Collective dynamics of molecular motors pulling on fluid membranes

The collective dynamics of $N$ weakly coupled processive molecular motors are considered theoretically. We show, using a discrete lattice model, that the velocity-force curves strongly depend on the effective dynamic interactions between motors and differ significantly from a simple mean field prediction. They become essentially independent of $N$ if it is large enough. For strongly biased motors such as kinesin this occurs if $N\gtrsim 5$. The study of a two-state model shows that the existence of internal states can induce effective interactions.Comment: 5 pages, 5 figure

Transient Nucleation near the Mean-Field Spinodal

Nucleation is considered near the pseudospinodal in a one-dimensional $\phi^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are derived, and theoretical results are compared to computer simulation. The analysis reveals a distribution of nucleation times with a distinct peak characteristic of a nonstationary nucleation rate. Under the quench conditions employed, transient critical droplets are more compact than the droplets found in metastable equilibrium simulations and theoretical predictions.Comment: 7 Pages, 5 Figure

Energy extraction from extremal charged black holes due to the BSW effect

Two particles can collide in the vicinity of a rotating black hole producing the divergent energy in the centre of mass frame (the BSW effect). However, it was shown recently that an observer at infinity can register quite modest energies E and masses m which obey some upper bounds. In the present work the counterpart of the original BSW effect is considered that may occur even for radial motion of colliding particles near charged static black holes. It is shown that in some scenarios there are no upper bound on E and m . Thus the high-energetic and superheavy products of the BSW effect in this situation are, in principle, detectable at infinity.Comment: 7 page

Mass of Clusters in Simulations

We show that dark matter haloes, in n--body simulations, have a boundary layer (BL) with precise features. In particular, it encloses all dynamically stable mass while, outside it, dynamical stability is lost soon. Particles can pass through such BL, which however acts as a confinement barrier for dynamical properties. BL is set by evaluating kinetic and potential energies (T(r) and W(r)) and calculating R=-2T/W. Then, on BL, R has a minimum which closely approaches a maximum of w= -dlog W/dlog r. Such $Rw$ ``requirement'' is consistent with virial equilibrium, but implies further regularities. We test the presence of a BL around haloes in spatially flat CDM simulations, with or without cosmological constant. We find that the mass M_c, enclosed within the radius r_c, where the $Rw$ requirement is fulfilled, closely approaches the mass M_{dyn}, evaluated from the velocities of all particles within r_c, according to the virial theorem. Using r_c we can then determine an individual density contrast Delta_c for each virialized halo, which can be compared with the "virial" density contrast $\Delta_v ~178 \Omega_m^{0.45}$ (Omega_m: matter density parameter) obtained assuming a spherically symmetric and unperturbed fluctuation growth. The spread in Delta_c is wide, and cannot be neglected when global physical quantities related to the clusters are calculated, while the average Delta_c is ~25 % smaller than the corresponding Delta_v; moreover if $M_{dyn}$ is defined from the radius linked to Delta_v, we have a much worse fit with particle mass then starting from {\it Rw} requirement.Comment: 4 pages, 5 figures, contribution to the XXXVIIth Rencontres de Moriond, The Cosmological Model, Les Arc March 16-23 2002, to appear in the proceeding

Theory of optomechanics: Oscillator-field model of moving mirrors

In this paper we present a model for the kinematics and dynamics of optomechanics which describe the coupling between an optical field, here modeled by a massless scalar field, and the internal (e.g., determining its reflectivity) and mechanical (e.g., displacement) degrees of freedom of a moveable mirror. As opposed to implementing boundary conditions on the field we highlight the internal dynamics of the mirror which provides added flexibility to describe a variety of setups relevant to current experiments. The inclusion of the internal degrees of freedom in this model allows for a variety of optical activities of mirrors from those exhibiting broadband reflective properties to the cases where reflection is suppressed except for a narrow band centered around the characteristic frequency associated with the mirror's internal dynamics. After establishing the model and the reflective properties of the mirror we show how appropriate parameter choices lead to useful optomechanical models such as the well known Barton-Calogeracos model [G. Barton and A. Calogeracos, Ann. Phys. 238, 227 (1995)] and the important yet lesser explored nonlinear models (e.g., $Nx$ coupling) for small photon numbers $N$, which present models based on side-band approximations [H. Kimble et al., Phys. Rev. D 65, 022002 (2001)] cannot cope with. As a simple illustrative application we consider classical radiation pressure cooling with this model. To expound its theoretical structure and physical meanings we connect our model to field-theoretical models using auxiliary fields and the ubiquitous Brownian motion model of quantum open systems. Finally we describe the range of applications of this model, from a full quantum mechanical treatment of radiation pressure cooling, quantum entanglement between macroscopic mirrors, to the backreaction of Hawking radiation on black hole evaporation in a moving mirror analog.Comment: 27 pages, 3 figure

Shell to shell energy transfer in MHD, Part II: Kinematic dynamo

We study the transfer of energy between different scales for forced three-dimensional MHD turbulent flows in the kinematic dynamo regime. Two different forces are examined: a non-helical Taylor Green flow with magnetic Prandtl number P_M=0.4, and a helical ABC flow with P_M=1. This analysis allows us to examine which scales of the velocity flow are responsible for dynamo action, and identify which scales of the magnetic field receive energy directly from the velocity field and which scales receive magnetic energy through the cascade of the magnetic field from large to small scales. Our results show that the turbulent velocity fluctuations are responsible for the magnetic field amplification in the small scales (small scale dynamo) while the large scale field is amplified mostly due to the large scale flow. A direct cascade of the magnetic field energy from large to small scales is also present and is a complementary mechanism for the increase of the magnetic field in the small scales. Input of energy from the velocity field in the small magnetic scales dominates over the energy that is cascaded down from the large scales until the large-scale peak of the magnetic energy spectrum is reached. At even smaller scales, most of the magnetic energy input is from the cascading process.Comment: Submitted to PR

Fock space relativistic coupled-Cluster calculations of Two-Valence Atoms

We have developed an all particle Fock-space relativistic coupled-cluster method for two-valence atomic systems. We then describe a scheme to employ the coupled-cluster wave function to calculate atomic properties. Based on these developments we calculate the excitation energies, magnetic hyperfine constants and electric dipole matrix elements of Sr, Ba and Yb. Further more, we calculate the electric quadrupole HFS constants and the electric dipole matrix elements of Sr$^+$, Ba$^+$ and Yb$^+$. For these we use the one-valence coupled-cluster wave functions obtained as an intermediate in the two-valence calculations. We also calculate the magnetic dipole hyperfine constants of Yb$^+$.Comment: 23 pages, 12 figures, 10 tables typos are corrected and some minor modifications in some of the section

Light propagation through closed-loop atomic media beyond the multiphoton resonance condition

The light propagation of a probe field pulse in a four-level double-lambda type system driven by laser fields that form a closed interaction loop is studied. Due to the finite frequency width of the probe pulse, a time-independent analysis relying on the multiphoton resonance assumption is insufficient. Thus we apply a Floquet decomposition of the equations of motion to solve the time-dependent problem beyond the multiphoton resonance condition. We find that the various Floquet components can be interpreted in terms of different scattering processes, and that the medium response oscillating in phase with the probe field in general is not phase-dependent. The phase dependence arises from a scattering of the coupling fields into the probe field mode at a frequency which in general differs from the probe field frequency. We thus conclude that in particular for short pulses with a large frequency width, inducing a closed loop interaction contour may not be advantageous, since otherwise the phase-dependent medium response may lead to a distortion of the pulse shape. Finally, using our time-dependent analysis, we demonstrate that both the closed-loop and the non-closed loop configuration allow for sub- and superluminal light propagation with small absorption or even gain. Further, we identify one of the coupling field Rabi frequencies as a control parameter that allows to conveniently switch between sub- and superluminal light propagation.Comment: 10 pages, 8 figure