Entanglement of Solitons in the Frenkel-Kontorova Model

We investigate entanglement of solitons in the continuum-limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particle-like behavior as they are characterized by localization of entanglement. The von-Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two solitons manifest long-range entanglement that decreases with the separation of the solitons more slowly than the universal decrease of the critical field. Interestingly, in the noncritical regime of the Frenkel-Kontorova model, entanglement can even increase with the separation of the solitons. We show that most of the entanglement of the so-called internal modes of the solitons is saturated by local degrees of freedom inside the core, and therefore we suggest using the internal modes as carriers of quantum information.Comment: 16 pages, 22 figure

Gauge Fixing and Scattering Amplitudes in String Field Theory Expanded around Universal Solutions

We study a gauge fixed action of open string field theory expanded around the universal solution which has been found as an analytic classical solution with one parameter a. For a>-1/2, we are able to reproduce open string scattering amplitudes in the theory fixed in the Siegel gauge. At a=-1/2, all scattering amplitudes vanish and there is no open string excitation in the gauge fixed theory. These results support the conjecture that the universal solution can be regarded as pure gauge or the tachyon vacuum solution.Comment: 23 pages, LaTeX with PTPTeX.cls, 1 eps figure. minor corrections, published versio

Two dimensional black-hole as a topological coset model of c=1 string theory

We show that a special superconformal coset (with $\hat c =3$) is equivalent to $c=1$ matter coupled to two dimensional gravity. This identification allows a direct computation of the correlation functions of the $c=1$ non-critical string to all genus, and at nonzero cosmological constant, directly from the continuum approach. The results agree with those of the matrix model. Moreover we connect our coset with a twisted version of a Euclidean two dimensional black hole, in which the ghost and matter systems are mixed.Comment: 51 pages. Appendix by E. Frenke

(In)commensurability, scaling and multiplicity of friction in nanocrystals and application to gold nanocrystals on graphite

The scaling of friction with the contact size $A$ and (in)commensurabilty of nanoscopic and mesoscopic crystals on a regular substrate are investigated analytically for triangular nanocrystals on hexagonal substrates. The crystals are assumed to be stiff, but not completely rigid. Commensurate and incommensurate configurations are identified systematically. It is shown that three distinct friction branches coexist, an incommensurate one that does not scale with the contact size ($A^0$) and two commensurate ones which scale differently (with $A^{1/2}$ and $A$) and are associated with various combinations of commensurate and incommensurate lattice parameters and orientations. This coexistence is a direct consequence of the two-dimensional nature of the contact layer, and such multiplicity exists in all geometries consisting of regular lattices. To demonstrate this, the procedure is repeated for rectangular geometry. The scaling of irregularly shaped crystals is also considered, and again three branches are found ($A^{1/4}, A^{3/4}, A$). Based on the scaling properties, a quantity is defined which can be used to classify commensurability in infinite as well as finite contacts. Finally, the consequences for friction experiments on gold nanocrystals on graphite are discussed

Devil's staircase of incompressible electron states in a nanotube

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

The static effective action for non-commutative QED at high temperature

In this paper, we systematically study the effective action for non-commutative QED in the static limit at high temperature. When $\theta p^{2}\ll 1$, where $\theta$ represents the magnitude of the parameter for non-commutativity and $p$ denotes a typical external three momentum, we show that this leads naturally to a derivative expansion in this model. The study of the self-energy, in this limit, leads to nontrivial $\theta$ dependent corrections to the electric and magnetic masses, which exist only above a certain critical temperature. The three point and the four point amplitudes are also studied as well as their relations to the Ward identities in this limit. We determine the closed form expression for the current involving only the spatial components of the gauge field and present the corresponding static effective action, which is gauge invariant.Comment: 13 pages and 4 figures. Revised version to be published in Phys. Rev.

Reaction rate calculation by parallel path swapping

The efficiency of path sampling simulations can be improved considerably using the approach of path swapping. For this purpose, we have devised a new algorithmic procedure based on the transition interface sampling technique. In the same spirit of parallel tempering, paths between different ensembles are swapped, but the role of temperature is here played by the interface position. We have tested the method on the denaturation transition of DNA using the Peyrard-Bishop-Dauxois model. We find that the new algorithm gives a reduction of the computational cost by a factor 20.Comment: 5 pages, 3 figure

Non-linear electromagnetic interactions in thermal QED

We examine the behavior of the non-linear interactions between electromagnetic fields at high temperature. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T tends to infinity. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.Comment: 7 pages, IFUSP/P-111

Forward Flux Sampling-type schemes for simulating rare events: Efficiency analysis

We analyse the efficiency of several simulation methods which we have recently proposed for calculating rate constants for rare events in stochastic dynamical systems, in or out of equilibrium. We derive analytical expressions for the computational cost of using these methods, and for the statistical error in the final estimate of the rate constant, for a given computational cost. These expressions can be used to determine which method to use for a given problem, to optimize the choice of parameters, and to evaluate the significance of the results obtained. We apply the expressions to the two-dimensional non-equilibrium rare event problem proposed by Maier and Stein. For this problem, our analysis gives accurate quantitative predictions for the computational efficiency of the three methods.Comment: 19 pages, 13 figure

Dynamical transitions in incommensurate systems

In the dynamics of the undamped Frenkel-Kontorova model with kinetic terms, we find a transition between two regimes, a floating incommensurate and a pinned incommensurate phase. This behavior is compared to the static version of the model. A remarkable difference is that, while in the static case the two regimes are separated by a single transition (the Aubry transition), in the dynamical case the transition is characterized by a critical region, in which different phenomena take place at different times. In this paper, the generalized angular momentum we have previously introduced, and the dynamical modulation function are used to begin a characterization of this critical region. We further elucidate the relation between these two quantities, and present preliminary results about the order of the dynamical transition.Comment: 7 pages, 6 figures, file 'epl.cls' necessary for compilation provided; subm. to Europhysics Letter