Exact Calculation of the Vortex-Antivortex Interaction Energy in the Anisotropic 3D XY-model

We have developed an exact method to calculate the vortex-antivortex interaction energy in the anisotropic 3D-XY model. For this calculation, dual transformation which is already known for the 2D XY-model was extended. We found an explicit form of this interaction energy as a function of the anisotropic ratio and the separation $r$ between the vortex and antivortex located on the same layer. The form of interaction energy is $\ln r$ at the small $r$ limi t but is proportional to $r$ at the opposite limit. This form of interaction energ y is consistent with the upper bound calculation using the variational method by Cataudella and Minnhagen.Comment: REVTeX 12 pages, In print for publication in Phys. Rev.

Observed Effect of Magnetic Fields on the Propagation of Magnetoacoustic Waves in the Lower Solar Atmosphere

We study Hinode/SOT-FG observations of intensity fluctuations in Ca II H-line and G-band image sequences and their relation to simultaneous and co-spatial magnetic field measurements. We explore the G-band and H-line intensity oscillation spectra both separately and comparatively via their relative phase differences, time delays and cross-coherences. In the non-magnetic situations, both sets of fluctuations show strong oscillatory power in the 3 - 7 mHz band centered at 4.5 mHz, but this is suppressed as magnetic field increases. A relative phase analysis gives a time delay of H-line after G-band of 20\pm1 s in non-magnetic situations implying a mean effective height difference of 140 km. The maximum coherence is at 4 - 7 mHz. Under strong magnetic influence the measured delay time shrinks to 11 s with the peak coherence near 4 mHz. A second coherence maximum appears between 7.5 - 10 mHz. Investigation of the locations of this doubled-frequency coherence locates it in diffuse rings outside photospheric magnetic structures. Some possible interpretations of these results are offered.Comment: 19 pages, 6 figure

Quasi-separatrix layers and three-dimensional reconnection diagnostics for line-tied tearing modes

In three-dimensional magnetic configurations for a plasma in which no closed field line or magnetic null exists, no magnetic reconnection can occur, by the strictest definition of reconnection. A finitely long pinch with line-tied boundary conditions, in which all the magnetic field lines start at one end of the system and proceed to the opposite end, is an example of such a system. Nevertheless, for a long system of this type, the physical behavior in resistive magnetohydrodynamics (MHD) essentially involves reconnection. This has been explained in terms comparing the geometric and tearing widths [1, 2]. The concept of a quasi-separatrix layer[3, 4] was developed for such systems. In this paper we study a model for a line-tied system in which the corresponding periodic system has an unstable tearing mode. We analyze this system in terms of two magnetic field line diagnostics, the squashing factor[3-5] and the electrostatic potential difference used in kinematic reconnection studies[6, 7]. We discuss the physical and geometric significance of these two diagnostics and compare them in the context of discerning tearing-like behavior in line-tied modes. [1] G. L. Delzanno and J. M. Finn. Physics of Plasmas, 15(3):032904, 2008. [2] Y.-M. Huang and E. G. Zweibel. Physics of Plasmas, 16(4):042102, 2009. [3] E. R. Priest and P. D\'emoulin. J. Geophys. Res., 100(A12):23443-23463, 1995. [4] P. D\'emoulin, J. C. Henoux, E. R. Priest, and C. H. Mandrini. Astron. Astrophys., 308:643-655, Apr. 1996. [5] V. S. Titov and G. Hornig. Advances in Space Research, 29(7):1087-1092, 2002. [6] Y. Lau and J. M. Finn. The Astrophysical Journal, 350:672-691, Feb. 1990. [7] Y. Lau and J. M. Finn. The Astrophysical Journal, 366:577-591, 1991.Comment: 13 pages, 9 figures, Submitted to Commun Nonlinear Sci Numer Simula

Random walks and the Hagedorn transition

We study details of the approach to the Hagedorn temperature in string theory in various static spacetime backgrounds. We show that the partition function for a {\it single} string at finite temperature is the torus amplitude restricted to unit winding around Euclidean time. We use the worldsheet path integral to derive the statement that the the sum over random walks of the thermal scalar near the Hagedorn transition is precisely the image under a modular transformation of the sum over spatial configurations of a single highly excited string. We compute the radius of gyration of thermally excited strings in $AdS_D\times S^n$. We show that the winding mode indicates an instability despite the AdS curvature at large radius, and that the negative mass squared decreases with decreasing AdS radius, much like the type 0 tachyon. We add further arguments to statements by Barbon and Rabinovici, and by Adams {\it et. al.}, that the Euclidean AdS black hole can thought of as a condensate of the thermal scalar. We use this to provide circumstantial evidence that the condensation of the thermal scalar decouples closed string modes.Comment: 34 pages (7 of references), 5 figures. v2: Reference added, grant acknowledgement added, typos correcte

Flat space physics from holography

We point out that aspects of quantum mechanics can be derived from the holographic principle, using only a perturbative limit of classical general relativity. In flat space, the covariant entropy bound reduces to the Bekenstein bound. The latter does not contain Newton's constant and cannot operate via gravitational backreaction. Instead, it is protected by - and in this sense, predicts - the Heisenberg uncertainty principle.Comment: 11 pages, 3 figures; v2: minor correction

Theory of the first-order isostructural valence phase transitions in mixed valence compounds YbIn_{x}Ag_{1-x}Cu_{4}

For describing the first-order isostructural valence phase transition in mixed valence compounds we develop a new approach based on the lattice Anderson model. We take into account the Coulomb interaction between localized f and conduction band electrons and two mechanisms of electron-lattice coupling. One is related to the volume dependence of the hybridization. The other is related to local deformations produced by f- shell size fluctuations accompanying valence fluctuations. The large f -state degeneracy allows us to use the 1/N expansion method. Within the model we develop a mean-field theory for the first-order valence phase transition in YbInCu_{4}. It is shown that the Coulomb interaction enhances the exchange interaction between f and conduction band electron spins and is the driving force of the phase transition. A comparison between the theoretical calculations and experimental measurements of the valence change, susceptibility, specific heat, entropy, elastic constants and volume change in YbInCu_{4} and YbAgCu_{4} are presented, and a good quantitative agreement is found. On the basis of the model we describe the evolution from the first-order valence phase transition to the continuous transition into the heavy-fermion ground state in the series of compounds YbIn_{1-x}Ag_{x}Cu_{4}. The effect of pressure on physical properties of YbInCu_{4} is studied and the H-T phase diagram is found.Comment: 17 pages RevTeX, 9 Postscript figures, to be submitted to Phys.Rev.

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page

Field-induced magnetic transitions in the quasi-two-dimensional heavy-fermion antiferromagnets Ce_{n}RhIn_{3n+2} (n=1 or 2)

We have measured the field-dependent heat capacity in the tetragonal antiferromagnets CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$, both of which have an enhanced value of the electronic specific heat coefficient $\gamma \sim 400$ mJ/mol-Ce K$^{2}$ above $T_{N}$. For $T<T_{N},$ the specific heat data at zero applied magnetic field are consistent with the existence of an anisotropic spin-density wave opening a gap in the Fermi surface for CeRhIn$_{5},$ while Ce$_{2}$RhIn$_{8}$ shows behavior consistent with a simple antiferromagnetic magnon. From these results, the magnetic structure, in a manner similar to the crystal structure, appears more two-dimensional in CeRhIn$_{5}$ than in Ce$_{2}$RhIn$_{8}$ where only about 12% of the Fermi surface remains ungapped relative to 92% for Ce$_{2}$RhIn$_{8}$. When $B||c,$ both compounds behave in a manner expected for heavy fermion systems as both $T_{N}$ and the electronic heat capacity decrease as field is applied. When the field is applied in the tetragonal basal plane ($B||a$), CeRhIn$_{5}$ and Ce$_{2}$RhIn$_{8}$ have very similar phase diagrams which contain both first- and second-order field-induced magnetic transitions .Comment: 15 pages, 4 figure

Real-time gauge/gravity duality: Prescription, Renormalization and Examples

We present a comprehensive analysis of the prescription we recently put forward for the computation of real-time correlation functions using gauge/gravity duality. The prescription is valid for any holographic supergravity background and it naturally maps initial and final data in the bulk to initial and final states or density matrices in the field theory. We show in detail how the technique of holographic renormalization can be applied in this setting and we provide numerous illustrative examples, including the computation of time-ordered, Wightman and retarded 2-point functions in Poincare and global coordinates, thermal correlators and higher-point functions.Comment: 85 pages, 13 figures; v2: added comments and reference

Pressure Induced Change in the Magnetic Modulation of CeRhIn5

We report the results of a high pressure neutron diffraction study of the heavy fermion compound CeRhIn5 down to 1.8 K. CeRhIn5 is known to order magnetically below 3.8 K with an incommensurate structure. The application of hydrostatic pressure up to 8.6 kbar produces no change in the magnetic wave vector qm. At 10 kbar of pressure however, a sudden change in the magnetic structure occurs. Although the magnetic transition temperature remains the same, qm increases from (0.5, 0.5, 0.298) to (0.5, 0.5, 0.396). This change in the magnetic modulation may be the outcome of a change in the electronic character of this material at 10 kbar.Comment: 4 pages, 3 figures include