Entanglement and particle correlations of Fermi gases in harmonic traps

We investigate quantum correlations in the ground state of noninteracting Fermi gases of N particles trapped by an external space-dependent harmonic potential, in any dimension. For this purpose, we compute one-particle correlations, particle fluctuations and bipartite entanglement entropies of extended space regions, and study their large-N scaling behaviors. The half-space von Neumann entanglement entropy is computed for any dimension, obtaining S_HS = c_l N^(d-1)/d ln N, analogously to homogenous systems, with c_l=1/6, 1/(6\sqrt{2}), 1/(6\sqrt{6}) in one, two and three dimensions respectively. We show that the asymptotic large-N relation S_A\approx \pi^2 V_A/3, between the von Neumann entanglement entropy S_A and particle variance V_A of an extended space region A, holds for any subsystem A and in any dimension, analogously to homogeneous noninteracting Fermi gases.Comment: 15 pages, 22 fig

Applications of Commutator-Type Operators to pp-Groups

For a p-group G admitting an automorphism $\phi$ of order $p^n$ with exactly $p^m$ fixed points such that $\phi^{p^{n-1}}$ has exactly $p^k$ fixed points, we prove that G has a fully-invariant subgroup of m-bounded nilpotency class with $(p,n,m,k)$-bounded index in G. We also establish its analogue for Lie p-rings. The proofs make use of the theory of commutator-type operators.Comment: 11 page

Concentrations of Follicle-Stimulating Hormone Correlate with Alkaline Phosphatase and a Marker for Vitamin K Status in the Perimenopause

Serum alkaline phosphatase (ALP), a gross marker of bone turnover, has been reported to be elevated after menopause, a period characterized by hallmark increases in follicle-stimulating hormone (FSH). Whether the ALP rise coincides with the perimenopausal transition when changes in FSH, estrogen levels, and menstrual cycles are first apparent is not known. The purpose of this cross-sectional study was twofold: (1) to characterize the influence of the perimenopausal transition on ALP activity and (2) to correlate ALP activity with more precise markers for bone, osteocalcin (OC), and vitamin K status assessed with undercarboxylated osteocalcin (ucOC). Thirty-eight studies of hourly FSH were conducted on cycle day 6 of the follicular phase in perimenopausal women volunteers, aged 40-54 years (mean body mass index [BMI] = 24.2 ± 0.5). Mean FSH was used to define the perimenopausal stage (early perimenopausal, mean FSH 15 IU/L, n = 27; late perimenopausal, mean FSH > 15 IU/L, n = 11). As expected, late perimenopausal women had irregular and longer menstrual cycles, lower estradiol (E2) and estrone (E1) levels, and a lower frequency of ovulations vs. the early group. ALP was higher (76.5 ± 8.3 vs. 58.3 ± 2.7 IU/L, p = 0.045) compared with the early perimenopausal group. In a subsample (n = 10), OC was associated with ALP (r = 0.69, p 40 pg/ml (46.3% ± 6.6% vs. 22.0% ± 3.1%, p < 0.006). Clinical markers of the perimenopause are associated with a nonspecific but inexpensive marker of enhanced bone turnover (i.e., higher ALP) and correlate well with more precise markers of bone activity. These findings suggest that health-promotion strategies for preserving bone should be instituted well before the last menstrual period.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/63215/1/15246090050147709.pd

Quantum dynamics and entanglement of a 1D Fermi gas released from a trap

We investigate the entanglement properties of the nonequilibrium dynamics of one-dimensional noninteracting Fermi gases released from a trap. The gas of N particles is initially in the ground state within hard-wall or harmonic traps, then it expands after dropping the trap. We compute the time dependence of the von Neumann and Renyi entanglement entropies and the particle fluctuations of spatial intervals around the original trap, in the limit of a large number N of particles. The results for these observables apply to one-dimensional gases of impenetrable bosons as well. We identify different dynamical regimes at small and large times, depending also on the initial condition, whether it is that of a hard-wall or harmonic trap. In particular, we analytically show that the expansion from hard-wall traps is characterized by the asymptotic small-time behavior $S \approx (1/3)\ln(1/t)$ of the von Neumann entanglement entropy, and the relation $S\approx \pi^2 V/3$ where V is the particle variance, which are analogous to the equilibrium behaviors whose leading logarithms are essentially determined by the corresponding conformal field theory with central charge $c=1$. The time dependence of the entanglement entropy of extended regions during the expansion from harmonic traps shows the remarkable property that it can be expressed as a global time-dependent rescaling of the space dependence of the initial equilibrium entanglement entropy.Comment: 19 pages, 18 fig

Mod-Gaussian convergence and its applications for models of statistical mechanics

In this paper we complete our understanding of the role played by the limiting (or residue) function in the context of mod-Gaussian convergence. The question about the probabilistic interpretation of such functions was initially raised by Marc Yor. After recalling our recent result which interprets the limiting function as a measure of "breaking of symmetry" in the Gaussian approximation in the framework of general central limit theorems type results, we introduce the framework of $L^1$-mod-Gaussian convergence in which the residue function is obtained as (up to a normalizing factor) the probability density of some sequences of random variables converging in law after a change of probability measure. In particular we recover some celebrated results due to Ellis and Newman on the convergence in law of dependent random variables arising in statistical mechanics. We complete our results by giving an alternative approach to the Stein method to obtain the rate of convergence in the Ellis-Newman convergence theorem and by proving a new local limit theorem. More generally we illustrate our results with simple models from statistical mechanics.Comment: 49 pages, 21 figure

Respiratory syncytial virus infection modifies and accelerates pulmonary disease via DC activation and migration

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141386/1/jlb0005.pd

Power-law random walks

We present some new results about the distribution of a random walk whose independent steps follow a $q-$Gaussian distribution with exponent $\frac{1}{1-q}; q \in \mathbb{R}$. In the case $q>1$ we show that a stochastic representation of the point reached after $n$ steps of the walk can be expressed explicitly for all $n$. In the case $q<1,$ we show that the random walk can be interpreted as a projection of an isotropic random walk, i.e. a random walk with fixed length steps and uniformly distributed directions.Comment: 5 pages, 4 figure

Statistics of work performed on a forced quantum oscillator

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the respective probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may grossly differ. This result in particular holds also true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed

Birth and death processes and quantum spin chains

This papers underscores the intimate connection between the quantum walks generated by certain spin chain Hamiltonians and classical birth and death processes. It is observed that transition amplitudes between single excitation states of the spin chains have an expression in terms of orthogonal polynomials which is analogous to the Karlin-McGregor representation formula of the transition probability functions for classes of birth and death processes. As an application, we present a characterization of spin systems for which the probability to return to the point of origin at some time is 1 or almost 1.Comment: 14 page

Confronting the Challenge of Whale Detection from Large Vessels

As a result of a moratorium on commercial whaling, most populations of large whales are increasing across the globe. However, concurrent growth in shipping means that lethal ship-whale collisions constitute a significant threat to whale conservation efforts. This study investigates the ability of ship operators to detect and avoid whales by quantifying the predictability of whale surfacing behaviors, which are the cues used to determine whale presence. Whale avoidance is challenging because whales spend most of their time underwater and thus unavailable to be detected (the “availability process”), but must be detected at sufficiently large distances (the “detection process”) to enact an effective avoidance maneuver.  We quantified one of the main characteristics of whale behavior that governs detectability – time breaking the surface – to create a novel model of whale surfacing patterns around ships while accounting for the detection process. We then estimated the frequency with which cues go undetected (i.e. whales break the surface but ship operators are unaware of them), as well as the frequency with which whales are present but unavailable for detection (i.e. below the surface of the water). This work will enable the prediction of close ship-whale encounters given different combinations of detected and/or missed cues at varying ship speeds. It will support ship operators’ avoidance efforts by quantifying the availability and detection processes in a way that facilitates the development of whale avoidance protocols