Directed random polymers via nested contour integrals

We study the partition function of two versions of the continuum directed polymer in 1+1$1+1$ dimension. In the full-space version, the polymer starts at the origin and is free to move transversally in R$\mathbb{R}$, and in the half-space version, the polymer starts at the origin but is reflected at the origin and stays in R₋${\mathbb{R}}_{-}$. The partition functions solve the stochastic heat equation in full-space or half-space with mixed boundary condition at the origin; or equivalently the free energy satisfies the Kardar–Parisi–Zhang equation.     

常规公交线网运力配置双层规划模型

双层规划研究的是两个各具有目标函数的决策者之间按有序的和非合作方式进行的相互作用,上层决策者优先作出决策,下层决策者在上层决策信息下按自己的利益作出反应,由于一方的行为影响另一方的策略选择和目标的实现,并且任何一方又不能完全控制另一方的选择行为,因此上层决策者要根据下层的反应做出符合自身利益的最终决策。而公交车辆配置正符合双层规划模型的思想,所以本论文采用双层规划模型来描述车辆配置与客流量之间的相互作用,从而优化公交线网的车辆配置。     

Phonon frequency shift and effect of correlation on the electron-phonon interaction in heavy fermion systems

The electron-phonon interaction in the periodic Anderson model (PAM) is considered. The PAM incorporates the effect of onsite Coulomb interaction (U) between f-electrons. The influence of Coulomb correlation U on the phonon response of the system is studied by evaluating the phonon spectral function for various parameters of the model. The numerical evaluation of the spectral function is carried out in the long wavelength limit at finite temperatures keeping only linear terms in U. The observed behaviour is found to agree well with the general features obtained experimentally for some heavy fermion (HF) systems.     

The Dilute Potts Model on Random Surfaces

We present a new solution of the asymmetric two-matrix model in the large-N limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with the topology of the sphere (resp. the disk) for closed (resp. open) surfaces; we elaborate on the resulting phase diagram. The method can be equally well applied to a more general (Q+1)-matrix model which represents the dilute Potts model on random dynamical lattices. We discuss in particular duality of boundary conditions for open random surfaces.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

Criticality and phase transitions in ionic fluids

Recent experimental investigations of criticality and phase separation in ionic fluids have revealed behavior of great theoretical interest. In seeking to understand the experiments, some of which appear to exhibit argonlike criticality and some of which exhibit classical (mean-field) criticality, a convenient starting point is the restricted primitive model (RPM) of symmetrically charged hard spheres, all of equal diameter , each sphere bearing a positive or negative charge of magnitudeq. There is overall charge neutrality, so that the expected number densities of the anions and cations are equal, ₊= _-. Studies of RPM charge-charge and density-density correlation functions indicate that the fluctuation-suppressing mechanism that yields mean-field critical behavior in nonionic systems with long-range interparticle potentials is not operative in the RPM. On the basis of plausible assumptions, Ising-like behavior is instead expected. The above work is summarized. New work of Zhang and the author is outlined, showing that when one loses the RPM symmetry (through, e.g., different valence, diameter, or dipole moment of anions and cations) a strong coupling between charge-charge and density-density correlation ensues. The way in which this can be expected to give rise to mean-field or mean-field-like behavior is noted. Other new observations concern the mean-field analogy found by Høye and the author between the parameter 2/(d–2) (d is the dimensionality) in that model and the monomer number in high polymers, with respect to the coexistence-curve shape dependence on those parameters.     

Neutrino emissivity of quark matter at finite temperatures

We evaluate the emissivity rates for d-decay and s-decay by exactly solving the angular integrals involved and without assuming the degeneracy of electrons. We have also studied the effects of QCD coupling constant as well as the s-quark mass on the emissivity rates. We find that these parameters are important in determining the threshold and extinction densities for d- and s-decays.     

Optical conductivity of cuprates from Yang–Rice–Zhang ansatz: Comparison with experiment

We report the results of a theoretical investigation on charge dynamics in weakly coupled CuO₂ planes of the cuprate Ca_2 − xNa_xCuO₂Cl₂ in the pseudogap regime by using the theory of Yang, Rice, and Zhang (YRZ) [1]. With a detailed numerical analysis at various impurity scattering rates (_γimp${\gamma }_{\mathit{imp}}$), we observe that YRZ model is not able to reproduce (in magnitude) the experimentally observed frequency evolution of optical conductivity at a fixed doping level. Further, to analyze the doping evolution, we have done a detailed comparison of calculated YRZ conductivity with the experimental one using Two-Component Drude–Lorentz model. We find that YRZ model is capable of reproducing (qualitatively) the experimentally observed doping evolution of Drude processes (low energy scale) and processes at the pseudogap (intermediate energy scale). We also discuss physical reasons of the discrepancy seen in magnitudes.