Boundary bootstrap principle in two-dimensional integrable quantum field theories

We study the reflection amplitudes of affine Toda field theories with boundary, following the ideas developed by Fring and Koberle [A. Fring, R. Koberle, Nucl. Phys. B 421 (1994) 159; A. Fring, R. Koberle, Nucl. Phys. B 419 (1994) 647; A. Fring, R. Koberle, Int. J. Mod. Phys. A 10 (1995) 739] and focusing our attention on the E_n series elements, because of their interesting structure of higher order poles. We also investigate the corresponding minimal reflection matrices, finding, with respect to the bulk case, a more complicated relation between the spectra of bound states associated to the minimal and to the “dressed” amplitudes.     

Liquid–gas and other unusual thermal phase transitions in some large-N magnets

Much insight into the low temperature properties of quantum magnets has been gained by generalizing them to symmetry groups of order N, and then studying the large-N limit. In this paper we consider an unusual aspect of their finite temperature behavior—their exhibiting a phase transition between a perfectly paramagnetic state and a paramagnetic state with a finite correlation length at N=∞. We analyze this phenomenon in some detail in the large “spin” (classical) limit of the SU(N) ferromagnet which is also a lattice discretization of the CP^N−1 model. We show that at N=∞ the order of the transition is governed by lattice connectivity. At finite values of N, the transition goes away in one or less dimension but survives on many lattices in two dimensions and higher, for sufficiently large N. The latter conclusion contradicts a recent conjecture of Sokal and Starinets [Nucl. Phys. B 601 (2001) 425], yet is consistent with the known finite temperature behavior of the SU(2) case. We also report closely related first order paramagnet–ferromagnet transitions at large N and shed light on a violation of Elitzur's theorem at infinite N via the large-q limit of the q state Potts model, reformulated as an Ising gauge theory.     

Comment on “proton single-particle reduced widths for unbound states”

In a recent paper, Iliadis [Nucl. Phys. A 618 (1997) 166] has estimated values of proton single-particle reduced widths for unbound states, for a range of target masses, bombarding energies, nl values and channel radii. These are “observed” values, in the sense of Lane and Thomas. Here “formal” values are calculated from an R-matrix formula, for the same range of parameter values. The formal values are more useful in general, and those obtained here differ appreciably from the observed values of Iliadis. Comparison is also made with values derived from phase shifts calculated using an optical potential.     

The perturbative approach to the critical behaviour of two-matrix models in the limit N → ∞

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators B_1,2 tend to differential operators of order l_2,1, respectively, the singularity is characterized by (l₁, l₂). Let l₁ ⩾ l₂. Then the two cases, (A) “l₂ does not divide l₁” and (B) “l₂ divides l₁”, need a different treatment. The universality classes are labelled [p, q] where [p, q] = [l₁,l₂] in case (A) and [p, q]=[l₁ + 1,l₂] in case (B).     

On ‘light’ fermions and proton stability in ‘big divisor’ D3/D7 large volume compactifications

Building on our earlier work (Misra and Shukla, Nucl. Phys. B 827:112, 2010; Phys. Lett. B 685:347–352, 2010), we show the possibility of generating “light” fermion mass scales of MeV–GeV range (possibly related to the first two generations of quarks/leptons) as well as eV (possibly related to first two generations of neutrinos) in type IIB string theory compactified on Swiss-Cheese orientifolds in the presence of a mobile space-time filling D3-brane restricted to (in principle) stacks of fluxed D7-branes wrapping the “big” divisor Σ _B . This part of the paper is an expanded version of the latter half of Sect. 3 of a published short invited review (Misra, Mod. Phys. Lett. A 26:1, 2011) written by one of the authors [AM]. Further, we also show that there are no SUSY GUT-type dimension-five operators corresponding to proton decay, and we estimate the proton lifetime from a SUSY GUT-type four-fermion dimension-six operator to be 10⁶¹ years. Based on GLSM calculations in (Misra and Shukla, Nucl. Phys. B 827:112, 2010) for obtaining the geometric K?hler potential for the “big divisor,” using further the Donaldson’s algorithm, we also briefly discuss in the first of the two appendices the metric for the Swiss-Cheese Calabi–Yau used, which we obtain and which becomes Ricci flat in the large-volume limit.     

Three-dimensional 3-state Potts model revisited with new techniques

We report a fairly detailed finite-size scaling analysis of the first-order phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed only by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binder-parameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with “large enough” q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves et al. [Phys. Rev. B 43 (1991) 5846], this leads to a refined estimate of β_t = 0.550 565(10) for the infinite-volume transition point.     

Supersymmetry in stochastic processes with higher-order time derivatives

A supersymmetric path-integral representation is developed for stochastic processes whose Langevin equation contains any number N of time derivatives, thus generalizing the presently available treatment of first-order Langevin equations by Parisi and Sourlas [Phys. Rev. Lett. 43 (1979) 744; Nucl. Phys. B 206 (1982) 321] to systems with inertia (Kramers' process) and beyond. The supersymmetric action contains N fermion fields with first-order time derivatives whose path integral is evaluated for fermionless asymptotic states.     

Non-unitarity in quantum affine Toda theory and perturbed conformal field theory

There has been some debate about the validity of quantum affine Toda field theory at imaginary coupling, owing to the non-unitarity of the action, and consequently of its usefulness as a model of perturbed conformal field theory. Drawing on our recent work, we investigate the two simplest affine Toda theories for which this is an issue –a₂⁽¹⁾ and a₂⁽²⁾. By investigating the S-matrices of these theories before RSOS restriction, we show that quantum Toda theory (with or without RSOS restriction) indeed has some fundamental problems, but that these problems are of two different sorts. For a₂⁽¹⁾, the scattering of solitons and breathers is flawed in both classical and quantum theories, and RSOS restriction cannot solve this problem. For a₂⁽²⁾ however, while there are no problems with breather-soliton scattering there are instead difficulties with soliton-excited soliton scattering in the unrestricted theory. After RSOS restriction, the problems with kink-excited kink may be cured or may remain, depending in part on the choice of gradation, as we found earlier [Nucl. Phys. B 489 [FS] (1997) 557]. We comment on the importance of regradations, and also on the survival of R-matrix unitarity and the S-matrix bootstrap in these circumstances.     

Supersymmetry and tensor coupling in

We study a possible explanation of the tensor currents in the weak radiative decay which was suggested recently by Bolotov et al. [Phys. Lett. B 243 (1990) 308] and Poblaguev [Phys. Lett. B 238 (1990) 108]. It can be shown that the supersymmetric particles can produce a tensor coupling at order (10⁻⁴−10⁻⁵)G_F which is 2–3 orders of magnitude smaller than the estimates extracted from the experimental data. A reliable calculation of the hadronic matrix element is done. The importance of a precision measurement of the tensor coupling in this decay is discussed as well as the possible relevance of the technicolour models.     

Counting colored random triangulations

We revisit the problem of enumeration of vertex-tricolored planar random triangulations solved in [Nucl. Phys. B 516 [FS] (1998) 543–587] in the light of recent combinatorial developments relating classical planar graph counting problems to the enumeration of decorated trees. We give a direct combinatorial derivation of the associated counting function, involving tricolored trees. This is generalized to arbitrary k-gonal tessellations with cyclic colorings and checked by use of matrix models.     

Uplifting the Iwasawa

The Iwasawa manifold is uplifted to seven‐folds of either G₂ holonomy or SU(3) structure, explicit new metrics for the same having been constructed in this work. We uplift the Iwasawa manifold to a G₂ manifold through “size” deformation (of the Iwasawa metric), via Hitchin's Flow equations, showing also the impossibility of the uplift for “shape” and “size” deformations (of the Iwasawa metric). Using results of Dall'Agata and Prezas, Phys. Rev. D 69 , 066004 (2004) [arXiv:hep‐th/0311146] [1], we also uplift the Iwasawa manifold to a 7‐fold with SU(3) structure through “size” and “shape” deformations via generalisation of Hitchin's Flow equations. For seven‐folds with SU(3)‐structure, the result could be interpreted as M5‐branes wrapping two‐cycles embedded in the seven‐fold (as in [1]) ‐ a warped product of either a special hermitian six‐fold or a balanced six‐fold with the unit interval. There can be no uplift to seven‐folds of SU(3) structure involving non‐trivial “size” and “shape” deformations (of the Iwasawa metric) retaining the “standard complex structure” ‐ the uplift generically makes one move in the space of almost complex structures such that one is neither at the standard complex structure point nor at the “edge”. Using the results of Konopelchenko and Landolfi, J. Geom. Phys. 29 , 319 (1999) [arXiv:math.DG/9804144] [2], we show that given two “shape deformation” functions, and the dilaton, one can construct a Riemann surface obtained via Weierstraß representation for the conformal immersion of a surface in R ^l, for a suitable l, with the condition of having conformal immersion being a quadric in CP ^l‐1.     

Parallel filtering in global gyrokinetic simulations

In this work, a Fourier solver [B.F. McMillan, S. Jolliet, A. Bottino, P. Angelino, T.M. Tran, L. Villard, Comp. Phys. Commun. 181 (2010) 715] is implemented in the global Eulerian gyrokinetic code GT5D [Y. Idomura, H. Urano, N. Aiba, S. Tokuda, Nucl. Fusion 49 (2009) 065029] and in the global Particle-In-Cell code ORB5 [S. Jolliet, A. Bottino, P. Angelino, R. Hatzky, T.M. Tran, B.F. McMillan, O. Sauter, K. Appert, Y. Idomura, L. Villard, Comp. Phys. Commun. 177 (2007) 409] in order to reduce the memory of the matrix associated with the field equation. This scheme is verified with linear and nonlinear simulations of turbulence. It is demonstrated that the straight-field-line angle is the coordinate that optimizes the Fourier solver, that both linear and nonlinear turbulent states are unaffected by the parallel filtering, and that the k_∥ spectrum is independent of plasma size at fixed normalized poloidal wave number.     

Ionization and Charge Transfer of Atomic Hydrogen by Highly Charged Ions

Cross sections for charge transfer and ionization of atomic hydrogen by highly charged ions A^q＋ （q =6 9） are evaluated using a simple and classical method based on the previous works by Bohr and Lindhard [K. Dan. Vidensk. Selsk. Mat. Fys. Medd 28 （1954） No 7], Brandt [Nucl. Instrum. Methods Phys. Res. 214 （1983） 93] and Ben-Itzhak et al. [J. Phys. B： At. Mol. Opt. Phys. 26 （1993） 1711]. It is proved that the present calculations are feasible to some extent in comparison with available experimental data and quantum calculations.     

Generalized susceptibilities and phonon anomalies in Pd and Pt metals

The generalized susceptibility, χ(q), in Pd and Pt for q along the [100], [110], [111], and [120] directions was determined from their APW and RAPW energy band structures, respectively, using the analytic tetrahedron linear energy scheme of Rath and Freeman. The band structures were previously found to yield Fermi surface radii, temperature dependencies of the static magnetic susceptibility, χ(T), resistivity, and a spin lattice relaxation, T₁T, in very good agreement with experiment. In the χ(q) calculations, we used 2048 tetrahedra in 1/48th irreducible BZ and the energy eigenvalues for bands 4, 5, and 6 which cross the Fermi energy as fitted to a Fourier series representation. The intraband parts of χ(q) at q = 0 for both metals are found to agree with the density of states at the Fermi energy to without 0.5%. Our results show that the dominant contribution to χ_intra arises from the dominant band 5 whose “jungle-gym” FS has strong nesting features; the main peak for Pd occurs at the same q value (= 0.65π/a) for q along the [0q0], [q, q, 0], and [q, q, q] directions. The locus of this main peak is a square in the (0, 0, 1) plane. The maximum of χ_intra for q along the [110] and [111] directions are 23% and 13%, respectively, higher than the value of χ(q) at q = 0. For q along the [010] and [120] directions, the peak is, however, lower than the value of χ_intra at q = 0. Hence, while phonon anomalies are predicted for the [110] and [111] directions, no anomaly is predicted for either the [100] or [120] direction. The predicted q value for the [110] anomaly, $\text{q}\text{= 0.65π/a}$ is close to the experimental value of ～0.7 π/a. Although there may be a hint of an anomaly at 0.56 [111] in the measurements, a more detailed investigation of this region is called for. For platinum, χ_intra for q along the [010], [110] and [111] directions has main peaks which occur at q = 0.68 π/a, 0.75 π/a, and 0.85 π/a, respectively. Here too, this main peak comes from the nesting of the jungle-gym Fermi surface which is not, however, as flat as that of palladium. Anomalies are predicted (although weaker in Pt than in Pd) along [110] and [111] but not along [100] and [120]. The [110] anomaly is close to the measured q value (～0.7–0.8 π/a). Also in agreement with experiment, we predict a weaker [110] anomaly for Pt than for Pd. In both Pd and Pt, weaker anomalies are predicted for the [111] direction than for the [110] direction.     

Shape Coexistence for 179Hg in Relativistic Mean-Field Theory

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Re-study of Nucleon Pole Contribution in J/

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Tsallis' quantum q-fields

We generalize several well known quantum equations to a Tsallis' q-scenario, and provide a quantum version of some classical fields associated with them in the recent literature. We refer to the q-Schro¨dinger, q-KleinGordon, q-Dirac, and q-Proca equations advanced in, respectively, Phys. Rev. Lett. 106, 140601(2011), EPL 118,61004(2017) and references therein. We also introduce here equations corresponding to q-Yang-Mills fields, both in the Abelian and non-Abelian instances. We show how to define the q-quantum field theories corresponding to the above equations, introduce the pertinent actions, and obtain equations of motion via the minimum action principle.These q-fields are meaningful at very high energies(Te V scale) for q = 1.15, high energies(Ge V scale) for q = 1.001,and low energies(Me V scale) for q =1.000001 [Nucl. Phys. A 955(2016) 16 and references therein].(See the ALICE experiment at the LHC). Surprisingly enough, these q-fields are simultaneously q-exponential functions of the usual linear fields' logarithms.     

Weitere Messungen zur Anisotropie der intermolekularen Wechselwirkung durch Streuung von Molekülen in definiertem Quantenzustand

The interaction between diatomic molecules and rare gas atoms can be described by the realistic, though simplified potentialV=?[(r_m/r)¹²(1 +q₁₂P₂(cosθ))?2(r_m/r)⁶(1+q₆P₂(cosθ))] The determination of the parameters?, r _m andq ₆has been treated in the two previous parts of this series. The present final paper describes the determination of the anisotropy parameter in the repulsive part of the potential, q₁₂, for the system CsF-He. Whileq ₆ could be derived using only the dependence of the total scattering cross section on the molecular rotational state, the determination ofq ₁₂ requires, in addition, knowledge of the velocity dependence. The comparison of the experimental data for CsF in the rotational states ¦J, M〉=¦1, 1〉 and ¦1, 0〉 with cross sections calculated by means of the “high energy” approximation yields the result:q ₁₂=0.9±0.2. The validity of the “high energy” approximation in the velocity range covered by the experiment is discussed.     

Uncertainties in the ground state structure of 8B and implications for the S17 Astrophysical S-factor

Quadrupole couplings for bound states of ⁷Be are included in describing the capture reaction ⁷Be(p,γ)⁸B. We verify, contrary to what we had initially stated (Nucl. Phys. A 615 (1997) 69), that the energy behaviour of the Astrophysical S-factor in the energy range of interest is not significantly sensitive to the core couplings in the g.s. of ⁸B, although its overall magnitude is shifted.