Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page

On the current correlators in QCD at finite temperature

Current correlators in QCD at a finite temperature $T$ are considered from the viewpoint of operator product expansion. It is stressed that at low $T$ the heat bath must be represented by hadronic, and not quark-gluon states. A possibility to express the results in terms of $T$-dependent resonance masses is discussed. It is demonstrated that in order $T^2$ the masses do not move and the only phenomenon which occurs is a parity and isospin mixing.Comment: 6 pages, TPI-MINN-92/64-

Domain Walls Zoo in Supersymmetric QCD

Solving numerically the equations of motion for the effective lagrangian describing supersymmetric QCD with the SU(2) gauge group, we find a menagerie of complex domain wall solutions connecting different chirally asymmetric vacua. Some of these solutions are BPS saturated walls; they exist when the mass of the matter fields does not exceed some critical value m < m* < 4.67059... There are also sphaleron branches (saddle points of the ebergy functional). In the range m* < m < m** \approx 4.83, one of these branches becomes a local minimum (which is not a BPS saturated one). At m > m*, the complex walls disappear altogether and only the walls connecting a chirally asymmetric vacuum with the chirally symmetric one survive.Comment: 23 pages, LaTeX, 11 figure

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

The Self Model and the Conception of Biological Identity in Immunology

The self/non-self model, first proposed by F.M. Burnet, has dominated immunology for sixty years now. According to this model, any foreign element will trigger an immune reaction in an organism, whereas endogenous elements will not, in normal circumstances, induce an immune reaction. In this paper we show that the self/non-self model is no longer an appropriate explanation of experimental data in immunology, and that this inadequacy may be rooted in an excessively strong metaphysical conception of biological identity. We suggest that another hypothesis, one based on the notion of continuity, gives a better account of immune phenomena. Finally, we underscore the mapping between this metaphysical deflation from self to continuity in immunology and the philosophical debate between substantialism and empiricism about identity

Theory of Coexistence of Superconductivity and Ferroelectricity : A Dynamical Symmetry Model

We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2) \otimes h(4)$ for the composite system. We assume a minimal symmetry-allowed coupling, and simplify the hamiltonian using a double mean field approximation (DMFA). A variational coherent state (VCS) trial wave-function is used for the ground state: the energy, and the relevant order parameters for SC and FE are obtained. For positive sign of the SC-FE coupling coefficient, a non-zero value of either order parameter can suppress the other (FE polarization suppresses SC and vice versa). This gives some support to "Matthias' Conjecture" [1964], that SC and FE tend to be mutually exclusive. For such a Ferroelectric Superconductor we predict: a) the SC gap $\Delta$ (and $T_c$) will increase with increasing applied pressure when pressure quenches FE as in many ferroelectrics, and b) the FE polarization will increase with increaesing magnetic field up to $H_c$. The last result is equivalent to the prediction of a new type of Magneto-Electric Effect in a coexistent SC-FE material. Some discussion will be given of the relation of these results to the cuprate superconductors.Comment: 46 page

Dynamics of barrier penetration in thermal medium: exact result for inverted harmonic oscillator

Time evolution of quantum tunneling is studied when the tunneling system is immersed in thermal medium. We analyze in detail the behavior of the system after integrating out the environment. Exact result for the inverted harmonic oscillator of the tunneling potential is derived and the barrier penetration factor is explicitly worked out as a function of time. Quantum mechanical formula without environment is modifed both by the potential renormalization effect and by a dynamical factor which may appreciably differ from the previously obtained one in the time range of 1/(curvature at the top of potential barrier).Comment: 30 pages, LATEX file with 11 PS figure

Velocity-selective sublevel resonance of atoms with an array of current-carrying wires

Resonance transitions between the Zeeman sublevels of optically-polarized Rb atoms traveling through a spatially periodic magnetic field are investigated in a radio-frequency (rf) range of sub-MHz. The atomic motion induces the resonance when the Zeeman splitting is equal to the frequency at which the moving atoms feel the magnetic field oscillating. Additional temporal oscillation of the spatially periodic field splits a motion-induced resonance peak into two by an amount of this oscillation frequency. At higher oscillation frequencies, it is more suitable to consider that the resonance is mainly driven by the temporal field oscillation, with its velocity-dependence or Doppler shift caused by the atomic motion through the periodic field. A theoretical description of motion-induced resonance is also given, with emphasis on the translational energy change associated with the internal transition.Comment: 7 pages, 3 figures, final versio

Electroweak Phase Transitions in left-right symmetric models

We study the finite-temperature effective potential of minimal left-right symmetric models containing a bidoublet and two triplets in the scalar sector. We perform a numerical analysis of the parameter space compatible with the requirement that baryon asymmetry is not washed out by sphaleron processes after the electroweak phase transition. We find that the spectrum of scalar particles for these acceptable cases is consistent with present experimental bounds.Comment: 20 pages, 5 figures (included), some comments added, typos corrected and new references included. Final version to appear in PR

Uniform convergence of discrete curvatures from nets of curvature lines

We study discrete curvatures computed from nets of curvature lines on a given smooth surface, and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.Comment: 21 pages, 8 figure