Condensation in ideal Fermi gases

I investigate the possibility of condensation in ideal Fermi systems of general single particle density of states. For this I calculate the probability $w_{N_0}$ of having exactly $N_0$ particles in the condensate and analyze its maxima. The existence of such maxima at macroscopic values of $N_0$ indicates a condensate. An interesting situation occurs for example in 1D systems, where $w_{N_0}$ may have two maxima. One is at $N_0=0$ and another one may exist at finite $N_0$ (for temperatures bellow a certain condensation temperature). This suggests the existence of a first order phase transition. % The calculation of $w_{N_0}$ allows for the exploration of ensemble equivalence of Fermi systems from a new perspective.Comment: 8 pages with 1 figure. Will appear in J. Phys. A: Math. Gen. Changes (minor): I updated Ref. [9] and its citation in the text. I introduced citation for figure 1 in the tex

Dimensionality effects in restricted bosonic and fermionic systems

The phenomenon of Bose-like condensation, the continuous change of the dimensionality of the particle distribution as a consequence of freezing out of one or more degrees of freedom in the low particle density limit, is investigated theoretically in the case of closed systems of massive bosons and fermions, described by general single-particle hamiltonians. This phenomenon is similar for both types of particles and, for some energy spectra, exhibits features specific to multiple-step Bose-Einstein condensation, for instance the appearance of maxima in the specific heat. In the case of fermions, as the particle density increases, another phenomenon is also observed. For certain types of single particle hamiltonians, the specific heat is approaching asymptotically a divergent behavior at zero temperature, as the Fermi energy $\epsilon_{\rm F}$ is converging towards any value from an infinite discrete set of energies: ${\epsilon_i}_{i\ge 1}$. If $\epsilon_{\rm F}=\epsilon_i$, for any i, the specific heat is divergent at T=0 just in infinite systems, whereas for any finite system the specific heat approaches zero at low enough temperatures. The results are particularized for particles trapped inside parallelepipedic boxes and harmonic potentials. PACS numbers: 05.30.Ch, 64.90.+b, 05.30.Fk, 05.30.JpComment: 7 pages, 3 figures (included

Scattering of slow-light gap solitons with charges in a two-level medium

The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at the very origin of nonlinearity. The resulting nonlinear coupling possesses particularly interesting consequences at the resonance (when the frequency of the excitation is close to the transition frequency of the two-level medium) as e.g. slow-light gap solitons that result from the nonlinear instability of the evanescent wave at the boundary. As nonlinearity couples the different polarizations of the electromagnetic field, the slow-light gap soliton is shown to experience effective scattering whith charges in the medium, allowing it for instance to be trapped or reflected. This scattering process is understood qualitatively as being governed by a nonlinear Schroedinger model in an external potential related to the charges (the electrostatic permanent background component of the field).Comment: RevTex, 14 pages with 5 figures, to appear in J. Phys. A: Math. Theo

Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network

We focus on the heterogeneity of social networks and its role to the emergence of prevailing cooperation and sustaining cooperators. The social networks are representative of the interaction relationships between players and their encounters in each round of games. We study an evolutionary Prisoner's Dilemma game on a variant of Watts-Strogatz small-world network, whose heterogeneity can be tuned by a parameter. It is found that optimal cooperation level exists at some intermediate topological heterogeneity for different temptations to defect. Moreover, neither the most heterogeneous case nor the most homogeneous one would favor the cooperators. At intermediate heterogeneity in degree sequences, cooperators could resist the invasion of defectors for large temptation to defect.Comment: Updated versio

Integer Partitions and Exclusion Statistics

We provide a combinatorial description of exclusion statistics in terms of minimal difference $p$ partitions. We compute the probability distribution of the number of parts in a random minimal $p$ partition. It is shown that the bosonic point $p=0$ is a repulsive fixed point for which the limiting distribution has a Gumbel form. For all positive $p$ the distribution is shown to be Gaussian.Comment: 16 pages, 4 .eps figures include

Expression of Interest: The Atmospheric Neutrino Neutron Interaction Experiment (ANNIE)

Submitted for the January 2014 Fermilab Physics Advisory Committee meetingSubmitted for the January 2014 Fermilab Physics Advisory Committee meetingSubmitted for the January 2014 Fermilab Physics Advisory Committee meetingSubmitted for the January 2014 Fermilab Physics Advisory Committee meetingNeutron tagging in Gadolinium-doped water may play a significant role in reducing backgrounds from atmospheric neutrinos in next generation proton-decay searches using megaton-scale Water Cherenkov detectors. Similar techniques might also be useful in the detection of supernova neutrinos. Accurate determination of neutron tagging efficiencies will require a detailed understanding of the number of neutrons produced by neutrino interactions in water as a function of momentum transferred. We propose the Atmospheric Neutrino Neutron Interaction Experiment (ANNIE), designed to measure the neutron yield of atmospheric neutrino interactions in gadolinium-doped water. An innovative aspect of the ANNIE design is the use of precision timing to localize interaction vertices in the small fiducial volume of the detector. We propose to achieve this by using early production of LAPPDs (Large Area Picosecond Photodetectors). This experiment will be a first application of these devices demonstrating their feasibility for Water Cherenkov neutrino detectors

Expression of Interest: The Atmospheric Neutrino Neutron Interaction Experiment (ANNIE)

Neutron tagging in Gadolinium-doped water may play a significant role in reducing backgrounds from atmospheric neutrinos in next generation proton-decay searches using megaton-scale Water Cherenkov detectors. Similar techniques might also be useful in the detection of supernova neutrinos. Accurate determination of neutron tagging efficiencies will require a detailed understanding of the number of neutrons produced by neutrino interactions in water as a function of momentum transferred. We propose the Atmospheric Neutrino Neutron Interaction Experiment (ANNIE), designed to measure the neutron yield of atmospheric neutrino interactions in gadolinium-doped water. An innovative aspect of the ANNIE design is the use of precision timing to localize interaction vertices in the small fiducial volume of the detector. We propose to achieve this by using early production of LAPPDs (Large Area Picosecond Photodetectors). This experiment will be a first application of these devices demonstrating their feasibility for Water Cherenkov neutrino detectors.Comment: Submitted for the January 2014 Fermilab Physics Advisory Committee meetin

Transition Metal Dopants Essential for Producing Ferromagnetism in Metal Oxide Nanoparticles

Recent claims that ferromagnetism can be produced in nanoparticles of metal oxides without the presence of transition metal dopants have been challenged in this work by investigating 62 high quality well-characterized nanoparticle samples of both undoped and Fe doped (0-10% Fe) ZnO. The undoped ZnO nanoparticles showed zero or negligible magnetization, without any dependence on the nanoparticle size. However, chemically synthesized Zn1-xFexO nanoparticles showed clear ferromagnetism, varying systematically with Fe concentration. Furthermore, the magnetic properties of Zn1-xFexO nanoparticles showed strong dependence on the reaction media used to prepare the samples. The zeta potentials of the Zn1-xFexO nanoparticles prepared using different reaction media were significantly different, indicating strong differences in the surface structure. Electron paramagnetic resonance studies indicate that the difference in the ferromagnetic properties of Zn1-xFexO nanoparticles with different surface structures originates from differences in the fraction of the doped Fe ions that participate in ferromagnetic resonance

Non-equilibrium Landauer Transport Model for Hawking radiation from a Black Hole

We propose that the Hawking radiation energy and entropy flow rates from a black hole can be viewed as a one-dimensional (1D), non-equilibrium Landauer transport process. Support for this viewpoint comes from previous calculations invoking conformal symmetry in the near-horizon region, which give radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The Landauer approach shows in a direct way the particle statistics independence of the energy and entropy fluxes of a black hole radiating into vacuum, as well as one near thermal equilibrium with its environment. As an application of the Landauer approach, we show that Hawking radiation gives a net entropy production that is 50% larger than that obtained assuming standard three-dimensional emission into vacuum.Comment: 14 pages, 2 figures, published versio