Loschmidt Echo and the Local Density of States

Loschmidt echo (LE) is a measure of reversibility and sensitivity to perturbations of quantum evolutions. For weak perturbations its decay rate is given by the width of the local density of states (LDOS). When the perturbation is strong enough, it has been shown in chaotic systems that its decay is dictated by the classical Lyapunov exponent. However, several recent studies have shown an unexpected non-uniform decay rate as a function of the perturbation strength instead of that Lyapunov decay. Here we study the systematic behavior of this regime in perturbed cat maps. We show that some perturbations produce coherent oscillations in the width of LDOS that imprint clear signals of the perturbation in LE decay. We also show that if the perturbation acts in a small region of phase space (local perturbation) the effect is magnified and the decay is given by the width of the LDOS.Comment: 8 pages, 8 figure

Modelling Disorder: the Cases of Wetting and DNA Denaturation

We study the effect of the composition of the genetic sequence on the melting temperature of double stranded DNA, using some simple analytically solvable models proposed in the framework of the wetting problem. We review previous work on disordered versions of these models and solve them when there were not preexistent solutions. We check the solutions with Monte Carlo simulations and transfer matrix numerical calculations. We present numerical evidence that suggests that the logarithmic corrections to the critical temperature due to disorder, previously found in RSOS models, apply more generally to ASOS and continuous models. The agreement between the theoretical models and experimental data shows that, in this context, disorder should be the crucial ingredient of any model while other aspects may be kept very simple, an approach that can be useful for a wider class of problems. Our work has also implications for the existence of correlations in DNA sequences.Comment: Final published version. Title and discussion modified. 6 pages, 3 figure

Universal Response of Quantum Systems with Chaotic Dynamics

The prediction of the response of a closed system to external perturbations is one of the central problems in quantum mechanics, and in this respect, the local density of states (LDOS) provides an in- depth description of such a response. The LDOS is the distribution of the overlaps squared connecting the set of eigenfunctions with the perturbed one. Here, we show that in the case of closed systems with classically chaotic dynamics, the LDOS is a Breit-Wigner distribution under very general perturbations of arbitrary high intensity. Consequently, we derive a semiclassical expression for the width of the LDOS which is shown to be very accurate for paradigmatic systems of quantum chaos. This Letter demonstrates the universal response of quantum systems with classically chaotic dynamics.Comment: 4 pages, 3 figure

Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte

Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter

Theory of Bubble Nucleation and Cooperativity in DNA Melting

The onset of intermediate states (denaturation bubbles) and their role during the melting transition of DNA are studied using the Peyrard-Bishop-Daxuois model by Monte Carlo simulations with no adjustable parameters. Comparison is made with previously published experimental results finding excellent agreement. Melting curves, critical DNA segment length for stability of bubbles and the possibility of a two states transition are studied.Comment: 4 figures. Accepted for publication in Physical Review Letter

Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions

Cell movement and intercellular signaling occur simultaneously during the development of tissues, but little is known about how movement affects signaling. Previous theoretical studies have shown that faster moving cells favor synchronization across a population of locally coupled genetic oscillators. An important assumption in these studies is that cells can immediately interact with their new neighbors after arriving at a new location. However, intercellular interactions in cellular systems may need some time to become fully established. How movement affects synchronization in this situation has not been examined. Here we develop a coupled phase oscillator model in which we consider cell movement and the gradual recovery of intercellular coupling experienced by a cell after movement, characterized by a moving rate and a coupling recovery rate respectively. We find (1) an optimal moving rate for synchronization, and (2) a critical moving rate above which achieving synchronization is not possible. These results indicate that the extent to which movement enhances synchrony is limited by a gradual recovery of coupling. These findings suggest that the ratio of time scales of movement and signaling recovery is critical for information transfer between moving cells.Comment: 18 single column pages + 1 table + 5 figures + Supporting Informatio

Evaluation of the changes in working limits in an automobile assembly line using simulation

The aim of the work presented in this paper consists of the development of a decision-making support system, based on discrete-event simulation models, of an automobile assembly line which was implemented within an Arena simulation environment and focused at a very specific class of production lines with a four closed-loop network configuration. This layout system reflects one of the most common configurations of automobile assembly and preassembly lines formed by conveyors. The sum of the number of pallets on the intermediate buffers, remains constant, except for the fourth closed-loop, which depends on the four-door car ratio (x) implemented between the door disassembly and assembly stations of the car body. Some governing equations of the four closed-loops are not compatible with the capacities of several intermediate buffers for certain values of variable x. This incompatibility shows how the assembly line cannot operate in practice for x0,97 in a stationary regime, due to the starvation phenomenon or the failure of supply to the machines on the production line. We have evaluated the impact of the pallet numbers circulating on the first closed-loop on the performance of the production line, translated into the number of cars produced/hour, in order to improve the availability of the entire manufacturing system for any value of x. Until the present date, these facts have not been presented in specialized literature. © 2012 American Institute of Physics