Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

Density-Density Propagator of the Luttinger Model of Spin-Half Fermions after an Interaction Quench

Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.     

在同位旋空间中正反质子弹性散射的重整化混合圈链图效应

本文采用描述荷电和中性 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型,计算出在 pion0 重整化混合圈链图传播下 p pbar -> p pbar 弹性散射微分截面的“精确”解析结果;并且将此结果与在 pion0 树图传播下的微分截面作了对比分析,得到相应的辐射修正重要信息。本文完成的工作对进一步深入研究 pion 介子与核子-反核子强相互作用的同位旋SU(2)不变耦合模型以及深入理论探讨正反质子对撞实验,都将提供理论研究的参考价值。     

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.     

NMR characterization of the pore structure and anisotropic self-diffusion in salt water Ice

NMR imaging and one- and two-dimensional self-diffusion propagator measurements of the liquid phase in salt water ice are presented. The properties of the network of brine-filled pores are found to depend on the growth conditions of the ice. Two types of samples are compared: (a) shock-frozen ice produced in the probe in situ and (b) ice grown over several hours under controlled conditions. By shock-freezing, an ice structure could be produced which featured streak-like porous channels of diameters of up to 300 μm allowing almost unrestricted self-diffusion along one preferential axis but reduced diffusivities in the remaining directions. In ice grown under controlled conditions, the pore sizes are near the resolution limit of the imaging experiment of typically 50 μm. For this type of samples, strongly non-Gaussian self-diffusion propagators are obtained, indicating restricted self-diffusion on rms scales of 30 μm. Common to all samples was the observation of highly anisotropic self-diffusion. One- and two-dimensional propagators are compared in order to estimate the degree of anisotropy and the size of the restrictions.     

经典粒子和量子微观粒子的运动轨道

用量子力学传播子讨论了经典粒子和量子微观粒子沿着不同轨道对传播子的贡献．通过这样的计算可以清楚地看到为什么经典粒子只是沿着满足最小作用原理的轨道，即经典轨道运动，而对于量子微观粒子沿着许多条路径都有可能．这篇短文将一些教科书中的讨论用具体的数学表达出来，使得读者更容易理解．计算表明，对于质量较大的经典粒子，沿着非经典轨道对传播子的贡献和它周围的临近轨道有强烈的抵消．只有在经典轨道附近对传播子的贡献才不为零．对于量子微观粒子没有这种差别，它可以沿着多种可能的轨道运动．     

二维无限深方势阱中粒子运动的路径积分解法

用路径积分的方法计算了二维无限深方势阱中粒子的传播子,并由传播函数推导出二维无限深方势阱中粒子的波函数和能量,进一步体现了路径积分与其他经典量子化方法的等价性,反映了路径积分应用于难以处理的量子力学问题的价值.     

Power Series Expansion of Propagator for Path Integral and Its Applications

In this paper we obtain a propagator of path integral for a harmonic oscillator and a driven harmonic oscillator by using the power series expansion. It is shown that our result for the harmonic oscillator is more exact than the previous one obtained with other approximation methods. By using the same method, we obtain a propagator of path integral for the driven harmonic oscillator, which does not have any exact expansion. The more exact propagators may improve the path integral results for these systems.     

高能重离子非对心碰撞中的整体夸克极化

There exists a large local relative orbital angular momentum between produced partons along the direction opposite to the reaction plane in the early stage of non-central heavy-ion collisions. This initial local orbital angular momentum can lead to quark polarization along the same direction due to spin-orbital coupling in QCD. We present the quark polarization by using hard thermal loop gluon propagator for quark-quark scattering in quark-gluon plasma and compare it with the result obtained from the static potential model.     

Dynamical adjustment of propagators in Renormalization Group flows

A class of continuous renormalization group flows with a dynamical adjustment of the propagator is introduced and studied theoretically for fermionic and bosonic quantum field theories. The adjustment allows to include self–energy effects nontrivially in the denominator of the propagator and to adapt the scale decomposition to a moving singularity, and hence to define flows of Fermi surfaces in a natural way. These flows require no counterterms, but the counterterms used in earlier treatments can be constructed using them. The influence of propagator adjustment on the strong–coupling behaviour of flows is examined for a simple example, and some conclusions about the strong coupling behaviour of renormalization group flows are drawn.