, Phys. Rev. B 89, 205111 (http://arxiv.org/abs/1310.7970). [pdf file]

[2014] I. Dana, Classical and Quantum Transport in One-Dimensional Periodically Kicked Systems, invited review paper in Canadian Journal of Chemistry 92, 77-84 (http://arxiv.org/abs/1310.7854). [link to pdf file]

[2013] I. Dana, Staggered-Ladder Quasienergy Spectra for Generic Quasimomentum and Quantum-Dynamical Manifestations, Phys. Rev. A 87, 043623 (http://arxiv.org/abs/1304.4873). [pdf file]

[2012] I. Dana, Generic Regularities in Quasienergy Spectra and Free Quantum Dynamics Independently of Chaos Strength (http://arxiv.org/abs/1205.6178).
[2011] I. Dana and V.B. Roitberg, Weak-Chaos Ratchet Accelerator, Phys. Rev. E 83, 066213 (http://arxiv.org/abs/1205.6187). [pdf file]
[2011] I. Dana, Statistical Approach to Quantum Chaotic Ratchets: First Results and Open Problems, J. Phys.: Conf. Ser. 285, 012048. [pdf file]
[2010] I. Dana, Statistical Approach to Quantum Chaotic Ratchets, Phys. Rev. E 81, 036210 (http://arxiv.org/abs/1003.2995). [pdf file]
[2010] I. Dana, V.B. Roitberg, V. Ramareddy, I. Talukdar, and G.S. Summy, Quantum-Resonance Ratchets: Theory and Experiment, International Journal of Bifurcation and Chaos 20, 255-261. [pdf file]
[2008] I. Dana, Quantum Ratchets on Maximally Uniform States in Phase Space: Semiclassical Full-Chaos Regime (http://arxiv.org/abs/0810.1831).
[2008] I. Dana, V. Ramareddy, I. Talukdar, and G.S. Summy, Experimental Realization of Quantum-Resonance Ratchets at Arbitrary Quasimomenta, Phys. Rev. Lett. 100, 024103 (http://arxiv.org/abs/0706.0871). [pdf file]
[2007] O. Barash and I. Dana, Quantum Accelerator Modes in the Absence of Gravity, International Review of Physics 1, 6-7. [pdf file]
[2007] I. Dana and V. Roitberg, Quantum Resonances and Ratchets in Free-Falling Frames, Phys. Rev. E 76, Rapid Communication, 015201(R) (http://arxiv.org/abs/0706.3993). [pdf file]
[2007] O. Barash and I. Dana, Rotating Accelerator-Mode Islands, Phys. Rev. E 75, 056209 (nlin/0612054). [pdf file]
[2006] I. Dana and D.L. Dorofeev, Fluctuations and Transients in Quantum-Resonant Evolution, Phys. Rev. E 74, Rapid Communication, 045201(R) (nlin/0608022). [pdf file]
[2006] O. Barash and I. Dana, Quasiregularity and Rigorous Diffusion of Strong Hamiltonian Chaos, Phys. Rev. E 74, 056202. [pdf file]
[2006] I. Dana and D.L. Dorofeev, General Quantum Resonances of the Kicked Particle, Phys. Rev. E 73, 026206 (nlin/0509035). [pdf file]
[2005] I. Dana and D.L. Dorofeev, General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition, Phys. Rev. E 72, 046205 (nlin/0504030). [pdf file]
[2005] O. Barash and I. Dana, Type Specification of Stability Islands and Chaotic Stickiness, Phys. Rev. E 71, 036222. [pdf file]
[2004] I. Dana and V.E. Chernov, Periodic Orbits and Chaotic-Diffusion Probability Distributions, Physica A 332, 219-229. [pdf file]
[2004] I. Dana, Global Superdiffusion of Weak Chaos, Phys. Rev. E 69, 016212. [pdf file]
[2003] I. Dana and V.E. Chernov, Chaotic Diffusion on Periodic Orbits and Uniformity, Physica A 330, 253-258. [pdf file]
[2003] I. Dana and V.E. Chernov, Chaotic Diffusion on Periodic Orbits: The Perturbed Arnold Cat Map, Phys. Rev. E 67, 046203. [pdf file]
[2002] I. Dana, General Quantization of Canonical Maps on a Two-Torus, J. Phys. A 35, 3447--3465. [pdf file]
[2002] I. Dana and V.E. Chernov, Vortex Structure and Characterization of Quasiperiodic Functions, J. Phys. A 35, 10101-10116. [pdf file]
[2001] I. Dana, Quantum Chaos on a Toral Phase Space for General Boundary Conditions: Recent New Results, Physica E 9, 542-547. [pdf file]
[2000] I. Dana, Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions, Phys. Rev. Lett. 84, 5994-5997. [pdf file]
[1998] I. Dana and T. Horesh, Strong Variation of Global-Transport Properties in Chaotic Ensembles, Lecture Notes in Physics 511, 51-58. [pdf file]
[1998] I. Dana, M. Feingold, and M. Wilkinson, Band Distributions for Quantum Chaos on a Torus, Phys. Rev. Lett. 81, 3124--3127. [pdf file]
[1998] I. Dana, Y. Rutman, and M. Feingold, Band Husimi Distributions and the Classical-Quantum Correspondence on the Torus, Phys. Rev. E 58, 5655-5667. [pdf file]
[1997] E. Eisenberg, N. Shnerb, and I. Dana, Solvable Model for Dynamical Localization near Quantum Antiresonance, Quantum-Classical Correspondence: Proceedings of the IV Drexel International Symposium on "Quantum Nonintegrability" (International Press, Boston), pp. 453-459.
[1997] I. Dana and I. Freund, Vortex-Lattice Wave Fields, Optics Communications 136, 93-113. [pdf file] 
[1997] E. Eisenberg and I. Dana, Limited Sensitivity to Analyticity: a Manifestation of Quantum Chaos, Foundations of Physics 27, 153-170. [pdf file]
[1996] I. Dana and T. Kalisky, Symbolic Dynamics for Strong Chaos on Stochastic Webs: General Quasisymmetry, Phys. Rev. E 53, Rapid Communication, R2025-R2028. [pdf file]
[1996] I. Dana, E. Eisenberg, and N. Shnerb, Antiresonance and Localization in Quantum Dynamics, Phys. Rev. E 54, 5948-5963. [pdf file]
[1995] I. Dana, E. Eisenberg, and N. Shnerb, Dynamical Localization near Quantum Antiresonance: Exact Results and a Solvable Case, Phys. Rev. Lett. 74, 686-689. [pdf file]
[1995] I. Dana, Kicked Harper Models and Kicked Charge in a Magnetic Field, Phys. Lett. A 197, 413-416. [pdf file]
[1995] I. Dana and M. Amit, General Approach to Diffusion of Periodically Kicked Charges in a Magnetic Field, Phys. Rev. E 51, Rapid Communication, R2731-R2734. [pdf file]
[1995] I. Dana, Extended and Localized States of Generalized Kicked Harper Models, Phys. Rev. E 52, 466-472. [pdf file]
[1994] I. Dana, Quantum Suppression of Diffusion on Stochastic Webs, Phys. Rev. Lett. 73, 1609-1612. [pdf file]
[1993] I. Dana, Type Specification of Chaos, Phys. Rev. Lett. 70, 2387-2390. [pdf file]
[1990] I. Dana, Quantized Hall Conductance in a Glide-Plane Symmetry, Phys. Lett. A 150, 253-256. [pdf file]
[1990] Q. Chen, I. Dana, J.D. Meiss, N.W. Murray, and I.C. Percival, Resonances and Transport in the Sawtooth Map, Physica D 46, 217-240. [pdf file]
[1990] I. Dana and J. Zak, Splitting of a Bloch Band into Magnetic Subbands?, Phys. Lett. A 146, 147-149. [pdf file]
[1990] I. Dana, Organization of Chaos in Area-Preserving Maps, Phys. Rev. Lett. 64, 2339-2342. [pdf file]
[1989] I. Dana, Hamiltonian Transport on Unstable Periodic Orbits, Physica D 39, 205-230. [pdf file]
[1989] I. Dana, N.W. Murray, and I.C. Percival, Resonances and Diffusion in Periodic Hamiltonian Maps, Phys. Rev. Lett. 62, 233-236. [pdf file]
[1987] W.P. Reinhardt and I. Dana, Semi-Classical Quantization, Adiabatic Invariants and Classical Chaos, Proceedings of the Royal Society of London A 413, 157-170.
[1987] I. Dana and W.P. Reinhardt, Intrinsic Nonadiabaticities on the Farey Tree, Lecture Notes in Physics 278, 146-150.
[1987] I. Dana and W.P. Reinhardt, Adiabatic Invariance in the Standard Map, Physica D 28, 115-142. [pdf file]
[1985] I. Dana and S. Fishman, Diffusion in the Standard Map, Physica D 17, 63-74. [pdf file]
[1985] I. Dana and J. Zak, Quantum Hall Conductances and Localization in a Magnetic Field, Phys. Rev. B 32, 3612--3621. [pdf file]
[1985] I. Dana, Y. Avron, and J. Zak, Quantised Hall Conductance in a Perfect Crystal, J. Phys. C: Solid State Phys. 18, L679-L683. [pdf file]
[1983] I. Dana and J. Zak, Adams Representation and Localization in a Magnetic Field, Phys. Rev. B 28, 811-820. [pdf file]
[1983] I. Dana, Composite Von-Neumann Lattice, Phys. Rev. A 28, Rapid Communication, R2594-R2596. [pdf file]
[1982] I. Dana and J. Zak, First-Principles Calculation of Diamagnetic Band Structure, Phys. Rev. Lett. 48, C1226-C1226. [pdf file]
[1982] I. Dana and J. Zak, Perturbation Approach to the Impurity Problem in Lattice Dynamics, J. Phys. C: Solid State Phys. 15, 2115-2125. [pdf file]
[1981] I. Dana, Retardation in Rigid Motion and Degree of Rigidity, General Relativity and Gravitation 13, 807-811. [pdf file] 

 

Courses

86-154: Ordinary Differential Equations

86-210: Analytical Mechanics

86-270: Mathematical Methods for Biophysicists

86-834: Introduction to the Physics of Chaos

 

Activities

 

  • Introducing models of classical and quantum Hamiltonian dynamics, exhibiting different kinds of new properties and phenomena.
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  • Study of basic aspects of classical nonintegrable Hamiltonian systems, such as quasiregularity of chaos or stability islands and chaotic/pseudochaotic transport, including "ratchet" transport.
  •  
  • Phase-space quantum mechanics, with applications in Quantum Chaos, Bloch electrons in magnetic fields, and in other areas.
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  • Study of spectra and quantum-dynamics/transport phenomena (e.g., quantum "ratchet" effects) in systems which are classically nonintegrable, including systems experimentally realizable by atom-optics techniques.
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  • See summary of selected works (with explanatory notes and links) in the research directions above and list of publications.
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  • Former students:  Maty Amit (M. Sc.), Tamir Horesh (M. Sc.), Vladislav E. Chernov (Postdoctorant), Oded Barash (M. Sc.), Dmitry L. Dorofeev (Postdoctorant), Vladislav Roitberg (Ph. D.), Ahiya Davidovitch (M. Sc.), Moti Ben-Harush (M. Sc.).
  •  
  • Present students: Guy Amit (M. Sc.), Kazuhiro Kubo (Postdoctorant).
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  • Conference Organization: Minisymposium on "Quantum-Chaotic Dynamics: Theory and Experiment" at Dynamics-Days-Europe 2013BIUCHAOS Meeting 2008BIUCHAOS Meeting 2006.