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  • 1
    Electronic Resource
    Electronic Resource
    (Global and local) fluctuations of phase space contraction in deterministic stationary nonequilibrium (1998)
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 8 (1998), S. 823-833 
    Details
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We studied numerically the validity of the fluctuation relation introduced in Evans et al. [Phys. Rev. Lett. 71, 2401–2404 (1993)] and proved under suitable conditions by Gallavotti and Cohen [J. Stat. Phys. 80, 931–970 (1995)] for a two-dimensional system of particles maintained in a steady shear flow by Maxwell demon boundary conditions [Chernov and Lebowitz, J. Stat. Phys. 86, 953–990 (1997)]. The theorem was found to hold if one considers the total phase space contraction σ occurring at collisions with both walls: σ=σ↑+σ↓. An attempt to extend it to more local quantities σ↑ and σ↓, corresponding to the collisions with the top or bottom wall only, gave negative results. The time decay of the correlations in σ↑,↓ was very slow compared to that of σ. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.166369
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  • 2
    Electronic Resource
    Electronic Resource
    Beta function and anomaly of the Fermi surface for a d=1 system of interacting fermions in a periodic potential (1995)
    Springer
    Communications in mathematical physics 172 (1995), S. 57-93 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We derive a perturbation theory, based on the renormalization group, for the Fermi surface of a one dimensional system of fermions in a periodic potential interacting via a short range, spin independent potential. The infrared problem is studied by writing the Schwinger functions in terms of running couplings. Their flow is described by a Beta function, whose existence and analyticity as a function of the running couplings is proved. If the fermions are spinless we prove that the Beta function is vanishing and the renormalization flow is bounded for any small interaction. If the fermions are spinning the Beta function is not vanishing but, if the conduction band is not filled or half filled and the interaction is repulsive, it is possible again to control the flow proving the partial asymptotic freedom of the theory. This is done showing that the Beta function is partially vanishing using the exact solution of the Mattis model, which is the spin analogue of the Luttinger model. In both these cases Schwinger functions are anomalous so that the system is a “Luttinger liquid”. Our results extend the work in [B.G.P.S.], where neither spin nor periodic potential were considered; an explicit proof of some technical results used but not explicitly proved there is also provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02104511
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  • 3
    Electronic Resource
    Electronic Resource
    Reversibility, Coarse Graining and the Chaoticity Principle (1997)
    Springer
    Communications in mathematical physics 189 (1997), S. 263-275 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We describe a way of interpreting the chaotic principle of [GC1] more extensively than it was meant in the original works. Mathematically the analysis is based on the dynamical notions of Axiom A and Axiom B and on the notion of Axiom C, that we introduce arguing that it is suggested by the results of an experiment ([BGG]) on chaotic motions. Physically we interpret a breakdown of the Anosov property of a time reversible attractor (replaced, as a control parameter changes, by an Axiom A property) as a spontaneous breakdown of the time reversal symmetry: the relation between time reversal and the symmetry that remains after the breakdown is analogous to the breakdown of T-invariance while TCP still holds.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050200
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  • 4
    Electronic Resource
    Electronic Resource
    Quasi Linear Flows on Tori:¶Regularity of their Linearization (1998)
    Springer
    Communications in mathematical physics 192 (1998), S. 707-736 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: Under suitable conditions a flow on a torus C (p) -close, with p large enough, to a quasi periodic diophantine rotation is shown to be “linearizable”, i.e. conjugable to the quasi periodic rotation, by a map that is analytic in the perturbation size. This result is parallel to Moser's theorem stating conjugability in class C (p') for some p'〈p. The extra conditions restrict the class of perturbations that are allowed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050316
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  • 5
    Electronic Resource
    Electronic Resource
    Properties of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas I: The One Particle System (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 35-60 
    Details
    ISSN: 1572-9613
    Keywords: thermostatted Lorentz gas ; steady state current ; smoothness ; regularity ; symbolic dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study numerically and analytically the properties of the stationary state of a particle moving under the influence of an electric field E in a two dimensional periodic Lorentz gas with the energy kept constant by a Gaussian thermostat. Numerically the current appears to be a continuous function of E whose derivative varies very irregularly, possibly in a discontinuous manner. We argue for the non differentiability of the current as a function of E utilizing a symbolic description of the dynamics based on the discontinuities of the collision map. The decay of correlations and the behavior of the diffusion constant are also investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026414222092
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  • 6
    Electronic Resource
    Electronic Resource
    Note on the Kaplan–Yorke Dimension and Linear Transport Coefficients (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 17-34 
    Details
    ISSN: 1572-9613
    Keywords: dynamical systems ; KY-dimension ; Lyapunov exponent ; transport coefficient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A number of new relations between the Kaplan–Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small but non-zero external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the linear transport coefficients in terms of the Kaplan–Yorke dimension is derived. Alternatively, the Kaplan–Yorke dimension for a dissipative macroscopic system can be expressed in terms of the linear transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026449702528
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  • 7
    Electronic Resource
    Electronic Resource
    On the Validity of the Conjugate Pairing Rule for Lyapunov Exponents (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 587-627 
    Details
    ISSN: 1572-9613
    Keywords: Dynamical systems ; Lyapunov exponents ; symmetry ; pairing rule
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For Hamiltonian systems subject to an external potential which in the presence of a thermostat will reach a nonequilibrium stationary state Dettmann and Morriss proved a strong conjugate pairing rule (SCPR) for pairs of Lyapunov exponents in the case of isokinetic (IK) stationary states which have a given kinetic energy. This SCPR holds for all initial phases of the system, all times t, and all numbers of particles N. This proof was generalized by Wojtkowski and Liverani to include hard interparticle potentials. A geometrical reformulation of those results is presented. The present paper proves numerically, using periodic orbits for the Lorentz gas, that SCPR cannot hold for isoenergetic (IE) stationary states which have a given total internal energy. In that case strong evidence is obtained for CPR to hold for large N and t, where it can be conjectured that the larger N, the smaller t will be. This suffices for statistical mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023040621826
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  • 8
    Electronic Resource
    Electronic Resource
    The interaction of background ocean air bubbles with a surface ship (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 571-600 
    Details
    ISSN: 0271-2091
    Keywords: two-phase flow ; bubbly wake ; ship hydrodynamics ; multidimensional two-fluid model ; spatial distribution of bubble size ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier-Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
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  • 9
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    Analyticity of the SRB measure of a lattice of coupled Anosov diffeomorphisms of the torus (2004)
    American Institute of Physics
    Details
    Publication Date: 2004-08-01
    Print ISSN: 0022-2488
    Electronic ISSN: 1089-7658
    Topics: Mathematics , Physics
    Published by American Institute of Physics
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  • 10
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    Erratum: Signals of strong electronic correlation in ion scattering processes [Phys. Rev. B 93, 195439 (2016)] (2018)
    American Physical Society
    Details
    Publication Date: 2018-05-29
    Print ISSN: 2469-9950
    Electronic ISSN: 2469-9969
    Topics: Physics
    Published by American Physical Society
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