Noninteracting Fermions in infinite dimensions

Usually, we study the statistical behaviours of noninteracting Fermions in finite (mainly two and three) dimensions. For a fixed number of fermions, the average energy per fermion is calculated in two and in three dimensions and it becomes equal to 50 and 60 per cent of the fermi energy respectively. However, in the higher dimensions this percentage increases as the dimensionality increases and in infinite dimensions it becomes 100 per cent. This is an intersting result, at least pedagogically. Which implies all fermions are moving with Fermi momentum. This result is not yet discussed in standard text books of quantum statistics. In this paper, this fact is discussed and explained. I hope, this article will be helpful for graduate students to study the behaviours of free fermions in generalised dimensionality.Comment: To appear in European Journal of Physics (2010

A Model for Phase Transition based on Statistical Disassembly of Nuclei at Intermediate Energies

Consider a model of particles (nucleons) which has a two-body interaction which leads to bound composites with saturation properties. These properties are : all composites have the same density and the ground state energies of composites with k nucleons are given by -kW+\sigma k^{2/3} where W and \sigma are positive constants. W represents a volume term and \sigma a surface tension term. These values are taken from nuclear physics. We show that in the large N limit where N is the number of particles such an assembly in a large enclosure at finite temperature shows properties of liquid-gas phase transition. We do not use the two-body interaction but the gross properties of the composites only. We show that (a) the p-\rho isotherms show a region where pressure does not change as $\rho$ changes just as in Maxwell construction of a Van der Waals gas, (b) in this region the chemical potential does not change and (c) the model obeys the celebrated Clausius-Clapeyron relations. A scaling law for the yields of composites emerges. For a finite number of particles N (upto some thousands) the problem can be easily solved on a computer. This allows us to study finite particle number effects which modify phase transition effects. The model is calculationally simple. Monte-Carlo simulations are not needed.Comment: RevTex file, 21 pages, 5 figure

How Much do Heavy Quarks Thermalize in a Heavy Ion Collision?

We investigate the thermalization of charm quarks in high energy heavy ion collisions. To this end, we calculate the diffusion coefficient in the perturbative Quark Gluon Plasma and relate it to collisional energy loss and momentum broadening. We then use these transport properties to formulate a Langevin model for the evolution of the heavy quark spectrum in the hot medium. The model is strictly valid in the non-relativistic limit and for all velocities \gamma v < \alphas^{-1/2} to leading logarithm in $T/m_D$. The corresponding Fokker-Planck equation can be solved analytically for a Bjorken expansion and the solution gives a simple estimate for the medium modifications of the heavy quark spectrum as a function of the diffusion coefficient. Finally we solve the Langevin equations numerically in a hydrodynamic simulation of the heavy ion reaction. The results of this simulation are the medium modifications of the charm spectrum $R_{AA}$ and the expected elliptic flow $v_2(p_T)$ as a function of the diffusion coefficient.Comment: 34 pages, 9 figures. Inculdes a detailed comparison with Boltzmann simulation

Reciprocity relations between ordinary temperature and the Frieden-Soffer's Fisher-temperature

Frieden and Soffer conjectured some years ago the existence of a ``Fisher temperature" T_F that would play, with regards to Fisher's information measure I, the same role that the ordinary temperature T plays vis-a-vis Shannon's logarithmic measure. Here we exhibit the existence of reciprocity relations between T_F and T and provide an interpretation with reference to the meaning of T_F for the canonical ensemble.Comment: 3 pages, no figure

The role of the nature of the noise in the thermal conductance of mechanical systems

Focussing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the thermal conductance. For white noises, we prove that the L\'evy-It\^o composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a non-equilibrium linearly coupled chain, which signals the independence between mechanical and thermodynamical properties. On the other hand, for the non-linearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.Comment: 9 pages, 2 figures. To be published in Physical Review

Microcanonical Lattice Gas Model for Nuclear Disassembly

Microcanonical calculations are no more difficult to implement than canonical calculations in the Lattice Gas Model. We report calculations for a few observables where we compare microcanonical model results with canonical model results.Comment: 7 pages, Revtex, 3 postscript figure

The Nature of Radio Continuum Emission in the Dwarf Starburst Galaxy NGC 625

We present new multi-frequency radio continuum imaging of the dwarf starburst galaxy NGC 625 obtained with the Very Large Array. Data at 20, 6, and 3.6 cm reveal global continuum emission dominated by free-free emission, with only mild synchrotron components. Each of the major HII regions is detected; the individual spectral indices are thermal for the youngest regions (showing strongest H Alpha emission) and nonthermal for the oldest. We do not detect any sources that appear to be associated with deeply embedded, dense, young clusters, though we have discovered one low-luminosity, obscured source that has no luminous optical counterpart and which resides in the region of highest optical extinction. Since NGC 625 is a Wolf-Rayet galaxy with strong recent star formation, these radio properties suggest that the youngest star formation complexes have not yet evolved to the point where their thermal spectra are significantly contaminated by synchrotron emission. The nonthermal components are associated with regions of older star formation that have smaller ionized gas components. These results imply a range of ages of the HII regions and radio components that agrees with our previous resolved stellar population analysis, where an extended burst of star formation has pervaded the disk of NGC 625 over the last ~ 50 Myr. We compare the nature of radio continuum emission in selected nearby dwarf starburst and Wolf-Rayet galaxies, demonstrating that thermal radio continuum emission appears to be more common in these systems than in typical HII galaxies with less recent star formation and more evolved stellar clusters.Comment: ApJ, in press; 27 pages, 5 figures. Full-resolution version may be obtained at http://www.astro.umn.edu/~cannon/n625.vla.p

Loading of a Rb magneto-optic trap from a getter source

We study the properties of a Rb magneto-optic trap loaded from a commercial getter source which provides a large flux of atoms for the trap along with the capability of rapid turn-off necessary for obtaining long trap lifetimes. We have studied the trap loading at two different values of background pressure to determine the cross-section for Rb--N$_2$ collisions to be 3.5(4)x10^{-14} cm^2 and that for Rb--Rb collisions to be of order 3x10^{-13} cm^2. At a background pressure of 1.3x10^{-9} torr, we load more than 10^8 atoms into the trap with a time constant of 3.3 s. The 1/e lifetime of trapped atoms is 13 s limited only by background collisions.Comment: 5 pages, 5 figure

Electronic Theory for the Nonlinear Magneto-Optical Response of Transition-Metals at Surfaces and Interfaces: Dependence of the Kerr-Rotation on Polarization and on the Magnetic Easy Axis

We extend our previous study of the polarization dependence of the nonlinear optical response to the case of magnetic surfaces and buried magnetic interfaces. We calculate for the longitudinal and polar configuration the nonlinear magneto-optical Kerr rotation angle. In particular, we show which tensor elements of the susceptibilities are involved in the enhancement of the Kerr rotation in nonlinear optics for different configurations and we demonstrate by a detailed analysis how the direction of the magnetization and thus the easy axis at surfaces and buried interfaces can be determined from the polarization dependence of the nonlinear magneto-optical response, since the nonlinear Kerr rotation is sensitive to the electromagnetic field components instead of merely the intensities. We also prove from the microscopic treatment of spin-orbit coupling that there is an intrinsic phase difference of 90$^{\circ }$ between tensor elements which are even or odd under magnetization reversal in contrast to linear magneto-optics. Finally, we compare our results with several experiments on Co/Cu films and on Co/Au and Fe/Cr multilayers. We conclude that the nonlinear magneto-optical Kerr-effect determines uniquely the magnetic structure and in particular the magnetic easy axis in films and at multilayer interfaces.Comment: 23 pages Revtex, preprintstyle, 2 uuencoded figure

A study of the phase transition in the usual statistical model for nuclear multifragmentation

We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of particles. This enables us to study a phase transition in the model. A first order phase transition can be tracked down. There are significant differences between this phase transition and some other well-known cases