Exact corrections for finite-time drift and diffusion coefficients

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on It\^o-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.Comment: 18 pages, 5 figure

Visualizing the Doppler Effect

The development of Information and Communication Technologies suggests some spectacular changes in the methods used for teaching scientific subjects. Nowadays, the development of software and hardware makes it possible to simulate processes as close to reality as we want. However, when we are trying to explain some complex physical processes, it is better to simplify the problem under study using simplified pictures of the total process by eliminating some elements that make it difficult to understand this process. In this work we focus our attention on the Doppler effect which requires the space-time visualization that is very difficult to obtain using the traditional teaching resources. We have designed digital simulations as a complement of the theoretical explanation in order to help students understand this phenomenon.Comment: 16 pages, 8 figure

Strong coupling corrections in quantum thermodynamics

Quantum systems strongly coupled to many-body systems equilibrate to the reduced state of a global thermal state, deviating from the local thermal state of the system as it occurs in the weak-coupling limit. Taking this insight as a starting point, we study the thermodynamics of systems strongly coupled to thermal baths. First, we provide strong-coupling corrections to the second law applicable to general systems in three of its different readings: As a statement of maximal extractable work, on heat dissipation, and bound to the Carnot efficiency. These corrections become relevant for small quantum systems and always vanish in first order in the interaction strength. We then move to the question of power of heat engines, obtaining a bound on the power enhancement due to strong coupling. Our results are exemplified on the paradigmatic situation of non-Markovian quantum Brownian motion.Comment: 20 pages, 3 figures, version two is substantially revised and contains new result

Work and entropy production in generalised Gibbs ensembles

Recent years have seen an enormously revived interest in the study of thermodynamic notions in the quantum regime. This applies both to the study of notions of work extraction in thermal machines in the quantum regime, as well as to questions of equilibration and thermalisation of interacting quantum many-body systems as such. In this work we bring together these two lines of research by studying work extraction in a closed system that undergoes a sequence of quenches and equilibration steps concomitant with free evolutions. In this way, we incorporate an important insight from the study of the dynamics of quantum many body systems: the evolution of closed systems is expected to be well described, for relevant observables and most times, by a suitable equilibrium state. We will consider three kinds of equilibration, namely to (i) the time averaged state, (ii) the Gibbs ensemble and (iii) the generalised Gibbs ensemble (GGE), reflecting further constants of motion in integrable models. For each effective description, we investigate notions of entropy production, the validity of the minimal work principle and properties of optimal work extraction protocols. While we keep the discussion general, much room is dedicated to the discussion of paradigmatic non-interacting fermionic quantum many-body systems, for which we identify significant differences with respect to the role of the minimal work principle. Our work not only has implications for experiments with cold atoms, but also can be viewed as suggesting a mindset for quantum thermodynamics where the role of the external heat baths is instead played by the system itself, with its internal degrees of freedom bringing coarse-grained observables to equilibrium.Comment: 22 pages, 4 figures, improvements in presentatio

Hole-Pairs in a Spin Liquid: Influence of Electrostatic Hole-Hole Repulsion

The stability of hole bound states in the t-J model including short-range Coulomb interactions is analyzed using computational techniques on ladders with up to $2 \times 30$ sites. For a nearest-neighbors (NN) hole-hole repulsion, the two-holes bound state is surprisingly robust and breaks only when the repulsion is several times the exchange $J$. At $\sim 10$ hole doping the pairs break only for a NN-repulsion as large as $V \sim 4J$. Pair-pair correlations remain robust in the regime of hole binding. The results support electronic hole-pairing mechanisms on ladders based on holes moving in spin-liquid backgrounds. Implications in two dimensions are also presented. The need for better estimations of the range and strength of the Coulomb interaction in copper-oxides is remarked.Comment: Revised version with new figures. 4 pages, 5 figure

Evolution of the Spin Gap Upon Doping a 2-Leg Ladder

The evolution of the spin gap of a 2-leg ladder upon doping depends upon the nature of the lowest triplet excitations in a ladder with two holes. Here we study this evolution using various numerical techniques for a t-t'-J ladder as the next-near-neighbor hopping t' is varied. We find that depending on the value of t', the spin gap can evolve continuously or discontinuously and the lowest triplet state can correspond to a magnon, a bound magnon-hole-pair, or two separate quasi-particles. Previous experimental results on the superconducting two-leg ladder Sr12Ca2Cu24O41 are discussed.Comment: 4 pages, latex, submitted to PR

Optical conductivity of the Hubbard model at finite temperature

The optical conductivity, $\sigma(\omega)$, of the two dimensional one-band Hubbard model is calculated at finite temperature using exact diagonalization techniques on finite clusters. The in-plane d.c. resistivity, $\rho_{ab}$, is also evaluated. We find that at large U/t and temperature T, $\rho_{ab}$ is approximately linear with temperature, in reasonable agreement with experiments on high-T$_c$ superconductors. Moreover, we note that $\sigma(\omega)$ displays charge excitations, a mid-infrared (MIR) band and a Drude peak, also as observed experimentally. The combination of the Drude peak and the MIR oscillator strengths leads to a conductivity that decays slower than $1/\omega^2$ at energies smaller than the insulator gap near half-filling.Comment: 12 pages, 3 figures appended, Revtex version 2.0, preprin

On the uniqueness of the surface sources of evoked potentials

The uniqueness of a surface density of sources localized inside a spatial region $R$ and producing a given electric potential distribution in its boundary $B_0$ is revisited. The situation in which $R$ is filled with various metallic subregions, each one having a definite constant value for the electric conductivity is considered. It is argued that the knowledge of the potential in all $B_0$ fully determines the surface density of sources over a wide class of surfaces supporting them. The class can be defined as a union of an arbitrary but finite number of open or closed surfaces. The only restriction upon them is that no one of the closed surfaces contains inside it another (nesting) of the closed or open surfaces.Comment: 16 pages, 5 figure

Diagonalization in Reduced Hilbert Spaces using a Systematically Improved Basis: Application to Spin Dynamics in Lightly Doped Ladders

A method is proposed to improve the accuracy of approximate techniques for strongly correlated electrons that use reduced Hilbert spaces. As a first step, the method involves a change of basis that incorporates exactly part of the short distance interactions. The Hamiltonian is rewritten in new variables that better represent the physics of the problem under study. A Hilbert space expansion performed in the new basis follows. The method is successfully tested using both the Heisenberg model and the $t-J$ model with holes on 2-leg ladders and chains, including estimations for ground state energies, static correlations, and spectra of excited states. An important feature of this technique is its ability to calculate dynamical responses on clusters larger than those that can be studied using Exact Diagonalization. The method is applied to the analysis of the dynamical spin structure factor $S(q,\omega)$ on clusters with $2 \times 16$ sites and 0 and 2 holes. Our results confirm previous studies (M. Troyer, H. Tsunetsugu, and T. M. Rice, Phys. Rev. $B 53$, 251 (1996)) which suggested that the state of the lowest energy in the spin-1 2-holes subspace corresponds to the bound state of a hole pair and a spin-triplet. Implications of this result for neutron scattering experiments both on ladders and planes are discussed.Comment: 9 pages, 8 figures, Revtex + psfig; changed conten