The evolution of markets and the revolution of industry : a quantitative model of England’s development, 1300-2000

This paper argues that an economy's transition from Malthusian stagnation to modern growth requires markets to reach a critical size, and competition to reach a critical level of intensity. By allowing an economy to produce a greater variety of goods, a larger market makes goods more substitutable, raising the price elasticity of demand, and lowering mark-ups. Firms must then become larger to break even, which facilitates amortizing the fixed costs of innovation. We demonstrate our theory in a dynamic general equilibrium model calibrated to England's long-run development and explore how various factors affect the timing of takeoff.European Community's Seventh Framework ProgramFinancial aid from the European Commission (EFIGE Grant 225343 and HI-POD Grant 225551), the Comunidad de Madrid (PROCIUDAD-CM), and the Spanish Ministry of Science (ECO2008-01300) is acknowledged

Freed by interaction kinetic states in the Harper model

We study the problem of two interacting particles in a one-dimensional quasiperiodic lattice of the Harper model. We show that a short or long range interaction between particles leads to emergence of delocalized pairs in the non-interacting localized phase. The properties of these Freed by Interaction Kinetic States (FIKS) are analyzed numerically including the advanced Arnoldi method. We find that the number of sites populated by FIKS pairs grows algebraically with the system size with the maximal exponent $b=1$, up to a largest lattice size $N=10946$ reached in our numerical simulations, thus corresponding to a complete delocalization of pairs. For delocalized FIKS pairs the spectral properties of such quasiperiodic operators represent a deep mathematical problem. We argue that FIKS pairs can be detected in the framework of recent cold atom experiments [M.~Schreiber {\it et al.} Science {\bf 349}, 842 (2015)] by a simple setup modification. We also discuss possible implications of FIKS pairs for electron transport in the regime of charge-density wave and high $T_c$ superconductivity.Comment: 26 pages, 21 pdf and png figures, additional data and high quality figures are available at http://www.quantware.ups-tlse.fr/QWLIB/fikspairs/ , parts of sections 2 and 3 moved to appendices, manuscript accepted for EPJ

Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole

We study the dynamical decoherence of a qubit weakly coupled to a two-body random interaction model (TBRIM) describing a quantum dot of interacting fermions or the Sachdev-Ye-Kitaev (SYK) black hole model. We determine the rates of qubit relaxation and dephasing for regimes of dynamical thermalization of the quantum dot or of quantum chaos in the SYK model. These rates are found to correspond to the Fermi golden rule and quantum Zeno regimes depending on the qubit-fermion coupling strength. An unusual regime is found where these rates are practically independent of TBRIM parameters. We push forward an analogy between TBRIM and quantum small-world networks with an explosive spreading over exponentially large number of states in a finite time being similar to six degrees of separation in small-world social networks. We find that the SYK model has approximately two-three degrees of separation.Comment: 17 pages, 15 pdf-figure

Poincar\'e recurrences and Ulam method for the Chirikov standard map

We study numerically the statistics of Poincar\'e recurrences for the Chirikov standard map and the separatrix map at parameters with a critical golden invariant curve. The properties of recurrences are analyzed with the help of a generalized Ulam method. This method allows to construct the corresponding Ulam matrix whose spectrum and eigenstates are analyzed by the powerful Arnoldi method. We also develop a new survival Monte Carlo method which allows us to study recurrences on times changing by ten orders of magnitude. We show that the recurrences at long times are determined by trajectory sticking in a vicinity of the critical golden curve and secondary resonance structures. The values of Poincar\'e exponents of recurrences are determined for the two maps studied. We also discuss the localization properties of eigenstates of the Ulam matrix and their relation with the Poincar\'e recurrences.Comment: 11 pages, 14 figures, high resolution figures and video mpeg files available at: http://www.quantware.ups-tlse.fr/QWLIB/ulammethod

The Evolution of Markets and the Revolution of Industry: A Unified Theory of Growth

This paper puts forth a unified theory of growth that captures a number of relevant features of countries transitions from stagnant, predominantly rural economies to vibrant, industrialized economies that have been overlooked by the literature. In our theory, increasing variety of consumer goods and increasing firm size, which are the consequence of a gradual expansion in the market, sow the seeds for process innovation and an economy’s take-off. We demonstrate this mechanism in a dynamic general equilibrium model calibrated to England’s long-run development, and explore how various factors affected the timing of its take-off.Uni�ed Growth Theory, Industrial Revolution, Innovation, Competition, Market Revolution

Bigger is better: Market size, demand elasticity and innovation

This paper proposes a novel mechanism whereby larger markets increase competition and facilitate process innovation. Larger markets, in the sense of more people or more open trade, support a larger variety of goods, resulting in a more crowded product space. This raises the price elasticity of demand and lowers mark-ups. Firms, therefore, become larger to break even. This facilitates process innovation as larger firms can amortize R&D costs over more goods. We demonstrate this mechanism in a standard model of process and product innovation. In doing so, we question some important results in the new trade and endogenous growth literatures.trade; population; price elasticity; competition; innovation; firm-size; scale effects; Dixit-Stiglitz; Hotelling