Double humped states in the nonlinear Schroedinger equation with a random potential (2009)
Veksler, Hagar, Krivolapov, Yevgeny, Fishman, Shmuel
The role of double humped states in spreading of wave packets for the nonlinear Schroedinger equation (NLSE) with a random potential is explored and the spreading mechanism is unraveled. Comparison...
Perturbation theory for the Nonlinear Schroedinger Equation with a random potential (2009)
Fishman, Shmuel, Krivolapov, Yevgeny, Soffer, Avy
A perturbation theory for the NLSE in 1D on a lattice was developed. The small parameter is the strength of the nonlinearity. For this purpose secular terms were removed and a probabilistic bound on...
On the distribution of linear combinations of eigenvalues of the Anderson model (2008)
Fishman, Shmuel, Krivolapov, Yevgeny, Soffer, Avy
Probabilistic estimates on linear combinations of eigenvalues of the one dimensional Anderson model are derived. So far only estimates on the density of eigenvalues and of pairs were found by Wegner...
Asymptotic localization of stationary states in the nonlinear Schroedinger equation (2008)
Fishman, Shmuel, Iomin, Alexander, Mallick, Kirone
The mapping of the Nonlinear Schroedinger Equation with a random potential on the Fokker-Planck equation is used to calculate the localization length of its stationary states. The asymptotic growth...
Ramsey interferometry with a spin embedded in a Coulomb chain (2008)
De Chiara, Gabriele, Calarco, Tommaso, Fishman, Shmuel, Morigi, Giovanna
We show that the statistical properties of a Coulomb crystal can be measured by means of a standard interferometric procedure performed on the spin of one ion in the chain. The ion spin, constituted...
Structural phase transitions in low-dimensional ion crystals (2007)
Fishman, Shmuel, De Chiara, Gabriele, Calarco, Tommaso, Morigi, Giovanna
A chain of singly-charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the...
The Localization Length of Stationary States in the Nonlinear Schreodinger Equation (2007)
Iomin, Alexander, Fishman, Shmuel
For the nonlinear Schreodinger equation (NLSE), in presence of disorder, exponentially localized stationary states are found. In the present Letter it is demonstrated analytically that the...
Effects of atomic interactions on Quantum Accelerator Modes (2007)
Rebuzzini, Laura, Artuso, Roberto, Fishman, Shmuel, Guarneri, Italo
We consider the influence of the inclusion of interatomic interactions on the delta-kicked accelerator model. Our analysis concerns in particular quantum accelerator modes, namely quantum ballistic...
Regimes of stability of accelerator modes (2006)
Hihinashvili, Rebecca, Oliker, Tali, Avizrats, Yaniv S., Iomin, Alexander, Fishman, Shmuel, Guarneri, Italo
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are...
Arnol'd Tongues and Quantum Accelerator Modes (2005)
Guarneri, Italo, Rebuzzini, Laura, Fishman, Shmuel
The stable periodic orbits of an area-preserving map on the 2-torus, which is formally a variant of the Standard Map, have been shown to explain the quantum accelerator modes that were discovered in...
Decay of Quantum Accelerator Modes (2005)
Sheinman, Michael, Fishman, Shmuel, Guarneri, Italo, Rebuzzini, Laura
Experimentally observable Quantum Accelerator Modes are used as a test case for the study of some general aspects of quantum decay from classical stable islands immersed in a chaotic sea. The modes...
Scaling and Universality of the Complexity of Analog Computation (2005)
Avizrats, Yaniv, Feinberg, Joshua, Fishman, Shmuel
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming...
A Universal Scaling Theory for Complexity of Analog Computation (2005)
Avizrats, Yaniv S., Feinberg, Joshua, Fishman, Shmuel
We discuss the computational complexity of solving linear programming problems by means of an analog computer. The latter is modeled by a dynamical system which converges to the optimal vertex...
Time-independent approximations for periodically driven systems with friction (2004)
Rahav, Saar, Geva, Eli, Fishman, Shmuel
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates...
Dynamics of an ion chain in a harmonic potential (2004)
Morigi, Giovanna, Fishman, Shmuel
Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, thus the eigenmodes are not phononic-like waves. We study chains of N>>1...
Eigenmodes and thermodynamics of a Coulomb chain in a harmonic potential (2004)
Morigi, Giovanna, Fishman, Shmuel
The density of ions trapped in a harmonic potential in one dimension is not uniform. Consequently the eigenmodes are not phonons. We calculate the long wavelength modes in the continuum limit, and...
Point perturbations of circle billiards (2003)
Rahav, Saar, Richman, Oran, Fishman, Shmuel
The spectral statistics of the circular billiard with a point-scatterer is investigated. In the semiclassical limit, the spectrum is demonstrated to be composed of two uncorrelated level sequences....
Decoherence as a Probe of Coherent Quantum Dynamics (2003)
D'Arcy, Michael B., Godun, Rachel M., Summy, Gil S., Guarneri, Italo, Wimberger, Sandro, Fishman, Shmuel, ...
The effect of decoherence, induced by spontaneous emission, on the dynamics of cold atoms periodically kicked by an optical lattice is experimentally and theoretically studied. Ideally, the mean...
A classical scaling theory of quantum resonances (2003)
Wimberger, Sandro, Guarneri, Italo, Fishman, Shmuel
The quantum resonances occurring with delta-kicked particles are studied with the help of a fictitious classical limit, establishing a direct correspondence between the nearly resonant quantum motion...
Time independent description of rapidly oscillating potentials (2003)
Rahav, Saar, Gilary, Ido, Fishman, Shmuel
The classical and quantum dynamics in a high frequency field are found to be described by an effective time independent Hamiltonian. It is calculated in a systematic expansion in the inverse of the...
Effective Hamiltonians for periodically driven systems (2003)
Rahav, Saar, Gilary, Ido, Fishman, Shmuel
The dynamics of classical and quantum systems which are driven by a high frequency ($\omega$) field is investigated. For classical systems the motion is separated into a slow part and a fast part....
Probabilistic analysis of a differential equation for linear programming (2003)
Asa Ben-hur, B Joshua Feinberg, Shmuel Fishman
ARTICLE IN PRESS
Quantum resonances and decoherence for delta-kicked atoms (2002)
Wimberger, Sandro, Guarneri, Italo, Fishman, Shmuel
The quantum resonances occurring with delta-kicked atoms when the kicking period is an integer multiple of the half-Talbot time are analyzed in detail. Exact results about the momentum distribution...
Stable Quantum Resonances in Atom Optics (2002)
Fishman, Shmuel, Guarneri, Italo, Rebuzzini, Laura
A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results,...
Relaxation and Noise in Chaotic Systems (2002)
For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott...
A Theory for Quantum Accelerator Modes in Atom Optics (2002)
Fishman, Shmuel, Guarneri, Italo, Rebuzzini, Laura
Unexpected accelerator modes were recently observed experimentally for cold cesium atoms when driven in the presence of gravity. A detailed theoretical explanation of this quantum effect is presented...
Spectral Statistics of Rectangular Billiards with Localized Perturbations (2001)
The form factor $K(\tau)$ is calculated analytically to the order $\tau^3$ as well as numerically for a rectangular billiard perturbed by a $\delta$-like scatterer with an angle independent...
Localized Perturbations of Integrable Systems (2001)
The statistics of energy levels of a rectangular billiard, that is perturbed by a strong localized potential, are studied analytically and numerically, when this perturbation is at the center or at a...
Probabilistic analysis of the phase space flow for linear programming (2001)
Ben-Hur, Asa, Feinberg, Joshua, Fishman, Shmuel, Siegelmann, Hava T.
The phase space flow of a dynamical system leading to the solution of Linear Programming (LP) problems is explored as an example of complexity analysis in an analog computation framework. An ensemble...
Probabilistic analysis of a differential equation for linear programming (2001)
Ben-Hur, Asa, Feinberg, Joshua, Fishman, Shmuel, Siegelmann, Hava T.
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a...
Semiclassical cross section correlations (2000)
Eckhardt, Bruno, Fishman, Shmuel, Varga, Imre
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator....
Localization of eigenstates in a modified Tomonaga-Luttinger model (2000)
Gangardt, Dimitry M., Fishman, Shmuel
We study the localization in the Hilbert space of a modified Tomonaga-Luttinger model. For the standard version of this model, the states are found to be extended in the basis of Slater determinants,...
The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems (1999)
Auslaender, Ophir M., Fishman, Shmuel
The autocorrelation function of the force acting on a slow classical system, resulting from interaction with a fast quantum system is calculated following Berry-Robbins and Jarzynski within the...
Correlations in the Adiabatic Response of Chaotic Systems (1999)
Auslaender, Ophir M., Fishman, Shmuel
Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. In the leading order in the adiabaticity parameter, a dissipative force, that is present in...
The Accuracy of Semiclassical Quantization for Integrable Systems (1999)
Rahav, Saar, Agam, Oded, Fishman, Shmuel
The eigenvalues of the Hyperspherical billiard are calculated in the semiclassical approximation. The eigenvalues where this approximation fails are identified and found to be related to caustics...
Analog Computation with Dynamical Systems (1997)
Hava T. Siegelmann, Shmuel Fishman
This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of...
Excitation of Small Quantum Systems by High-Frequency Fields (1996)
Brenner, Naama, Fishman, Shmuel
The excitation by a high frequency field of multi--level quantum systems with a slowly varying density of states is investigated. A general approach to study such systems is presented. The Floquet...
Approach to ergodicity in quantum wave functions (1995)
Eckhardt, Bruno, Fishman, Shmuel, Keating, Jonathan, Agam, Oded, Main, Jörg, Müller, Kirsten
According to theorems of Shnirelman and followers, in the semiclassical limit the quantum wavefunctions of classically ergodic systems tend to the microcanonical density on the energy shell. We here...