Energy from the gauge invariant observables

For a classical solution |Psi> in Witten's cubic string field theory, the gauge invariant observable is conjectured to be equal to the difference of the one-point functions of the closed string state corresponding to V, between the trivial vacuum and the one described by |Psi>. For a static solution |Psi>, if V is taken to be the graviton vertex operator with vanishing momentum, the gauge invariant observable is expected to be proportional to the energy of |Psi>. We prove this relation assuming that |Psi> satisfies equation of motion and some regularity conditions. We discuss how this relation can be applied to various solutions obtained recently.Comment: 27 pages; v5: minor revision in section 2, results unchange

Tropical Krichever construction for the non-periodic box and ball system

A solution for an initial value problem of the box and ball system is constructed from a solution of the periodic box and ball system. The construction is done through a specific limiting process based on the theory of tropical geometry. This method gives a tropical analogue of the Krichever construction, which is an algebro-geometric method to construct exact solutions to integrable systems, for the non-periodic system.Comment: 13 pages, 1 figur

Magnetic Determination of Hc2H_{c2} under Accurate Alignment in (TMTSF)2_2ClO4_4

Cantilever magnetometry has been used to measure the upper critical magnetic field $H_{c2}$ of the quasi-one dimensional molecular organic superconductor (TMTSF)$_2$ClO$_4$. From simultaneous resistivity and torque magnetization experiments conducted under precise field alignment, $H_{c2}$ at low temperature is shown to reach 5T, nearly twice the Pauli paramagnetic limit imposed on spin singlet superconductors. These results constitute the first thermodynamic evidence for a large $H_{c2}$ in this system and provide support for spin triplet pairing in this unconventional superconductorComment: Submitted July 1, 2003, Accepted December 9, 2003, Physical Review Letter

The boundary state for a class of analytic solutions in open string field theory

We construct a boundary state for a class of analytic solutions in the Witten's open string field theory. The result is consistent with the property of the zero limit of a propagator's length, which was claimed in [19]. And we show that our boundary state becomes expected one for the perturbative vacuum solution and the tachyon vacuum solution. We also comment on possible presence of multi-brane solutions and ghost brane solutions from our boundary state.Comment: 19 pages, 2 figure

Phase Diagram of Pressure-Induced Superconductivity in EuFe2As2 Probed by High-Pressure Resistivity up to 3.2 GPa

We have constructed a pressure$-$temperature ($P-T$) phase diagram of $P$-induced superconductivity in EuFe$_2$As$_2$ single crystals, via resistivity ($\rho$) measurements up to 3.2 GPa. As hydrostatic pressure is applied, an antiferromagnetic (AF) transition attributed to the FeAs layers at $T_\mathrm{0}$ shifts to lower temperatures, and the corresponding resistive anomaly becomes undetectable for $P$ $\ge$ 2.5 GPa. This suggests that the critical pressure $P_\mathrm{c}$ where $T_\mathrm{0}$ becomes zero is about 2.5 GPa. We have found that the AF order of the Eu$^{2+}$ moments survives up to 3.2 GPa without significant changes in the AF ordering temperature $T_\mathrm{N}$. The superconducting (SC) ground state with a sharp transition to zero resistivity at $T_\mathrm{c}$ $\sim$ 30 K, indicative of bulk superconductivity, emerges in a pressure range from $P_\mathrm{c}$ $\sim$ 2.5 GPa to $\sim$ 3.0 GPa. At pressures close to but outside the SC phase, the $\rho(T)$ curve shows a partial SC transition (i.e., zero resistivity is not attained) followed by a reentrant-like hump at approximately $T_\mathrm{N}$ with decreasing temperature. When nonhydrostatic pressure with a uniaxial-like strain component is applied using a solid pressure medium, the partial superconductivity is continuously observed in a wide pressure range from 1.1 GPa to 3.2 GPa.Comment: 7 pages, 6 figures, accepted for publication in Physical Review B, selected as "Editors' Suggestion

Selection of the ground state for nonlinear Schroedinger equations

We prove for a class of nonlinear Schr\"odinger systems (NLS) having two nonlinear bound states that the (generic) large time behavior is characterized by decay of the excited state, asymptotic approach to the nonlinear ground state and dispersive radiation. Our analysis elucidates the mechanism through which initial conditions which are very near the excited state branch evolve into a (nonlinear) ground state, a phenomenon known as {\it ground state selection}. Key steps in the analysis are the introduction of a particular linearization and the derivation of a normal form which reflects the dynamics on all time scales and yields, in particular, nonlinear Master equations. Then, a novel multiple time scale dynamic stability theory is developed. Consequently, we give a detailed description of the asymptotic behavior of the two bound state NLS for all small initial data. The methods are general and can be extended to treat NLS with more than two bound states and more general nonlinearities including those of Hartree-Fock type.Comment: Revision of 2001 preprint; 108 pages Te

Structure of the Fulde-Ferrell-Larkin-Ovchinnikov state in two-dimensional superconductors

Nonuniform superconducting state due to strong spin magnetism is studied in two-dimensional type-II superconductors near the second order phase transition line between the normal and the superconducting states. The optimum spatial structure of the orderparameter is examined in systems with cylindrical symmetric Fermi surfaces. It is found that states with two-dimensional structures have lower free energies than the traditional one-dimensional solutions, at low temperatures and high magnetic fields. For s-wave pairing, triangular, square, hexagonal states are favored depending on the temperature, while square states are favored at low temperatures for d-wave pairing. In these states, orderparameters have two-dimensional structures such as square and triangular lattices.Comment: 11 pages (LaTeX, revtex.sty), 3 figures; added reference

Initial wave packets and the various power-law decreases of scattered wave packets at long times

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.Comment: 5 pages, 1 figur

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

On a q-difference Painlev\'e III equation: II. Rational solutions

Rational solutions for a $q$-difference analogue of the Painlev\'e III equation are considered. A Determinant formula of Jacobi-Trudi type for the solutions is constructed.Comment: Archive version is already official. Published by JNMP at http://www.sm.luth.se/math/JNMP