Research Interests & Publications: Chaos (Classical and Quantum), Models of Quantum Matter, Statistical Physics
Research interests:
Simple models for cold atoms for example collapses and revivals for BoseHubbard models and generalizations of the LiebLiniger model are explored. These are sufficiently simple for analytical treatment but capture most the physics. Validity and generalizations of the GrossPitaevskii equation that is the main approximation in exploration of cold atoms are studied. . Phase transitions in ion chains and surfaces are studied, motivated by recent experiments. Statistical description of mixed systems (Where in some parts of phase space the dynamics are regular and in other parts these are chaotic) is developed in order to extract the most robust, hopefully experimentally relevant, properties of such systems
Nonlinear Physics (Quantum and Classical): For a long time physics focused on phenomena which can be described by linear models. There are however phenomena which are essentially nonlinear. Although such phenomena were discovered more than a hundred years ago, only in the second half of the previous century investigation such phenomena became a central field of physics. The most remarkable nonlinear phenomenon is “Chaos”, namely deterministic motion of a system which is modelled by few simple (nonlinear) equations, looks random. I studied extensively the fingerprints of classical chaos in the behavior of the corresponding quantum systems. For some of these systems Anderson localization is found in analogy with disordered lattices, in spite of the fact that deterministic systems are considered.Currently I study models for waves in disordered nonlinear media, where competition between interference (enhancing localization) and chaos (enhancing spreading) takes place. These phenomena are relevant for classical optics as well as for atom optics (where quantum mechanics is relevant for the motion of the center of mass of the atoms). Phase Transitions in systems consisting of cold atoms and ions are explored as well.
Selected Publications:
 S. Rahav, E. Geva and S. Fishman, Time independent approximations for periodically driven systems with friction, Phys. Rev. E 71, 036210 (2005) (arXiv: nlin.CD/0408030).
 A. Buchleitner, M.B. d’Arcy, S. Fishman, S.A. Gardiner, I. Guarneri, Y.Z. Ma, L. Bebuzzini and G.S. Summy, Quantum accelerator modes from the Farey tree, Phys. Rev. Lett. 96, 164101 (2006) (arXiv:physics/0501146).
 C.E. Creffield, S. Fishman, and T.S. Monteiro, Theory of 2δkicked Quantum Rotors, Phys. Rev. E 73, 066202 (2006)(Physics/0510161).
 Y.S. Avizrats, S. Fishman and Joshua Feinberg, A Universal Scaling for Analog Computation, Phys. Lett. A 371, 271274 (2007) (condmat/0508152).
 Y.S. Avizrats, S. Fishman and Joshua Feinberg, Scaling and Universality of the Complexity of Analog Computation, Chaos 16, 023108 (2006) (condmat/0511354).
 M. Sheinman, S. Fishman, I. Guarneri, L. Rebuzzini, Decay of Quantum Accelerator Modes, Phys. Rev. A 73, 052110 (2006) (quantph/0512072).
 I. Guarneri, L. Rebuzzini and S. Fishman, Arnol’d Tongues and Quantum Accelerator Modes, Nonlinearity bf 19 11411164 (2006), (quantph/0512086).
 G. Morigi and S. Fishman, Onedimensional Coulomb crystals at low temperatures, J. Phys. B 39 S221S230 (2006), special issue on ”Theory of quantum gases and quantum coherence”.
 R. Hihinashvili, T. Oliker, Y. S. Avizrats, A. Iomin, S. Fishman, I. Guarneri, Regimes of stability of accelerator modes, Physica D 226, 110 (2007)(quantph/0604006)
 T. Schwartz, G. Bartal, S. Fishman and M. Segev, Transport and Anderson Localization in Disordered TwoDimensional Photonic Lattices, Nature 446, 5255 (March 2007).
 L. Rebuzzini, R. Artuso, S. Fishman and I. Guarneri, Effects of Atomic interactions on Quantum Accelerator Modes, Phys. Rev. A 76, 031603(R) (2007).
 A. Iomin and S. Fishman, The Localization Length of Stationary States in the Nonlinear Schr¨odinger Equation, Phys. Rev E 76, 056607 (2007), (arXiv:0705.2320v1).
 S. Fishman, Y. Krivolapov and A. Soffer, On the problem of dynamical localization in the Nonlinear Schr¨odinger Equation with a random potential, J. Stat. Phys. 131, 843865 (2008).
 S. Fishman, G. DeChiara, T. Calarco and G. Morigi, Structural phase transitions in lowdimensional ion crystals, Phys. Rev. B 77, 064111 (2008) (condmat.statmech arXiv:0710.1831v1).
 G. DeChiara, T. Calarco, S. Fishman and G. Morigi, Ramsey interferometry with a spin embedded in a Coulomb chain, Phys. Rev. A 78, 043414 (2008), and November 2008 issue of Virtual Journal of Ultrafast Science.
 J. Wang, T.S. Monteiro, S. Fishman, J.P. Keating and R. Schubert, Fractional ¯hscaling for Quantum Kicked Rotors Without Cantori, Phys. Rev. Lett. 99, 234101 (2007).
 S. Fishman, A. Iomin and K. Mallick, Asymptotic localization of stationary states in the nonlinear Schr¨odinger Equation, Phys. Rev. E 78, 066605 (2008).
 S. Fishman, Y. Krivolapov and A. Soffer, Perturbation Theory for the Nonlinear Schr¨odinger Equation with a random potential, Nonlinearity 22 28612887 (2009) ( condmat arXiv:0901.4951).
 H. Veksler, Y. Krivolapov and S. Fishman, Spreading for tbe generalized nonlinear Schroedinger equation with disorder, Phys. Rev. E, 80, 037201 (2009).
 H. Veksler, Y. Krivolapov and S. Fishman, Double humped states in the nonlinear Schroedinger equation with a random potential, Phys. Rev. E 81, 017201 (2010).
 Y. Krivolapov , S. Fishman and A. Soffer, A numerical and symbolical approximation of the Nonlinear Anderson Model, New J. Phys. 12 063035 (2010)(arXiv:0912.3906v1).
