Dimensionality of Local Minimizers of the Interaction Energy

In this work we consider local minimizers (in the topology of transport distances) of the interaction energy associated to a repulsive-attractive potential. We show how the imensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin.Comment: 27 page

Nonlocal interactions by repulsive-attractive potentials: radial ins/stability

In this paper, we investigate nonlocal interaction equations with repulsive-attractive radial potentials. Such equations describe the evolution of a continuum density of particles in which they repulse each other in the short range and attract each other in the long range. We prove that under some conditions on the potential, radially symmetric solutions converge exponentially fast in some transport distance toward a spherical shell stationary state. Otherwise we prove that it is not possible for a radially symmetric solution to converge weakly toward the spherical shell stationary state. We also investigate under which condition it is possible for a non-radially symmetric solution to converge toward a singular stationary state supported on a general hypersurface. Finally we provide a detailed analysis of the specific case of the repulsive-attractive power law potential as well as numerical results. We point out the the conditions of radial ins/stability are sharp.Comment: 42 pages, 7 figure

Alien Registration- Belisle, Raoul G. (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/29991/thumbnail.jp

Dressed Polyakov loop and phase diagram of hot quark matter under magnetic field

We evaluate the dressed Polyakov loop for hot quark matter in strong magnetic field. To compute the finite temperature effective potential, we use the Polyakov extended Nambu-Jona Lasinio model with eight-quark interactions taken into account. The bare quark mass is adjusted in order to reproduce the physical value of the vacuum pion mass. Our results show that the dressed Polyakov loop is very sensitive to the strenght of the magnetic field, and it is capable to capture both the deconfinement crossover and the chiral crossover. Besides, we compute self-consistently the phase diagram of the model. We find a tiny split of the two aforementioned crossovers as the strength of the magnetic field is increased. Concretely, for the largest value of magnetic field investigated here, $eB=19 m_\pi^2$, the split is of the order of $10\%$. A qualitative comparison with other effective models and recent Lattice results is also performed.Comment: 10 pages, 3 figures, RevTeX4-1 styl

Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature

We study the effect of site occupation on the description of quantum spin systems at finite temperature and mean-field level. We impose each lattice site to be occupied by a single electron. This is realized by means of a specific prescription. The outcome of the prescription is compared to the result obtained by means of a projection procedure which fixes the site occupation to one particle per site on an average. The comparison is performed for different representations of the Hamiltonian in Fock space leading to different types of mean-field solutions. The behaviour of order parameters is analyzed for each choice of the mean-field and constraint which fixes the occupation rate at each site. Sizable quantitative differences between the outcomes obtained with the two different constraints are observed.Comment: 18 pages, 2 figure

Chiral magnetic effect in the PNJL model

We study the two-flavor Nambu--Jona-Lasinio model with the Polyakov loop (PNJL model) in the presence of a strong magnetic field and a chiral chemical potential $\mu_5$ which mimics the effect of imbalanced chirality due to QCD instanton and/or sphaleron transitions. Firstly we focus on the properties of chiral symmetry breaking and deconfinement crossover under the strong magnetic field. Then we discuss the role of $\mu_5$ on the phase structure. Finally the chirality charge, electric current, and their susceptibility, which are relevant to the Chiral Magnetic Effect, are computed in the model.Comment: Some reference added. Minor revisions. One figure added. To appear on Phys. Rev.

Chiral symmetry restoration in (2+1)-dimensional QEDQED with a Maxwell-Chern-Simons term at finite temperature

We study the role played by a Chern-Simons contribution to the action in the $QED_3$ formulation of a two-dimensional Heisenberg model of quantum spin systems with a strictly fixed site occupation at finite temperature. We show how this contribution affects the screening of the potential which acts between spinons and contributes to the restoration of chiral symmetry in the spinon sector. The constant which characterizes the Chern-Simons term can be related to the critical temperature $T_c$ above which the dynamical mass goes to zero.Comment: 8 pages, 4 figure

Chiral magnetic effect in the PNJL model

We study the two-flavor Nambu--Jona-Lasinio model with the Polyakov loop (PNJL model) in the presence of a strong magnetic field and a chiral chemical potential $\mu_5$ which mimics the effect of imbalanced chirality due to QCD instanton and/or sphaleron transitions. Firstly we focus on the properties of chiral symmetry breaking and deconfinement crossover under the strong magnetic field. Then we discuss the role of $\mu_5$ on the phase structure. Finally the chirality charge, electric current, and their susceptibility, which are relevant to the Chiral Magnetic Effect, are computed in the model.Comment: Some reference added. Minor revisions. One figure added. To appear on Phys. Rev.

A compact fluorescence and polarization near-field scanning optical microscope

We present a transmission, fluorescence, and polarization near-field scanning optical microscope with shear-force feedback control that is small in size and simple to operate. This microscope features an ultrafine mechanical tip/sample approach with continuous manual submicron control over a range of several millimeters. The piezo-driven 12 μm x-yx-y scan range is complimented by a 4 mm coarse mechanical translation range in each direction. The construction materials used in the mechanical feedback loop have been carefully chosen for thermal compatibility in order to reduce differential expansion and contraction between the tip and sample. A unique pressure-fit sample mount allows for quick and reliable sample exchange. Shear-force feedback light is delivered to the scan head via an optical fiber so that a remote laser of any type may be used as a source. This dither light is collimated and refocused onto the tip, delivering a consistently small spot which is collected by a high numerical aperture objective. This new scan head incorporates an optical system which will permit the linearization of scan piezo response similar to a scheme used successfully with atomic force microscopy. This is designed to both overcome the piezo’s inherent hysteresis and to eliminate drift during long duration spatial scans or spectroscopic measurements at a single location. The scan head design offers added flexibility due to the use of optical fibers to deliver the dither and scan linearization light, and functions in any orientation for use in conjunction with upright or inverted optical microscopes. © 1998 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70291/2/RSINAK-69-7-2685-1.pd