Biomedical subjects

Itzhack Dana

Publications and source records attributed to Itzhack Dana.

6 recordsLinked to original sources

PubMed2006

Fluctuations and transients in quantum-resonant evolution.

The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked particle is studied in detail on different time scales for general periodic kicking potentials. It is shown that the asymptotic time behavior of a wave-packet MKE is typically a linear growth with bounded fluctuations having a simple number-theoretical origin. For a large class of wave packets, the MKE is shown to be exactly the superposition of its asymptotic behavior and transient logarithmic corrections. Both fluctuations and transients can be significant for not too large times but they may vanish identically under some conditions. In the case of incoherent mixtures of plane waves, it is shown that the MKE never exhibits asymptotic fluctuations but transients usually occur.

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PubMed2006

General quantum resonances of the kicked particle.

The quantum resonances (QRs) of the kicked particle are studied in a most general framework by also considering arbitrary periodic kicking potentials. It is shown that QR can arise, in general, for any rational value of the Bloch quasimomentum. This is illustrated in the case of the main QRs for arbitrary potentials. In this case, which is shown to be precisely described by the linear kicked rotor, exact formulas are derived for the diffusion coefficients determining the asymptotic evolution of the average kinetic energy of either an incoherent mixture of plane waves or a general wave packet. The momentum probability distribution is exactly calculated and studied for a two-harmonic potential. It clearly exhibits additional resonant values of the quasimomentum and it is robust under small deviations from QR.

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PubMed2005

General approach to the quantum kicked particle in a magnetic field: quantum-antiresonance transition.

The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for general values of the conserved coordinate x(c) of the cyclotron orbit center. The system exhibits spectral structures ["Hofstadter butterflies" (HBs)] and quantum diffusion depending sensitively on x(c). Most significant changes take place when x(c) approaches the value at which quantum antiresonance (exactly periodic recurrences) can occur: the HB essentially "doubles" and the quantum-diffusion coefficient D(x(c)) is strongly reduced. An explanation of these phenomena, including an approximate formula for D(x(c)) in a class of wave packets, is given on the basis of an effective Hamiltonian which is derived as a power expansion in a small parameter. The global quantum diffusion of a two-dimensional wave packet for all x(c) is briefly considered.

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PubMed2005

Type specification of stability islands and chaotic stickiness.

A detailed characterization of stability islands in area-preserving maps is introduced on the basis of the resonance partition of phase space and it is used to define chaotic stickiness in these maps. It is shown that a general island can be characterized by a well-defined quasiregularity "type," specifying the sequence of resonances visited by the island. In particular, a "tangle" island lies entirely not just within the turnstile lobe of a resonance but also within the turnstile overlap of two resonances. Chaotic stickiness to a given island is then defined as the coincidence of the type of a chaotic orbit with that of the island in some time interval. This definition allows one to study stickiness systematically on all time scales, including short or nonasymptotic time regimes, as illustrated in the case of an accelerator-mode island of the standard map. A physically significant identification of the "sticky layer" and its "sublayers" in this case is made and discussed.

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PubMed2004

Global superdiffusion of weak chaos.

A class of kicked rotors is introduced, exhibiting accelerator-mode islands (AIs) and global superdiffusion for arbitrarily weak chaos. The corresponding standard maps are shown to be exactly related to generalized web maps taken modulo an "oblique cylinder." Then, in a case that the web-map orbit structure is periodic in the phase plane, the AIs are essentially normal web islands folded back into the cylinder. As a consequence, chaotic orbits sticking around the AI boundary are accelerated only when they traverse tiny "acceleration spots." This leads to chaotic flights having a quasiregular steplike structure. The global weak-chaos superdiffusion is thus basically different in nature from the strong-chaos one in the usual standard and web maps.

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PubMed2003

Chaotic diffusion on periodic orbits: the perturbed Arnold cat map.

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-number squared, w(2), weighted by a stability factor; (3). the uniform (nonweighted) average of w(2). The results from formulas (1). and (2). agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (3). gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisfied by the PO Lyapunov eigenvalues at fixed w. These sum rules follow from general arguments and are supported by much numerical evidence.

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