On integrable natural Hamiltonian systems on the suspensions of toric automorphism

We point out a mistake in the main statement of \cite{liu} and suggest and proof a correct statement.Comment: 5 pages, no figure

Coulomb blockade and Non-Fermi-liquid behavior in quantum dots

The non-Fermi-liquid properties of an ultrasmall quantum dot coupled to a lead and to a quantum box are investigated. Tuning the ratio of the tunneling amplitudes to the lead and box, we find a line of two-channel Kondo fixed points for arbitrary Coulomb repulsion on the dot, governing the transition between two distinct Fermi-liquid regimes. The Fermi liquids are characterized by different values of the conductance. For an asymmetric dot, spin and charge degrees of freedom are entangled: a continuous transition from a spin to a charge two-channel Kondo effect evolves. The crossover temperature to the two-channel Kondo effect is greatly enhanced away from the local-moment regime, making this exotic effect accessible in realistic quantum-dot devices.Comment: 5 figure

Propagation of an Acoustic Pulse of Finite Amplitude in a Granular Medium

A study of propagation of a wide-band acoustic signal in a granular medium is reported. Experimental data on the propagation of pulses with an amplitude up to 3 MPa and characteristic length about 1 µs through a sample of cobalt-manganese nodules are compared with a computer model of the process. An anomalous sig'rfal absorption in the high-frequency range observed with relatively weak sounding pulses is explained under the assumption of a fractal sample structure on a certain scale. When the signal amplitude increases, the ahsorption assumes a normal power form which is evidence of substance structural changes

Skewed Sudakov Regime, Harmonic Numbers, and Multiple Polylogarithms

On the example of massless QED we study an asymptotic of the vertex when only one of the two virtualities of the external fermions is sent to zero. We call this regime the skewed Sudakov regime. First, we show that the asymptotic is described with a single form factor, for which we derive a linear evolution equation. The linear operator involved in this equation has a discrete spectrum. Its eigenfunctions and eigenvalues are found. The spectrum is a shifted sequence of harmonic numbers. With the spectrum found, we represent the expansion of the asymptotic in the fine structure constant in terms of multiple polylogarithms. Using this representation, the exponentiation of the doubly logarithmic corrections of the Sudakov form factor is recovered. It is pointed out that the form factor of the skewed Sudakov regime is growing with the virtuality of a fermion decreasing at a fixed virtuality of another fermion.Comment: 6 page

Possible ferro-spin nematic order in NiGa2S4

We explore the possibility that the spin-1 triangular lattice magnet NiGa2 S4 may have a ferro-nematic ground state with no frozen magnetic moment but a uniform quadrupole moment. Such a state may be stabilized by biquadratic spin interactions. We describe the physical properties of this state and suggest experiments to help verify this proposal. We also contrast this state with a `non-collinear' nematic state proposed earlier by Tsunetsugu and Arikawa for NiGa2S4

Algebro-Geometric Solutions of the Boussinesq Hierarchy

We continue a recently developed systematic approach to the Bousinesq (Bsq) hierarchy and its algebro-geometric solutions. Our formalism includes a recursive construction of Lax pairs and establishes associated Burchnall-Chaundy curves, Baker-Akhiezer functions and Dubrovin-type equations for analogs of Dirichlet and Neumann divisors. The principal aim of this paper is a detailed theta function representation of all algebro-geometric quasi-periodic solutions and related quantities of the Bsq hierarchy.Comment: LaTeX, 48 page

Zeros of the Partition Function for Higher--Spin 2D Ising Models

We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin $s=1$, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the thermodynamic limit. Support is adduced for a conjecture that all divergences of the magnetisation occur at endpoints of arcs of zeros protruding into the FM phase. We conjecture that there are $4[s^2]-2$ such arcs for $s \ge 1$, where $[x]$ denotes the integral part of $x$.Comment: 8 pages, latex, 3 uuencoded figure