Spectral Equivalence of Bosons and Fermions in One-Dimensional Harmonic Potentials

Recently, Schmidt and Schnack (cond-mat/9803151, cond-mat/9810036), following earlier references, reiterate that the specific heat of N non-interacting bosons in a one-dimensional harmonic well equals that of N fermions in the same potential. We show that this peculiar relationship between specific heats results from a more dramatic equivalence between bose and fermi systems. Namely, we prove that the excitation spectrums of such bose and fermi systems are spectrally equivalent. Two complementary proofs are provided, one based on an analysis of the dynamical symmetry group of the N-body system, the other using combinatoric analysis.Comment: Six Pages, No Figures, Submitted to Phys. Rev.

Digging into Lipid Membrane Permeation for Cardiac Ion Channel Blocker d-Sotalol with All-Atom Simulations.

Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state) or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel Kv11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic) and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD) simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety pharmacology, and identifies some of the challenges that lie therein

Limits to Sympathetic Evaporative Cooling of a Two-Component Fermi Gas

We find a limit cycle in a quasi-equilibrium model of evaporative cooling of a two-component fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively the \beta\mu ~ 1. We speculate that one may be able to cool an atomic fermi gas further by photoassociating dimers near the bottom of the fermi sea.Comment: Submitted to Phys. Rev

Rapidly Rotating Fermi Gases

We show that the density profile of a Fermi gas in rapidly rotating potential will develop prominent features reflecting the underlying Landau level like energy spectrum. Depending on the aspect ratio of the trap, these features can be a sequence of ellipsoidal volumes or a sequence of quantized steps.Comment: 4 pages, 1 postscript fil

Moderating online child sexual abuse material (CSAM): Does self-regulation work, or is greater state regulation needed?

Social media platforms serve a role in the Internet age as crucial public forums connecting users around the world through a decentralised cyberspace. These platforms host high volumes of content and, as such, the role of content moderators (CMs) employed to safeguard users against harmful content like child sexual abuse material and gore is critical — however, despite how essential CMs are to the social media landscape, their work as “first responders” is complicated by legal and systemic debates over whether policing cyberspace should be left to the self-regulation of tech companies, or if greater state-regulation is required. In this scoping review, major debates in this area are identified and evaluated. This includes the issue of territorial jurisdiction, and how it obstructs traditional policing online; concerns over free speech and privacy if CMs are given greater powers; debates over whether tech companies should be legally liable for user-generated content and; the impacts (mental and professional) on the very CMs now operating as the new frontline against harmful, often traumatic, materials shared on social media. In outlining these issues, our objective is to highlight issues requiring further attention in order to best support CMs, and to enhance responses to harmful online content

Formation epochs, star formation histories and sizes of massive early-type galaxies in cluster and field environments at z=1.2: insights from the rest-frame UV

We derive stellar masses, ages and star formation histories of massive early-type galaxies in the z=1.237 RDCS1252.9-2927 cluster and compare them with those measured in a similarly mass-selected sample of field contemporaries drawn from the GOODS South Field. Robust estimates of these parameters are obtained by comparing a large grid of composite stellar population models with 8-9 band photometry in the rest-frame NUV, optical and IR, thus sampling the entire relevant domain of emission of the different stellar populations. Additionally, we present new, deep $U$-band photometry of both fields, giving access to the critical FUV rest-frame, in order to constrain empirically the dependence on the environment of the most recent star formation processes. We find that early-type galaxies, both in the cluster and in the field, show analogous optical morphologies, follow comparable mass vs. size relation, have congruent average surface stellar mass densities and lie on the same Kormendy relation. We also that a fraction of early-type galaxies in the field employ longer timescales, $\tau$, to assemble their mass than their cluster contemporaries. Hence we conclude that, while the formation epoch of early-type only depends on their mass, the environment does regulate the timescales of their star formation histories. Our deep $U$-band imaging strongly supports this conclusions. It shows that cluster galaxies are at least 0.5 mag fainter than their field contemporaries of similar mass and optical-to-infrared colors, implying that the last episode of star formation must have happened more recently in the field than in the cluster.Comment: 20pages, 10 figures. to appear on Ap

Collective Modes in a Dilute Bose-Fermi Mixture

We here study the collective excitations of a dilute spin-polarized Bose-Fermi mixture at zero temperature, considering in particular the features arising from the interaction between the two species. We show that a propagating zero-sound mode is possible for the fermions even when they do not interact among themselves.Comment: latex, 6 eps figure

Effective s- and p-Wave Contact Interactions in Trapped Degenerate Fermi Gases

The structure and stability of dilute degenerate Fermi gases trapped in an external potential is discussed with special emphasis on the influence of s- and p-wave interactions. In a first step an Effective Contact Interaction for all partial waves is derived, which reproduces the energy spectrum of the full potential within a mean-field model space. Using the s- and p-wave part the energy density of the multi-component Fermi gas is calculated in Thomas-Fermi approximation. On this basis the stability of the one- and two-component Fermi gas against mean-field induced collapse is investigated. Explicit stability conditions in terms of density and total particle number are given. For the single-component system attractive p-wave interactions limit the density of the gas. In the two-component case a subtle competition of s- and p-wave interactions occurs and gives rise to a rich variety of phenomena. A repulsive p-wave part, for example, can stabilize a two-component system that would otherwise collapse due to an attractive s-wave interaction. It is concluded that the p-wave interaction may have important influence on the structure of degenerate Fermi gases and should not be discarded from the outset.Comment: 18 pages, 11 figures (using RevTEX4