5,803 research outputs found
Quenching of phase coherence in quasi-one dimensional ring crystals
The comparison of the single-particle (SP) dynamics between the whisker and
ring NbSe 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
BiSrCaCuO (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 and B symmetries, and for the PG excitations, present in
A and B 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 function . 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 and
.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
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