Ground state properties of a Tonks-Girardeau Gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.Comment: 9 pages, 10 figure

Optimization of electron microscopy for human brains with long-term fixation and fixed-frozen sections.

BackgroundAbnormal connectivity across brain regions underlies many neurological disorders including multiple sclerosis, schizophrenia and autism, possibly due to atypical axonal organization within white matter. Attempts at investigating axonal organization on post-mortem human brains have been hindered by the availability of high-quality, morphologically preserved tissue, particularly for neurodevelopmental disorders such as autism. Brains are generally stored in a fixative for long periods of time (often greater than 10 years) and in many cases, already frozen and sectioned on a microtome for histology and immunohistochemistry. Here we present a method to assess the quality and quantity of axons from long-term fixed and frozen-sectioned human brain samples to demonstrate their use for electron microscopy (EM) measures of axonal ultrastructure.ResultsSix samples were collected from white matter below the superior temporal cortex of three typically developing human brains and prepared for EM analyses. Five samples were stored in fixative for over 10 years, two of which were also flash frozen and sectioned on a freezing microtome, and one additional case was fixed for 3 years and sectioned on a freezing microtome. In all six samples, ultrastructural qualitative and quantitative analyses demonstrate that myelinated axons can be identified and counted on the EM images. Although axon density differed between brains, axonal ultrastructure and density was well preserved and did not differ within cases for fixed and frozen tissue. There was no significant difference between cases in axon myelin sheath thickness (g-ratio) or axon diameter; approximately 70% of axons were in the small (0.25 μm) to medium (0.75 μm) range. Axon diameter and g-ratio were positively correlated, indicating that larger axons may have thinner myelin sheaths.ConclusionThe current study demonstrates that long term formalin fixed and frozen-sectioned human brain tissue can be used for ultrastructural analyses. Axon integrity is well preserved and can be quantified using the methods presented here. The ability to carry out EM on frozen sections allows for investigation of axonal organization in conjunction with other cellular and histological methods, such as immunohistochemistry and stereology, within the same brain and even within the same frozen cut section

Nature of Quasielectrons and the Continuum of Neutral Bulk Excitations in the Laughlin Quantum Hall Fluids

We construct model wavefunctions for a family of single-quasielectron states supported by the $\nu=1/3$ fractional quantum Hall (FQH) fluid. The charge $e^*$ = $e/3$ quasielectron state is identified as a composite of a charge-$2e^*$ quasiparticle and a $-e^*$ quasihole, orbiting around their common center of charge with relative angular momentum $n\hbar > 0$, and corresponds precisely to the "composite fermion" construction based on a filled $n=0$ Landau level plus an extra particle in level $n > 0$. An effective three-body model (one $2e^*$ quasiparticle and two $-e^*$ quasiholes) is introduced to capture the essential physics of the neutral bulk excitations.Comment: 4 pages, 3 figs, minor modifications for the published versio

Stability of tetrons

We consider the interactions in a mesonic system, referred here to as `tetron', consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally $Q_a Q_b \bar q_c \bar q_d$, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors $N_c$, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large $N_c$ limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable $b b \bar u \bar d$ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.Comment: 10 pages, 2 figure