Nonlocal continuous variable correlations and violation of Bell's inequality for light beams with topological singularities

We consider optical beams with topological singularities which possess Schmidt decomposition and show that such classical beams share many features of two mode entanglement in quantum optics. We demonstrate the coherence properties of such beams through the violations of Bell inequality for continuous variables using the Wigner function. This violation is a consequence of correlations between the $(x, p_x)$ and $(y, p_y)$ spaces which mathematically play the same role as nonlocality in quantum mechanics. The Bell violation for the LG beams is shown to increase with higher orbital angular momenta $l$ of the vortex beam. This increase is reminiscent of enhancement of nonlocality for many particle Greenberger-Horne-Zeilinger states or for higher spins. The states with large $l$ can be easily produced using spatial light modulators.Comment: 6 pages and 2 figure

Flow properties of driven-diffusive lattice gases: theory and computer simulation

We develop n-cluster mean-field theories (0 < n < 5) for calculating the flow properties of the non-equilibrium steady-states of the Katz-Lebowitz-Spohn model of the driven diffusive lattice gas, with attractive and repulsive inter-particle interactions, in both one and two dimensions for arbitrary particle densities, temperature as well as the driving field. We compare our theoretical results with the corresponding numerical data we have obtained from the computer simulations to demonstrate the level of accuracy of our theoretical predictions. We also compare our results with those for some other prototype models, notably particle-hopping models of vehicular traffic, to demonstrate the novel qualitative features we have observed in the Katz-Lebowitz-Spohn model, emphasizing, in particular, the consequences of repulsive inter-particle interactions.Comment: 12 RevTex page

Stochastic kinetics of ribosomes: single motor properties and collective behavior

Synthesis of protein molecules in a cell are carried out by ribosomes. A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an {\it exact} analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a ``Michaelis-Menten-like'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechano-chemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes simultaneously move on the same mRNA track, while each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in 3-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.Comment: Final published versio

Calibrated quantum thermometry in cavity optomechanics

Cavity optomechanics has achieved the major breakthrough of the preparation and observation of macroscopic mechanical oscillators in peculiarly quantum states. The development of reliable indicators of the oscillator properties in these conditions is important also for applications to quantum technologies. We compare two procedures to infer the oscillator occupation number, minimizing the necessity of system calibrations. The former starts from homodyne spectra, the latter is based on the measurement of the motional sidebands asymmetry in heterodyne spectra. Moreover, we describe and discuss a method to control the cavity detuning, that is a crucial parameter for the accuracy of the latter, intrinsically superior procedure

Distribution of dwell times of a ribosome: effects of infidelity, kinetic proofreading and ribosome crowding

Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechano-chemical cycle of a ribosome. The stochastic movement of the ribosome consists of an alternating sequence of pause and translocation; the sum of the durations of a pause and the following translocation is the time of dwell of the ribosome at the corresponding codon. We derive the analytical expression for the distribution of the dwell times of a ribosome in our model. Whereever experimental data are available, our theoretical predictions are consistent with those results. We suggest appropriate experiments to test the new predictions of our model, particularly, the effects of the quality control mechanism of the ribosome and that of their crowding on the mRNA track.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at DOI:10.1088/1478-3975/8/2/02600

Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure

Microscopic energy flows in disordered Ising spin systems

An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics allows a coherent definition of local temperatures also when open boundaries are coupled to thermostats, imposing an energy flow. Within this framework, here we introduce a consistent definition for local energy currents and we study their dependence on the disorder. In the linear response regime, when the global gradient between thermostats is small, we also define local conductivities following a Fourier dicretized picture. Then, we work out a linearized "mean-field approximation", where local conductivities are supposed to depend on local couplings and temperatures only. We compare the approximated currents with the exact results of the nonlinear system, showing the reliability range of the mean-field approach, which proves very good at high temperatures and not so efficient in the critical region. In the numerical studies we focus on the disordered cylinder but our results could be extended to an arbitrary, disordered spin model on a generic discrete structures.Comment: 12 pages, 6 figure

Intertwining Relations for the Deformed D1D5 CFT

The Higgs branch of the D1D5 system flows in the infrared to a two-dimensional N=(4,4) SCFT. This system is believed to have an "orbifold point" in its moduli space where the SCFT is a free sigma model with target space the symmetric product of copies of four-tori; however, at the orbifold point gravity is strongly coupled and to reach the supergravity point one needs to turn on the four exactly marginal deformations corresponding to the blow-up modes of the orbifold SCFT. Recently, technology has been developed for studying these deformations and perturbing the D1D5 CFT off its orbifold point. We present a new method for computing the general effect of a single application of the deformation operators. The method takes the form of intertwining relations that map operators in the untwisted sector before application of the deformation operator to operators in the 2-twisted sector after the application of the deformation operator. This method is computationally more direct, and may be of theoretical interest. This line of inquiry should ultimately have relevance for black hole physics.Comment: latex, 23 pages, 3 figure

Instability of dilute granular flow on rough slope

We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle collisions stabilize the flow above a certain density in the parameter region where a single particle shows an accelerated behavior. Within this parameter regime, however, the uniform flow is only metastable and is shown to be unstable against clustering when the particle density is not high enough.Comment: 4 pages, 6 figures, submitted to J. Phys. Soc. Jpn.; Fig. 2 replaced; references added; comments added; misprints correcte