Quenching of phase coherence in quasi-one dimensional ring crystals

The comparison of the single-particle (SP) dynamics between the whisker and ring NbSe$_3$ crystals provides new insight into the phase transition properties in quasi-one-dimensional charge density wave (CDW) systems.Comment: 9 pages, 4 figure

Thermodynamic interpretation of the uniformity of the phase space probability measure

Uniformity of the probability measure of phase space is considered in the framework of classical equilibrium thermodynamics. For the canonical and the grand canonical ensembles, relations are given between the phase space uniformities and thermodynamic potentials, their fluctuations and correlations. For the binary system in the vicinity of the critical point the uniformity is interpreted in terms of temperature dependent rates of phases of well defined uniformities. Examples of a liquid-gas system and the mass spectrum of nuclear fragments are presented.Comment: 11 pages, 2 figure

Gopakumar-Vafa invariants via vanishing cycles

In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT invariants for irreducible one-cycles. We also give a counter-example to the Kiem-Li conjectures, where our invariants match the predicted answer. Finally, we give examples where our invariant matches the expected answer in cases where the cycle is non-reduced, non-planar, or non-primitive.Comment: 63 pages, many improvements of the exposition following referee comments, final version to appear in Inventione

Dynamics of broken symmetry nodal and anti-nodal excitations in Bi_{2} Sr_{2} CaCu_{2} O_{8+\delta} probed by polarized femtosecond spectroscopy

The dynamics of excitations with different symmetry is investigated in the superconducting (SC) and normal state of the high-temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) using optical pump-probe (Pp) experiments with different light polarizations at different doping levels. The observation of distinct selection rules for SC excitations, present in A$_{{\rm 1g}}$ and B$_{{\rm 1g}}$ symmetries, and for the PG excitations, present in A$_{{\rm 1g}}$ and B$_{{\rm 2g}}$ symmetries, by the probe and absence of any dependence on the pump beam polarization leads to the unequivocal conclusion of the existence of a spontaneous spatial symmetry breaking in the pseudogap (PG) state

Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy

In this paper we generalize the Sato theory to the extended bigraded Toda hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato equations, wave operators, Hirota bilinear identities (HBI) and show the existence of $tau$ function $\tau(t)$. Meanwhile we prove the validity of its Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex operators whose coefficients take values in the algebra of differential operators. In contrast with HBEs of the usual integrable system, the current HBEs are equations of product of operators involving $e^{\partial_x}$ and $\tau(t)$.Comment: 29 pages, to appear Journal of Mathematical Physics(2010

Ultradiscretization of the solution of periodic Toda equation

A periodic box-ball system (pBBS) is obtained by ultradiscretizing the periodic discrete Toda equation (pd Toda eq.). We show the relation between a Young diagram of the pBBS and a spectral curve of the pd Toda eq.. The formula for the fundamental cycle of the pBBS is obtained as a colloraly.Comment: 41 pages; 7 figure