Multi-point local height probabilities of the CSOS model within the algebraic Bethe Ansatz framework

We study the local height probabilities of the exactly solvable cyclic solid-on-solid model within the algebraic Bethe Ansatz framework. We more specifically consider multi-point local height probabilities at adjacent sites on the lattice. We derive multiple integral representations for these quantities at the thermodynamic limit, starting from finite-size expressions for the corresponding multi-point matrix elements in the Bethe basis as sums of determinants of elliptic functions.Comment: 39 page

Antiperiodic dynamical 6-vertex model by separation of variables II: Functional equations and form factors

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are completely characterized by a system of discrete equations. We prove the existence of different reformulations of this characterization in terms of functional equations of Baxter's type. We notably consider the homogeneous functional $T$-$Q$ equation which is the continuous analog of the aforementioned discrete system and show, in the case of a model with an even number of sites, that the complete spectrum and eigenstates of the antiperiodic transfer matrix can equivalently be described in terms of a particular class of its $Q$-solutions, hence leading to a complete system of Bethe equations. Finally, we compute the form factors of local operators for which we obtain determinant representations in finite volume.Comment: 52 page

Modified quasilinearization method for solving nonlinear equations

Modified quasilinearization algorithm for solving nonlinear equation

Modelling financial markets by the multiplicative sequence of trades

We introduce the stochastic multiplicative point process modelling trading activity of financial markets. Such a model system exhibits power-law spectral density S(f) ~ 1/f**beta, scaled as power of frequency for various values of beta between 0.5 and 2. Furthermore, we analyze the relation between the power-law autocorrelations and the origin of the power-law probability distribution of the trading activity. The model reproduces the spectral properties of trading activity and explains the mechanism of power-law distribution in real markets.Comment: 6 pages, 2 figure

Shock-waves and commutation speed of memristors

Progress of silicon based technology is nearing its physical limit, as minimum feature size of components is reaching a mere 10 nm. The resistive switching behaviour of transition metal oxides and the associated memristor device is emerging as a competitive technology for next generation electronics. Significant progress has already been made in the past decade and devices are beginning to hit the market; however, it has been mainly the result of empirical trial and error. Hence, gaining theoretical insight is of essence. In the present work we report the striking result of a connection between the resistive switching and {\em shock wave} formation, a classic topic of non-linear dynamics. We argue that the profile of oxygen vacancies that migrate during the commutation forms a shock wave that propagates through a highly resistive region of the device. We validate the scenario by means of model simulations and experiments in a manganese-oxide based memristor device. The shock wave scenario brings unprecedented physical insight and enables to rationalize the process of oxygen-vacancy-driven resistive change with direct implications for a key technological aspect -- the commutation speed.Comment: Featured in Physics Synopsis: "Waves that Shock Resistance" (Mar. 15, 2016). http://physics.aps.org/synopsis-for/10.1103/PhysRevX.6.01102

Different steady states for spin currents in noncollinear multilayers

We find there are at least two different steady states for transport across noncollinear magnetic multilayers. In the conventional one there is a discontinuity in the spin current across the interfaces which has been identified as the source of current induced magnetic reversal; in the one advocated herein the spin torque arises from the spin accumulation transverse to the magnetization of a magnetic layer. These two states have quite different attributes which should be discerned by current experiments.Comment: 8 pages, no figure. Accepted for publication in Journal of Physics: Condensed Matte

Lorentz Transformation from Symmetry of Reference Principle

The Lorentz Transformation is traditionally derived requiring the Principle of Relativity and light-speed universality. While the latter can be relaxed, the Principle of Relativity is seen as core to the transformation. The present letter relaxes both statements to the weaker, Symmetry of Reference Principle. Thus the resulting Lorentz transformation and its consequences (time dilatation, length contraction) are, in turn, effects of how we manage space and time.Comment: 2 page