Based on the t-J model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight Z at the ground-state energy. Implication for finite doping is also discussed.[ S0031-9007(96) PACS numbers: 71.27.+a, 74.20.Mn, 75.10.Jm A hole injected into a two-dimensional (2D) antiferromagnet has been studied extensively [1][2][3] based on the t-J model. It is well known that a string of spin mismatches left by the hopping of the injected hole on the spin background can be repaired through the spin flip process. Consequently the hole is believed to be mobile without a confining potential linearly proportional to the length of the path. However, whether such a mobile hole can be described as a quasiparticle is still controversial.The key issue [4] involves the spectral weight Z at the ground-state energy E G . Z͑E G ͒ fi 0 means a finite overlap of the "bare" hole state with the true ground state. It implies that the real hole in the ground state behaves like a spin polaron with the bare hole carrying a spin distortion around it. If Z͑E G ͒ 0, then each injected hole will cause a global adjustment in the original ground state with a breakdown of the perturbatively treatable quasiparticle picture. The main difficulty in this problem arises from the fact that as different from the usual phonon-polaron picture, SU(2) spins are involved here and a U(1) phase plays an important role in shaping the long-distance part of a spin polaron with little energy cost. The spectral weight Z͑E G ͒ at the ground-state energy is particularly sensitive to such long-wavelength, lowenergy correlations in the system. Even though exact diagonalization calculations on small lattices [2,3] have indicated a quasiparticle peak at the energy bottom of the spectral function, when the lattice size goes to infinity it is hard to tell whether such a quasiparticle peak would still stay at the lower end of the spectra or there could be some weight (e.g., a tail) emerging below the peak which vanishes at the ground-state energy [such that Z͑E G ͒ 0]. Therefore, a more accurate approach would be desirable in order to get access to this long-distance regime. In this Letter, by explicitly tracking the Marshall sign, we show that the injected hole always has to pick up a sequence of signs (phases) from the quantum spin background. In contrast to the well-known repairable string defect of spin mismatches, we find that the phase string revealed here cannot be dynamically "eliminated" through the low-lying spin dynamics. Consequently, it dramatically modifies the long-wavelength behaviors of the doped hole. In particular, the spectral weight Z͑E G ͒ has to vanish due to such a nonrepairable phase-string effect.Let us start with ...

A sudden reduction in the feed temperature of a packed-bed reactor may lead to a transient temperature rise, referred to as a wrong-way behavior. As expected, the axial dispersion of heat decreases the magnitude of the temperature excursion and prolongs the transient shift to a new steady state. In addition, the thermal dispersion may enable the wrong-way behavior to ignite a low-temperature steady state leading to a disastrous runaway of the reactor. Moreover, it may create a transient high-temperature wave, which moves initially in the upstream direction. The axial dispersion of heat can lead to some behavioral features which are qualitatively different from those of a model which ignores it. The transient temperature excursion does not exceed a value, which can be estimated by a simple analytical expression.

Large transient temperature excursions may be caused by a sudden reduction in the feed temperature to a packed-bed reactor operating at an intermediate conversion. When a unique steady state exists for all feed temperatures, the magnitude of the wrong-way behavior predicted by a two-phase model is very close to that predicted by a pseudohomogeneous model if Pe, is equal to the dimensionless heat transfer coefficient H. The two-phase model enables a more efficient numerical sirnulation in such cases. The predictions of these two models may be rather different when steady-state multiplicity exists for some feed temperatures. In such cases, a two-phase model, which accounts for the axial dispersion of heat, should be used to simulate the transient behavior.The wrong-way behavior may lead to an ignition of a low-temperature state or an upstream propagation of a transient temperature wave.

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