String theory beyond the Planck scale

The high-energy behavior of string scattering amplitudes is studied to all orders in perturbation theory, with the aim of exploring the short-distance structure of string theory. It is shown that the sum over all Riemann surfaces is dominated by a saddle point. Consequently, the high-energy limit is universal and simple to calculate. In this limit, furthermore, the amplitudes fall off in a stringy way - much faster than that allowed by field theory. The dominant saddle points are identified as coming from world sheets which are Z_G+1 symmetric algebraic curves, and their contribution to the scattering amplitude is evaluated. An interesting spacetime picture of the high-energy limit emerges. The issue of summing the perturbation expansion is addressed.     

Influence of the orthorhombic distortion on the van Hove singularities in the DOS and ARPES spectra of layered cuprates

Four atom states Cu3d_{x² −  y²}, Cu4s, O_a2p_xare involved in a tight-binding model for the superconducting CuO₂plane. The orthorhombic distortion is taken into account by the differences of Cu–O hopping amplitudes and single-site oxygen energies ε_aand ε_bof two oxygen positions in the elementary cell as well. An effective ‘oxygen’ Hamiltonian including only the electron amplitudes at the oxygen ions is derived. Simple expressions for the constant energy contours and the Fermi surface are obtained and they qualitatively describe the photoemission spectra. Extended saddle points nearp = (π,0) andp = (0,π) are observed in qualitative agreement with the ARPES data. The van Hove singularities of the density of states (DOS) related to the extended saddle points are calculated by a Monte Carlo method. It is found that the splitting of the singularity of the DOS at the bottom of the conduction band is created by the energy difference ε_a −  ε_b = 2δ.     

Critical bubbles and fluctuations at the electroweak phase transition

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field ϕ. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g3 (T) z in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(ϕ) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small ϕ values increasing with the Higgs mass m_H Taking a functional S_z [ϕ] with constant Z(ϕ) = z instead of the full non-local effective action in some neighborhood of the saddle point we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.     

Non-trivial saddle points and band structure of bound states of the two-dimensional O(N) vector model

We discuss O(N) invariant scalar field theories in 0 + 1 space-time dimensions (quantum mechanics) and in 1 + 1 space-time dimensions (field theory). Combining ordinary “Large N” saddle point techniques and simple properties of the diagonal resolvent of one-dimensional Schrödinger operators we find non-trivial (non-constant) solutions to the saddle point equations of these models in addition to the saddle point describing the ground state of the theory. In the “Large N” limit these saddle points are exact for the quantum mechanical case, but only approximate in the two-dimensional theory. In the latter case they are the leading contributions to the time evolution kernel at short times, or equivalently, the leading contribution to the high temperature expansion of partition function stemming from space dependent static configurations in case of the Euclidean theory. We interpret these novel saddle points as collective O(N) singlet excitations of the field theory, each embracing a host of finer quantum states arranged in O(N) multiplets, in an analogous manner to the band structure of molecular spectra.     

High Tc superconductors – Soliton lattices?

Based on the experimental ARPES data we have shown that the band structure of high T_c compounds is compatible with the soliton lattice model, which was developed for one-dimensional case. In spite of higher dimensionality of CuO₂ layers the kink behavior of the electronic dispersion and flat bands near the saddle points find their essential explanation in the frame of this model. Recently measured de Haas–van Alphen values of electron and hole pockets in YBa₂Cu₃O_6.5 1 and 2 are derived on the same basis. The similarities and fundamental differences from stripe models are discussed.     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Organizational dynamics of formation of the color center saddle point in KCl: Li

Emission from the relaxed saddle point configuration of the F_A(II) color center of KCl: Li is delayed by over 200 psec. The intermediate state initially formed following optical excitation is suggested to be the relaxed F_A(I) configuration, and the delay is associated with the mean time for first passage towards the F_A(II) saddle point configuration.     

Energy spectrum of (Sn0.65Pb0.35)0.95Ge0.05Te solid solutions

The paper reports the study on the resistivity ρ and thermoemf S of the (Sn_0.65Pb_0.35)_0.95Ge_0.05Te solid solution layers. The dependences of ρ and S on the hole concentrations in the range 3×10¹⁹–2×10²¹ cm^?3 exhibit jumps in the resistivity and thermoemf minima at close hole concentrations p ₁≈9×10¹⁹ cm^?3, p ₂≈2.5×10²⁰ cm^?3, and p ₃≈4.5×10²⁰ cm^?3. The observed jumps and minima suggest a complex structure of the valence band and the presence of critical points in the energy spectrum of holes. According to the data for SnTe, the critical points in the energy spectrum at the given hole concentrations are identified as the Σ-extremum, saddle point LΣ, and Δ-extremum, respectively.     

Analysis of fragment mass distribution in asymmetric area at fission of <Superscript>235</Superscript>U induced by thermal neutrons

The fragment mass yields in fission of ²³⁵U induced by thermal neutrons for A = 145–160 and E_K = 50–75 MeV were measured using a mass spectrometer. The fine structure is observed at A = 153, 154 and E_K = 50–60 MeV. The obtained results were described in the framework of a model based on the dinuclear system concept. The analyzed correlation between the total kinetic energy and mass distribution of fission fragments is connected with the shell structure of the formed fragments of fission. From this correlation and the time dependence of the calculated mass distribution of the binary reaction products, one can conclude that the descent time from a saddle point to a scission point for the more deformed fragments is longer than that for fragments of more compact shape.     

Disorder broadening of E2 optical spectra in GeSi alloys

he E₂ transitions in GeSi alloys are analyzed quantitatively using low-field electroreflectance data. The model of M₁ saddle point transitions is found to be in fair agreement with differentiated electroreflectance spectra in the whole composttion range. The broadening parameter of pure Ge and Si increases by 0.035 eV in the alloy with equal content of both components.     

An effective potential for classical Yang-Mills fields as outline for bifurcation on gauge orbit space

Classical Yang-Mills (Y.M.) equations with static external sources are formulated as a Hamiltonian system with gauge symmetry in A₀ = 0 gauge. Using the concept of a “momentum mapping” (J. Marsden and A. Weinstein, Rep. Math. Phys.5 (1974), 121) on symplectic manifolds with symmetry, an analogue of centrifugal potential of a mass point in a spherically symmetric potential is derived. This gives rise to an effective potentialV_eff, whose critical points are rigorously proved to be in one-to-one correspondence with static Y.M. solutions. V_eff additionally depends on the prescribed external source ?, which is as a constant of motion analogous to angular moment of the mass point. Thus bifurcation of static solutions is caused by bifurcation of critical points of V_eff under variation of the external parameter ?. Some closing remarks on dynamics and stability on gauge orbit space are added.     

Fragment mass dependence of angular anisotropy in 15 MeV proton-induced fission of 244Pu

Angular distributions of fission fragments with mass number A=97-159 have been measured by the radiochemical recoil-catcher method in the proton-induced fission of ²⁴⁴Pu with the incident energy of 15 MeV. Angular anisotropies of extreme asymmetric mass division products even up to the fragment mass ratio of A _H /A _L ∼ 1.85 are found not any different from those of the typical asymmetric mass division products with A∼ 138, which indicates that no clear evidence is observed for the existence of an additional saddle point configuration in the extreme asymmetric mass division. The correlation between the saddle point state evaluated from the angular anisotropy and the mass division mode is discussed.     

Systematics of charge distribution studies in low-energy fission of actinides

Charge distribution studies were carried out in the thermal neutron-induced fission of ²²⁹Th, ²⁴¹Pu and ²⁴⁵Cm as well as in the spontaneous fission of ²⁵²Cf. The width parameter (σ_z/σ_A), the most probable charge/mass (Z_p/A_p) and the charge polarization (ΔZ) as a function of fragment mass were deduced. The slope of charge polarization as a function of fragment mass [δ(ΔZ)/δA′], average charge dispersion parameter (〈σ_z〉) and proton odd-even effect (δ_p) were also obtained for these fissioning systems. These data along with the literature data for even-Z fissioning systems such as ²³³Th¹, ²³³U¹, ²³⁴U¹, ²³⁶U¹, ²³⁹U¹, ²³⁹Pu¹, ²⁴⁰Pu¹ and ²⁵⁰Cf¹ are discussed in terms of nuclear-structure effects and dynamics of descent from saddle point to the point of neck formation and from the formation of the neck to the scission point.     

The vacuum energy of QED with four-fermion interaction

We consider quantum electrodynamics in the quenched approximation including a four-fermion interaction with coupling constantg. The effective potential at stationary points is computed as a function of the coupling constants α andg and an ultraviolet cutoff Λ, showing a minimum of energy in the (α,g) plane for α=α _c =π/3 andg=∞. When we go to the continuum limit (Λ→∞), keeping finite the dynamical mass, the minimum of energy moves to (α=0,g=1), which correspond to a point where the theory is trivial.     

Resonant Γ–X–Γ tunneling in GaAs/AlAs/GaAs single barrier heterostructures at zero and elevated magnetic field

We report the observation of resonant tunneling and magneto-tunneling between states of different effective mass derived from zone centre (Γ) and zone edge (X) points of the Brillouin zone in single AlAs barrier diodes. The nature of the X states involved (longitudinal X_zor transverseX_xy ) is deduced from the observed resonances in the conductance versus bias characteristics at zero magnetic field (B). At finite B, the σ–V curves exhibit resonant magneto-tunneling with X_zLandau levels (LL), whilst no evidence of resonances withX_xy LLs is found. Clear observation of both LL index (in-plane momentum) conserving and non-conserving tunneling to X_zallows the transverse effective mass in AlAs to be determined. As a consequence of the different effective masses, momentum-conserving tunneling is inhibited at B = 0, but is restored when high B is applied.     

Far-infrared photoconductivity from the shallow donors in n-InP

The wavenumber of the 1s → 2p transition of the shallow donor in n-type InP is found to be 46.3 ± 0.4 cm⁻¹ in zero magnetic field, giving a conduction band effective mass of 0.085 ± 0.005 m₀ and a donor binding energy of 0.00765 eV. The Zeeman splitting of this transition is observed and yields an effective mass of 0.0810 ± 0.0005 m₀. Sharp structure is found in the spectral response of the photoconductivity close to the frequency of the LO phonons. This structure may be related to ‘total negative photoconductivity’.     

Enhanced effective mass in doped SrTiO3 and related perovskites

The effective mass is one of the main factors determining the Seebeck coefficient and electrical conductivity of thermo-electrics. In this ab-initio LDA-GGA study the effective mass is estimated from the curvature of electronic bands by one-band-approximation and is in excellent agreement with experimental data of Nb- and La-doped SrTiO₃. It is clarified that the deformation of SrTiO₃ crystals has a significant influence on the bandgap, effective electronic DOS-mass and band-mass, but the electronic effect due to the e_g-band flattening near the Γ-point due to Nb-doping up to 0.2 at% is the main factor for the effective mass increase. Doping of La shows a linear decrease of the effective mass; this can be explained by the different surroundings of A- and B-sites in perovskite. Substitution with other elements such as Ba on the A-site and V on the B-site in SrTiO₃ increases the effective mass as well.     

Terahertz spectroscopy of quantum-well narrow-bandgap HgTe/CdTe-based heterostructures

The energy spectra of quantum-well narrow-bandgap Hg_{1 ? y} Cd _y Te/Cd _x Hg_{1 ? x} Te heterostructures have been studied. The dependences of the effective cyclotron mass on the density (in classical magnetic fields) and the transition energy (in quantizing fields) have been obtained from the cyclotron resonance measurements. These dependences confirm the near-linear dispersion law for the electrons with small mass at the band bottom (the minimum cyclotron mass measured is 0.003 m ₀). The interband photoconductivity of the CdHgTe-based structures with the long-wavelength photoresponse edge lower than 6 meV has been demonstrated.     

Behavior of Fermi systems approaching the fermion condensation quantum phase transition from the disordered phase

The behavior of Fermi systems that approach the fermion condensation quantum phase transition (FCQPT) from the disordered phase is considered. We show that the quasiparticle effective mass M* diverges as M* ∝ 1/¦x?x_FC¦, where x is the system density and x_FC is the critical point at which FCQPT occurs. Such behavior is of general form and takes place in both three-dimensional (3D) and two-dimensional (2D) systems. Since the effective mass M* is finite, the system exhibits the Landau Fermi liquid behavior. At ¦x? x_FC¦/x_FC?1, the behavior can be viewed as highly correlated, because the effective mass is large and strongly depends on the density. In the case of electronic systems, the Wiedemann-Franz law is valid and the Kadowaki-Woods ratio is preserved. Beyond the region ¦x–x_FC¦/x_FC?1, the effective mass is approximately constant and the system becomes a conventional Landau Fermi liquid.