Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a non-interacting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the exact particle density profiles, momentum distributions and behaviour of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C p^{-4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions "fermionize" under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.Comment: revised version; 8 pages, 7 figure

Isospin dependence of pseudospin symmetry in nuclear resonant states

The relativistic mean field theory in combination with the analytic continuation in the coupling constant method is used to determine the energies and widths of single-particle resonant states in Sn isotopes. It is shown that there exists clear shell structure in the resonant levels as appearing in the bound levels. In particular, the isospin dependence of pseudospin symmetry is clearly shown in the resonant states, is consistent with that in the bound states, where the splittings of energies and widths between pseudospin doublets are found in correlation with the quantum numbers of single-particle states, as well as the nuclear mass number. The similar phenomenon also emerges in the spin partners.Comment: 7 pages, 6 figure

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

In this paper we give an affirmative answer to an open question mentioned in [Le Bris and Lions, Comm. Partial Differential Equations 33 (2008), 1272--1317], that is, we prove the well-posedness of the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.Comment: 11 pages. The proof has been modifie

Relation between phase and dwell times for quantum tunneling of a relativistically propagating particle

The general and explicit relation between the phase time and the dwell time for quantum tunneling of a relativistically propagating particle is investigated and quantified. In analogy with previously obtained non-relativistic results, it is shown that the group delay can be described in terms of the dwell time and a self-interference delay. Lessons concerning the phenomenology of the relativistic tunneling are drawn

Novel approach to a perfect lens

Within the framework of an exact analytical solution of Maxwell equations in a space domain, it is shown that optical scheme based on a slab with negative refractive index ($n=-1$) (Veselago lens or Pendry lens) does not possess focusing properties in the usual sense . In fact, the energy in such systems does not go from object to its "image", but from object and its "image" to an intersection point inside a metamaterial layer, or vice versa. A possibility of applying this phenomenon to a creation of entangled states of two atoms is discussed.Comment: 4 pages, 6 figure

An Evolving Entropy Floor in the Intracluster Gas?

Non-gravitational processes, such as feedback from galaxies and their active nuclei, are believed to have injected excess entropy into the intracluster gas, and therefore to have modified the density profiles in galaxy clusters during their formation. Here we study a simple model for this so-called preheating scenario, and ask (i) whether it can simultaneously explain both global X-ray scaling relations and number counts of galaxy clusters, and (ii) whether the amount of entropy required evolves with redshift. We adopt a baseline entropy profile that fits recent hydrodynamic simulations, modify the hydrostatic equilibrium condition for the gas by including approx. 20% non-thermal pressure support, and add an entropy floor K_0 that is allowed to vary with redshift. We find that the observed luminosity-temperature (L-T) relations of low-redshift (z=0.05) HIFLUGCS clusters and high-redshift (z=0.8) WARPS clusters are best simultaneously reproduced with an evolving entropy floor of K_0(z)=341(1+z)^{-0.83}h^{-1/3} keV cm^2. If we restrict our analysis to the subset of bright (kT > 3 keV) clusters, we find that the evolving entropy floor can mimic a self-similar evolution in the L-T scaling relation. This degeneracy with self-similar evolution is, however, broken when (0.5 < kT < 3 keV) clusters are also included. The approx. 60% entropy increase we find from z=0.8 to z=0.05 is roughly consistent with that expected if the heating is provided by the evolving global quasar population. Using the cosmological parameters from the WMAP 3-year data with sigma_8=0.76, our best-fit model underpredicts the number counts of the X-ray galaxy clusters compared to those derived from the 158 deg^2 ROSAT PSPC survey. Treating sigma_8 as a free parameter, we find a best-fit value of sigma_8=0.80+/- 0.02.Comment: 14 emulateapj pages with 9 figures, submitted to Ap

Spin Degree of Freedom in a Two-Dimensional Electron Liquid

We have investigated correlation between spin polarization and magnetotransport in a high mobility silicon inversion layer which shows the metal-insulator transition. Increase in the resistivity in a parallel magnetic field reaches saturation at the critical field for the full polarization evaluated from an analysis of low-field Shubnikov-de Haas oscillations. By rotating the sample at various total strength of the magnetic field, we found that the normal component of the magnetic field at minima in the diagonal resistivity increases linearly with the concentration of ``spin-up'' electrons.Comment: 4 pages, RevTeX, 6 eps-figures, to appear in PR

Attentive Neural Architecture Incorporating Song Features For Music Recommendation

Recommender Systems are an integral part of music sharing platforms. Often the aim of these systems is to increase the time, the user spends on the platform and hence having a high commercial value. The systems which aim at increasing the average time a user spends on the platform often need to recommend songs which the user might want to listen to next at each point in time. This is different from recommendation systems which try to predict the item which might be of interest to the user at some point in the user lifetime but not necessarily in the very near future. Prediction of the next song the user might like requires some kind of modeling of the user interests at the given point of time. Attentive neural networks have been exploiting the sequence in which the items were selected by the user to model the implicit short-term interests of the user for the task of next item prediction, however we feel that the features of the songs occurring in the sequence could also convey some important information about the short-term user interest which only the items cannot. In this direction, we propose a novel attentive neural architecture which in addition to the sequence of items selected by the user, uses the features of these items to better learn the user short-term preferences and recommend the next song to the user.Comment: Accepted as a paper at the 12th ACM Conference on Recommender Systems (RecSys 18

The Consistent Result of Cosmological Constant From Quantum Cosmology and Inflation with Born-Infeld Scalar Field

The Quantum cosmology with Born-Infeld(B-I) type scalar field is considered. In the extreme limits of small cosmological scale factor the wave function of the universe can also be obtained by applying the methods developed by Hartle-Hawking(H-H) and Vilenkin. H-H wave function predicts that most Probable cosmological constant $\Lambda$ equals to $\frac{1}{\eta}$($\frac{1}{2\eta}$ equals to the maximum of the kinetic energy of scalar field). It is different from the original results($\Lambda=0$) in cosmological constant obtained by Hartle-Hawking. The Vilenkin wave function predicts a nucleating unverse with largest possible cosmological constant and it is larger than $1/\eta$. The conclusions have been nicely to reconcile with cosmic inflation. We investigate the inflation model with B-I type scalar field, and find that $\eta$ depends on the amplitude of tensor perturbation $\delta_h$, with the form $\frac{1}{\eta}\simeq \frac{m^2}{12\pi[(\frac{9\delta_{\Phi}^2}{N \delta_h^2})^2-1]}.$ The vacuum energy in inflation epoch depends on the tensor-to-scalar ratio $\frac{\delta_h}{\delta_{\Phi}}$. The amplitude of the tensor perturbation ${\delta_{h}}$ can, in principle, be large enough to be discovered. However, it is only on the border of detectability in future experiments. If it has been observed in future, this is very interesting to determine the vacuum energy in inflation epoch.Comment: 12 pages, one figure, references added, accepted by European Physical Journal

Manual of Water Quality Models for Virginia Estuaries

It is not the purpose of this manual to make a nonmodeler able to develop a model by reading through it, since no manual of this nature can accomplish such a task. This manual is intended to increase the planner or manager\u27s options by acquainting him with various types of models and informing him of the availability of currently working models. This manual contains the following: 1. A scheme indicating the types of water quality models which could be constructed, i.e. an overview of choices in models. 2. A brief description of each type of models developed under the Cooperative State ~gencies program. 3. A list of empirical formulas or values for the rate constants used in the models. 4. A directory of water quality models which have been applied to Virginia estuaries