ABSTRACT
Different attempts to describe financial markets, and stock prices in particular, with the tools of statistical mechanics can be found in the literature, although a general framework has not been achieved yet. In this paper we use the physics of many-particle systems and the typical concepts of soft matter to study two sets of US and European stocks, comprising the biggest and most stable companies in terms of stock price and trading. Upon correcting for the center-of-mass motion, the structure and dynamics of the systems are studied (in the European set, the structure is studied for the UK subset only). The pair distribution of the stocks, corrected to account for the nonuniform distribution of prices, is close to 1, indicating that there is no direct interaction between stocks, similar to an ideal gas of particles. The dynamics is studied with the mean-squared price displacement (MSPD); the price correlation function, equivalent to the intermediate scattering function; the price fluctuation distribution; and two parameters for collective motions. The MSPD grows linearly and the velocity autocorrelation function is zero, as for isolated Brownian particles. However, the intermediate scattering function follows a stretched exponential decay, the fluctuation distributions deviate from the Gaussian shape, and strong collective motions are identified. These results indicate that the dynamics is much more complex than an ideal gas of Brownian particles, and similar, to some extent, to that of undercooled systems. Finally, two physical systems are discussed to aid in the understanding of these results: a low density colloidal gel, and a dense system of ideal, infinitely thin stars. The former reproduces the dynamical properties of stocks, linear mean-squared displacement (MSD), non-Gaussian fluctuation distribution, and collective motions, but also has strong structural correlations, whereas the latter undergoes a glass transition with the structure of an ideal gas, but the MSD has the typical two-step growth of undercooled systems.
ABSTRACT
We synthesize and characterize pH-responsive hybrid nanocomposites with SERS and drug loading applications. This colloidal system is structured by spherical 50â¯nm Au cores individually coated by a pH-sensitive shell of poly4-vinylpyridine (Au@p4VP). The synthesis of these hybrid nanocomposites is performed in two steps, a first one involves the fabrication of vinyl-functionalized Au nanoparticles, and a second one includes the controlled overgrowth of a p4VP shell by free radical polymerization. As a result, Au@p4VP hybrid systems with a mean diameter ranging from 150 to 57â¯nm are obtained upon varying the monomer concentration at synthesis. Au@p4VP nanocomposite exhibits pH-response capabilities, confirmed by cryo-TEM analysis, Small Angle X-ray Scattering (SAXS) and Zeta Potential (ZP) measurements at different pH conditions. The Au@p4VP particles also display a controllable swelling response, which depends on the cross-linker density within the polymer. This swelling capability is analyzed by Dynamic Light Scattering (DLS), and UV-vis spectroscopy at different pHs. The pH-responsive capability is here exploited for the chemical entrapment of doxorubicin hydrochloride (Dox) into the polymer network. The presence of this molecule is resolved by Surface Enhanced Raman Spectroscopy (SERS) measurements. The entrapment efficiency of Dox by the Au@p4VP system is determined via NMR spectroscopy of the supernatants.
