Lattice QCD at non-zero isospin chemical potential

Quantum chromodynamics (QCD) at non-zero isospin chemical potential is studied in a canonical approach by analyzing systems of fixed isospin number density. To construct these systems, we develop a range of new algorithms for performing the factorially large numbers of Wick contractions required in multi-hadron systems. We then use these methods to study systems with the quantum numbers of up to 72 $\pi^+$'s on three ensembles of gauge configurations with spatial extents $L\sim$ 2.0, 2.5 and 3.0 fm, and light quark masses corresponding to a pion mass of {390 MeV}. The ground state energies of these systems are extracted and the volume dependence of these energies is utilized to determine the two- and three- body interactions amongst $\pi^+$'s. The systems studied correspond to isospin densities of up to $\rho_I\sim 9\ {\rm fm}^{-3}$ and probe isospin chemical potentials, $\mu_I$, in the range m_\pi\ \lsim \mu_I\ \lsim 4.5\ m_\pi, allowing us to investigate aspects of the QCD phase diagram at low temperature and for varying isospin chemical potential. By studying the energy density of the system, we provide numerical evidence for the conjectured transition of the system to a Bose-Einstein condensed phase at \mu_I\ \gsim m_\pi.Comment: 32 pages, 22 figure

The Road to Human Emancipation - The Moral and Political Foundations of Markets

The thesis aims to provide both a real public ideology and the legal and socioeconomic structures to realize Karl Marx’s ideal of human emancipation. Marx argues that in capitalist society, the legal and political superstructure forces the ruling class to represent its interest as the public interest, which legitimizes the massive inequality in resources and social power. To demonstrate how to realize the substantive public interest, the two parts of the thesis have two goals. The first part aims to formulate a rightful candidate to the public ideology of human emancipation, which represents the substantive public interest rather than the hypocrisy of the ruling class. The second part aims to formulate the legal and socioeconomic structures of the Social Economy, which is the social system that corresponds to the public ideology and restores the equality of both resources and social power. The first part is the philosophical analysis, and the second part can be viewed as a set of proposals informed by both normative and empirical research to transform the economy and society

Anti-lecture Hall Compositions and Overpartitions

We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k-2 equals the number of overpartitions of n with non-overlined parts not congruent to $0,\pm 1$ modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two Rogers-Ramanujan type identities for overpartition which are analogous to the Rogers-Ramanjan type identities due to Andrews. When k is odd, we give an alternative proof by using a generalized Rogers-Ramanujan identity due to Andrews, a bijection of Corteel and Savage and a refined version of a bijection also due to Corteel and Savage.Comment: 16 page

The Rogers-Ramanujan-Gordon Theorem for Overpartitions

Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a function introduced by Andrews, we obtain a recurrence relation which implies that the generating function of $D_{k,i}(n)$ equals the generating function of $C_{k,i}(n)$. We also find a generating function formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.Comment: 26 page

Prediction of the Size Distributions of Methanol-Ethanol Clusters Detected in VUV Laser/Time-of-flight Mass Spectrometry

The size distributions and geometries of vapor clusters equilibrated with methanol−ethanol (Me−Et) liquid mixtures were recently studied by vacuum ultraviolet (VUV) laser time-of-flight (TOF) mass spectrometry and density functional theory (DFT) calculations (Liu, Y.; Consta, S.; Ogeer, F.; Shi, Y. J.; Lipson, R. H. Can. J. Chem. 2007, 85, 843−852). On the basis of the mass spectra recorded, it was concluded that the formation of neutral tetramers is particularly prominent. Here we develop grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) frameworks to compute cluster size distributions in vapor mixtures that allow a direct comparison with experimental mass spectra. Using the all-atom optimized potential for liquid simulations (OPLS-AA) force field, we systematically examined the neutral cluster size distributions as functions of pressure and temperature. These neutral cluster distributions were then used to derive ionized cluster distributions to compare directly with the experiments. The simulations suggest that supersaturation at 12 to 16 times the equilibrium vapor pressure at 298 K or supercooling at temperature 240 to 260 K at the equilibrium vapor pressure can lead to the relatively abundant tetramer population observed in the experiments. Our simulations capture the most distinct features observed in the experimental TOF mass spectra: Et3H+ at m/z = 139 in the vapor corresponding to 10:90% Me−Et liquid mixture and Me3H+ at m/z = 97 in the vapors corresponding to 50:50% and 90:10% Me−Et liquid mixtures. The hybrid GCMC scheme developed in this work extends the capability of studying the size distributions of neat clusters to mixed species and provides a useful tool for studying environmentally important systems such as atmospheric aerosols