Calogero-Moser and Toda systems for twisted and untwisted affine Lie algebras

The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra G are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus τ and the Calogero-Moser couplings m to infinity, while keeping fixed the combination M = m e^iδθτ for some exponent δ. Critical scaling limits arise when 1/δ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras G⁽¹⁾ and (G⁽¹⁾)^V. The limits of the untwisted or twisted Calogero-Moser system, for δ less than these critical values, but non-zero, consists of the ordinary Toda system, while for δ = 0, it consists of the trigonometric Calogero-Moser systems for the algebras G and G^V respectively.     

The geometry of the SU(2) Kepler problem

The SU(2) Kepler problem is defined and analyzed, which is a Hamiltonian system reduced from the conformal Kepler problem on T^*( ⁸ − {0}) by the use of the symplectic SU(2) action lifted from the SU(2) left action on the SU(2) bundle ⁸ − {0} → ⁵ − {0}. This reduced system has a parameter μ ε su(2) coming from the value of the moment map associated with the symplectic SU(2) action. If μ ≠ 0, the phase space of this system have a bundle structure with base space T^*( ⁵ − {0}) and fibre S². The fibre, a (co)adjoint orbit through μ for SU(2), represents the internal degrees of freedom, called the isospin, of the particle of this system. The SU(2) Kepler problem with μ ≠ 0 is then interpreted as describing the motion of a classical particle with isospin in the Newtonian potential plus a specific repulsive potential together with a Yang-Mills field. This Yang-Mills field is to be referred to as BPST Yang's monopole field in ⁵ − {0};, since it becomes the Belavin-Polyakov-Schwartz-Tyupkin instanton, restricted on S⁴. If μ = 0, the SU(2) Kepler problem reduces to the ordinary Kepler problem. Like the ordinary Kepler problem, the Hamiltonian flows of the SU(2) Kepler problem of negative energy are all closed. It is shown in an explicit manner that the energy manifolds and isoenergetic orbit spaces for the SU(2) Kepler problem of negative energy are both homogeneous manifolds on which SU(4) acts transitively to the right; those homogeneous manifold are classified into two, according as the parameter μ is zero or not. For a certain value of μ, however, they contracts to the manifold which represents the set of all the equilibrium states. The isoenergetic orbit spaces are finally shown to be symplectomorphic to certain Kirillov-Konstant-Souriau coadjoint orbits for U(4), if μ is not the exceptional value mentioned above.     

Resonance bands in a two degree of freedom Hamiltonian system

In perturbations of integrable two degree of freedom Hamiltonian systems, the invariant (KAM) tori are typically separated by zones of instability or resonance bands inhabited by elliptic and hyperbolic periodic orbits and homoclinic orbits. We indicate how the Melnikov method or the method of averaging can asymptotically predict the widths of these bands in specific cases and we compare these predictions with numerical computations for a pair of linearly coupled simple pendula. We conclude that, even for low order resonances, the first order asymptotic results are generally useful only for very small coupling (ε10^-4).     

Geometrical approach to the thermodynamical theory of phase transitions of the second kind

A geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure P and variable temperature T is proposed. Equilibrium states of a system at zero external field and fixed P and T are described by points in three-dimensional space with coordinates η, the order parameter, T, the temperature and /gf, the thermodynamic potential. These points form the so-called zero field curve in the (η, T, /gf) space. Its branch point coincides with the critical point of the system. The small parameter of the theory (the distance from the critical point along the zero-field curve) is shown to be more convenient than the small parameter of the Landau theory. It is emphasized that no explicit functional dependency of /gf on η and T is imposed.

It is shown that using (η, T, /gf) space one cannot overcome well-known difficulties of the Landau theory of phase transitions and describe non-analytical behavior of real systems in the vicinity of the critical point. This becomes possible only if one increases the dimensionality of the space, taking into account the dependency of the thermodynamic potential not only on η and T, but also on near (local) order parameters λ_i. In this case under certain conditions it is possible to describe anomalous increase of the specific heat when the temperature of the system approaches the critical point from above as well as from below the critical temperature T_c.     

The Landau-Ginzburg-Wilson model in 2 and 2+ε dimensions at low temperatures

By introducing a collective variable the two-dimensional Landau-Ginzburg-Wilson model (classical order parameter of non-rigid magnitude) may, if the order parameter dimension exceeds one, be solved at absolute zero. A low temperature expansion about this solution is developed. The low temperature expansion supports the hypothesis that d = 2 systems with a two-component order parameter will have a non-zero critical point, below which the susceptibility diverges, although no symmetry breaking occurs. The leading order temperature dependence of η is determined. In addition an ε expansion for systems of spatial dimension 2 + ε is developed. The critical exponents, calculated here to lowest order in ε, agree with those found for stiff spins.     

Patterns of lepton-flavour violation motivated by decoupling and sneutrino inflation

We present predictions for flavour-violating charged-lepton decays induced by the seesaw mechanism implemented within the constrained minimal supersymmetric standard model (CMSSM) with universal input soft supersymmetry breaking terms. We assume that one heavy singlet neutrino almost decouples from the seesaw mechanism, as suggested by the pattern of light neutrino masses and mixing angles. This is suggested independently by sneutrino inflation with a low reheating temperature, T_RH10⁷ GeV, so as to avoid overproducing gravitinos. This requirement further fixes the mass of the weakly-coupled sneutrino, whose decays may lead to leptogenesis. We find that BR(μ→eγ)10⁻¹³ but BR(τ→μγ)10⁻⁹ in the bulk of the acceptable parameter space, apart from a few isolated points. The ratio BR(μ→eγ)/BR(τ→eγ) depends on only one complex parameter, and is particularly interesting to compare with experiment.     

Z′ mediated flavor changing neutral currents in B meson decays

We study the effects of an extra U(1)′ gauge boson with flavor changing couplings with fermion mass eigenstates on certain B meson decays that are sensitive to such new physics contributions. In particular, we examine to what extent the current data on B_d→φK and B_d→η′K decays may be explained in such models, concentrating on the example in which the flavor changing couplings are left-chiral. We find that within reasonable ranges of parameters, the Z′ contribution can readily account for the anomaly in S_φKS but is not sufficient to explain large branching ratio of B_d→η′K with the same parameter value. S_φKS and S_η′KS are seen to be the dominant observables that constrain the extra weak phase in the model.     

Magnetic anisotropy in the paramagnetic phase of TbAl2

The magnetic anisotropy of a single crystal of TbAl₂ has been measured by torque magnetometry from below the Curie point up to 170 K, well into the paramagnetic phase. Within a (110) plane the torque can be described by the expression L(θ) = {P sin 2θ} H² + {Q sin 2θ + S sin 4θ} H⁴ + {T sin 4θ} H⁶, where θ is the an gle formed by the magnetization vector with a [001] axis. The first term (in H²) is interpreted as produced by arrays of defects with axial symmetry. The second (in H⁴) and third (in H⁶) terms arise from anisotropic fourth and sixth rank tensor paramagnetic susceptibilities. On the other hand if the anisotropy is described in terms of effective conventional anisotropy constants K₁ and K₂ within the temperature range 90–170 K it is found that both constants change continuously across the Curie temperature and furthermore the [111] direction remains the easy direction in the paramagnetic range. Anisotropy measurements reveal themselves as a sensitive indicator of the level of macroscopic defects in magnetic crystals.     

27Al NMR study in ZrNiAl

We have studied the microscopic properties of the hexagonal ZrNiAl, a model compound for a wide family of intermetallic compounds crystallizing in this type of structure, by using ²⁷Al NMR spectroscopy. We have investigated the lineshape of static and MAS NMR spectra as a function of magnetic field strength (4.7–9.4 T) and temperature (5–300 K). Our data indicate that the ²⁷Al NMR spectra result from a combined effect of quadrupole and anisotropic shift interactions. The ²⁷Al nuclei are in an environment characterized by the quadrupole coupling constant e²qQ/h of 3.3 MHz, asymmetry parameter η_Q of 0.42, isotropic shift δ_iso of 393 ppm, shift anisotropy δ_anis = δ_zz − (δ_xx + δ_yy)/2 of 150 ppm, and asymmetry factor η_S of 0.5. They are found to be temperature independent. The spin–lattice relaxation rate measured at 7.05 T is proportional to the temperature with T₁T = 135 s K. The mechanisms responsible for observed values of δ_iso, δ_anis, T₁T, and the enhanced Korringa constant are discussed.     

Kondo screening in gapless magnetic alloys

The low-energy physics of a spin- Kondo impurity in a gapless host, in which the density of band states ρ₀(ε)=|ε|^r/(|ε|^r+β^r) vanishes at the Fermi level ε=0, is studied by the Bethe ansatz. It is shown that the growth of the parameter Γ_r=βg^−1/r (where g is an exchange coupling constant) drives the ground state of the system from the Kondo regime with a screened impurity spin to the Anderson regime, where the impurity spin is unscreened. However, in a weak magnetic field H, the impurity spin exceeds its free value, , due to a strong coupling to a band.     

Critical dynamics of a stochastic n-vector model below Tc

The dynamic properties of a stochastic n-vector model are investigated for T < T_c in d=4−ε dimensions. Besides the non-conserved order parameter the model involves also the conserved densities of generators of the symmetry group O(n). We calculate the excitation spectra of those conserved densities and the transverse fluctuations of the order parameter to linear order in ε in the hydrodynamic region kξ1. The propagating modes have linear dispersion and quadratic damping in accordance with the phenomenological theory. The relaxing modes, however, exhibit non-hydrodynamic wavenumber dependence with a relaxation rate ω_k ∞ k^d/2.     

Fabrication, microstructure and critical current density of screen-printed Ag-(Bi, Pb)2Sr2Ca2Cu3Ox superconducting tapes

The influence of the sintering conditions on the microstructure and critical current density J_c has been studied on screen-printed Ag-(Bi, Pb)₂Sr₂Ca₂Cu₃O_x tapes with a ceramics mono-layer core. Three kinds of fabrication processes, which consist of a combination of cold working (rolling and/or pressing) and sintering, are applied. Four times repetition of pressing and sintering after the pre-sintering produces the highest c-axis alignment and achieves J_c= 1.5 × 10⁴ A/cm² (77 K, 0 T). The J_c versus θ data with an angle θ between B and the c-axis elucidate the relation between the anisotropy ratio γ=J_c(Bc)/J_c(B|c and the half-height angular width Δθ of a peak for Bc. This is related to both grain alignment and the J_c value. An increase in J_c, which comes from an improvement for grain alignment, enhances γ and narrows Δθ. The J_c versus θ data are fitted to the expression J_c(B, θ)=J _c(B, 90°)/[(γ−1)|cos θ|ⁿ+1] by regarding both γ and n as adjustable parameters. Fabrication of screen-printed tapes with multilayers (1≤N≤5) is presented, where the critical current increases from 8.0 A to 30.2 A at 77 K and 0 T as N increases.     

Incommensurability in an exactly-soluble quantal and classical model for a kicked rotator

The Hamiltonian H = 2πp + V(θ) Σ^∞_−∞ δ(t − n)(0 θ < 2π) is solved exactly, classically and quantally; the so lutions depend strongly on . There is no classical chaos and the phase cylinder p, θ is filled with invariant curves, which are finite loops around the cylinder if is sufficiently irrational and are translates of the infinitely long p axis if is rational. Quantal quasi-energy states correspond exactly to these invariant curves: localized in p and extended in θ if is sufficiently irrational, and extended in p and localized in θ if is rational. For a classical or quantal initial pure-momentum state, the energy at time t = n grows as n² if is rational (resonance) and remains bounded if is sufficiently irrational (non-resonance). If is very nearly rational (marginal resonance), the energy may grow as n^λ where λ is expressed in terms of exponents describing the irrationality of and the continuity class of V(θ). If the value of is uncertain, ensemble-averaging over shows that the energy grows ultimately as n, i.e. diffusively, as though under random impulses.     

Dynamics of surface roughening in disordered media

In this paper the roughening of interfaces moving in inhomogeneous media is investigated by examining the corresponding stochastic differential equations using (i) numerical methods and (ii) dimensional analysis. We consider interface evolution equations where disorder is represented by quenched noise which can be both additive and multiplicative. Our main finding is that quenched noise leads to a new universality class as concerning the exponents δ and β describing respectively the spatial and temporal scaling of surface roughness. In particular, additive noise close to the pinning transition results in a behaviour with δ = 0.71 ± 0.08 and β = 0.61±0.06 up to a crossover time. These estimates are in very good agreement with the theoretical prediction and that we derive from a dimensional analysis of the equation. Furthermore, we argue that multiplicative noise is the appropriate choice to describe experiments where the interface between two flowing phases is considered. By numerically integrating the proposed equation we have obtained (i) surfaces remarkably similar to those observed in the experiments and (ii) a scaling of the surface width as a function of time with an exponent β = 0.65 being in an excellent agreement with the experimental value. In addition to the exponents we discuss other relevant features of the surfaces, including the scaling of the average velocity of the surface ν_a close to pinning and the non-trivial, power law distribution of waiting times and noise along the interface in the stationary regime.     

Phase transitions and dimensional reduction

Using field theoretic methods a formalism is presented within which the critical behaviour of a system undergoing a dimensional reduction may be investigated. As a paradigm we study an Ising-like system on S¹ × R^3−ε. If the size of the system is L, and the correlation length ξ, then as L/ξ varies it is possible to get critical behaviour associated with two different fixed points. By exploiting a set of renormalization schemes which lead to manifest dimensional reduction in the loop expansion, and utilizing the renormalization group and an expansion about the fixed point of the finite system, we quantitatively investigate such crossover behaviour in its entirety. In particular, effective susceptibility and correlation length exponents are defined and computed. These exponents interpolate between those associated with a (4 − ε)-dimensional and a (3 − ε)-dimensional Ising model.     

Systematic thermopower measurements of the thallium cuprates Tl(Ba,Sr)2Cam−1CumO2m+3−δ and Tl2Ba2Cam−1CumO2m+4+δ

The thermoelectric power (TEP) S versus temperature has been systematically investigated for several series of the superconducting cuprates Tl(Ba,Sr)₂Ca_m−1Cu_mO_2m+3−δ (m = 2, 3) and Tl₂Ba₂Ca_m−1Cu_mO_2m+4+δ (m = 1, 2, 3). The consideration of the S(T_c) curves allows two important points to be found evidence for. The first one deals with the fact that all these superconducting thallium cuprates are systematically overdoped whatever T_c, and whatever the number of Cu or Tl layers; no underdoped superconducting cuprate could be obtained. The second point shows that there exist two classes of Tl cuprates: the weakly overdoped cuprates that exhibit a T_{c max} ≥ 100 K (all the triple copper layer cuprates and the 2212 cuprates) and those which can be heavily doped that exhibit a T_{c max} ≤ 90 K (the 2201 and the 1212 cuprates). The different behavior of thallium cuprates compared to YBa₂Cu₃O_7−δ and to bismuth cuprates is discussed.     

Realization and properties of ramp-type YBa2Cu3O7−δ/Au/Nb junctions

All-thin-film ramp type Josephson junctions between YBa₂Cu₃O_7−δ and Nb have been fabricated. This procedure allows connections between high-T_c and low-T_c superconductors at different crystal sides of the high-T_c superconductor on one chip, which is of great interest for novel phase devices. A thin Au layer is incorporated as a chemical barrier to avoid oxygen transfer from the YBa₂Cu₃O_7−δ to the Nb. Critical current densities up to 600 A/cm² are obtained at T=4.2 K, with typical R_nA values of 0.8 μΩ cm². The variation of the magnetic field dependence of the critical current with the angle between the junction barrier and the YBa₂Cu₃O_7−δ crystal axes is explained by considering a predominant d_x²−y² order parameter symmetry of the YBa₂Cu₃O_7−δ. The successful fabrication of these junctions allows the implementation of novel superconducting electronics, such as complementary Josephson circuitry or proposed qubit concepts, using the unconventional order parameter symmetry of the high-T_c superconductor.     

The Fermi matrix elements inferred from β-γ(CP) correlation measurements in Fe decay

Measurements have been made of the β-γ circular-polarization correlation paramter A for the 273 keV β-branch in the decay of ⁵⁹Fe. It has recently been established that each of the principal β-branches of ⁵⁹Fe involves ΔJ=0 and thus has a possible non-zero Fermi matrix element M_F which can be determined from the ƒt value and A. Previous β-γ (_CP) measurements on this nucleide have all employed the usual γ-ray scattering technique. This method is suitable for the 475 keV β-branch but does not produce an accurate measurement of the lower energy branch because of energy discrimination difficulties. A transmission polarimeter with γ-discrimination has been used in the present work to obtain clean data on the 273 keV β-1.29 MeV γ-cascade. Calibration with ⁶⁰Co (1.33 MeV) and ²⁸Al (1.79 MeV) yielded A = −0.154±0.023. This gives for the isospin impurity coefficient and the effective Coulomb matrix element of the 1.29 MeV state (1.1±1.4) × 10⁻³ and 9±11 keV, respectively.     

Influence of electromagnetic fluctuations on the resonant tunneling of electrons

We have considered the influence of electromagnetic fluctuations on electron tunneling via one non-degenerate resonant level, the problem that is relevant for electron transport through quantum dots in the Coulomb blockade regime. We show that the overall effect of the fluctuations depends on whether the electron bands in external electrodes are empty or filled. In the empty band case, depending on the relation between the tunneling rate Γ and characteristic frequency Ω of the fluctuations, the field either simply shifts the conductance peak (for rapid tunneling, Γ Ω) or broadens it (for Γ Ω). In the latter case, the system can be in three different regimes for different values of the coupling g between electrons and the field. Increasing interaction strength in the region g < 1 leads to gradual suppression of the conductance peak at the bare energy of the resonant level ε₀, while at g 1 it leads to the formation of a new peak of width at the energy ε₀ + E_cis a charging energy. For intermediate values of g the conductance is non-vanishing in the entire energy range from ε₀ to ε₀ + E_c. For filled bands the problem is essentially multi-electron in character. One consequence of this is that, in contrast to the situation with the empty band, the fluctuations of the resonant level do not suppress conductance at resonance for g < 1. At g> 1 a Coulomb gap appears in the position of the resonant level as a function of its bare energy which leads to suppression of conductance.