Dynamics and Thermodynamics of the Low-Temperature Strongly Interacting Bose Gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of $^7$Li atoms by analyzing the \emph{in-situ} density distributions of trapped samples. For increasing repulsive interactions our data shows a clear departure from mean-field theory and provides a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang and Yang. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant $\xi>0.44(8)$ that would characterize the universal Bose gas at the unitary limit

Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis

Universal prethermal dynamics of Bose gases quenched to unitarity.

Understanding strongly correlated phases of matter, such as the quark-gluon plasma and neutron stars, and in particular the dynamics of such systems, for example, following a Hamiltonian quench (a sudden change in some Hamiltonian parameter, such as the strength of interparticle interactions) is a fundamental challenge in modern physics. Ultracold atomic gases are excellent quantum simulators for these problems, owing to their tunable interparticle interactions and experimentally resolvable intrinsic timescales. In particular, they provide access to the unitary regime, in which the interactions are as strong as allowed by quantum mechanics. This regime has been extensively studied in Fermi gases1,2. The less-explored unitary Bose gases3-11 offer possibilities12 such as universal physics controlled solely by the gas density13,14 and new forms of superfluidity15-17. Here, through momentum- and time-resolved studies, we explore degenerate and thermal homogeneous Bose gases quenched to unitarity. In degenerate samples, we observe universal post-quench dynamics in agreement with the emergence of a prethermal state18-24 with a universal non-zero condensed fraction22,24. In thermal gases, the dynamic and thermodynamic properties generally depend on the gas density and the temperature, but we find that they can still be expressed in terms of universal dimensionless functions. Surprisingly, we find that the total quench-induced correlation energy is independent of the gas temperature. These measurements provide quantitative benchmarks and challenges for the theory of unitary Bose gases

Mesoscopic modelling of financial markets

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investment alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model (Econ. Lett., 45, (1994), 103--111) using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupled with an equation for the price of the stock. From this model, under a suitable scaling, we derive a Fokker-Planck equation and show that the equation admits a self-similar lognormal behavior. Several numerical examples are also reported to validate our analysis.

Microscopic and kinetic models in financial markets

We review dierent microscopic and kinetic models of nancial markets which have been developed by economists, physicists and mathematicians in the last years. We rst give a summary of the microscopic models and then introduce the corresponding kinetic equations. Our selective review outlines the main ingredients of some in uential models of multi-agent dynamics in nancial markets like Levy-Levy-Solomon [24] and Lux-Marchesi [29]. The introduction of kinetic equations permits to study the asymptotic behavior of the wealth and the price distributions and to characterize the regimes of lognormal behavior and the ones with power law tails

Innovation in hospitals: a survey of the literature

Innovation, Hospitals, Survey, O3, I1,