Eigenstates of boson creation operator

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a and determine their coordinate and their Bargmann representation. The eigenkets of the creation operator are ultrasingular and cannot be considered as a limiting case of normalizable states. Applications of these eigenstates as auxiliary states for purposes of representation of states by path integrals over coherent states are discussed. A completeness relation for coherent states on paths through the complex plane is derived and special examples of its application are considered. Received 9 March 2001 and Received in final form 13 June 2001     

Classical paths and the WKB approximation

Recently, new connection formulas for the WKB method have been proposed, without justification, for quantum tunneling problems. We show that these formulas can be associated with diagrammatic rules within the complex time framework of the path integral formalism and then we express the relevant Green functions in terms of a sum of contributions coming from (easily interpreted) classical paths. The method is applied to barrier penetration and the double well. Received: 6 June 2000 / Published online: 27 October 2000     

Semi-classical quantum mechanics and stochastic calculus of variations

Within the framework of the general theory of stochastic calculus of variations, we examine mainly the notion of second variation in the stochastic mechanics of E. Nelson, a representative of quantum mechanics in which the concept of path for particles keep a sense. We show that the two approaches used in classical calculus of variation to know if a path is not only an extremum but also the minimum of the action, namely, the local one (weak minimum) and the global one (strong minimum), can be generalized to include the quantum-mechanical paths. Thus, we can prove that locally, a solution of the classical equation of motion is really the minimum, even in a large class of quantum paths containing the semi-classical trajectories. By introducing a stochastic version of the excess function of Weierstrass, we show the analogous global property. There, of course, one can speak of the principle of least action in a strict sense. Several explicit examples are discussed.     

Numerical evaluation of the Feynman integral-over-paths in real and imaginary-time

New techniques are described for Monte Carlo evaluation of the propagation of quantum mechanical systems in both real and imaginary-time using the Feynman integral-over-paths formulation of quantum mechanics. For imaginary-time calculations path translation is used to augment the technique of Lawande et. al. This simple-yet-powerful technique allows the equilibrium probability density to be accurately evaluated in the presence of multiple potential wells. It is shown that path translation permits the calculation of the unknown ground-state energy of one confining potential by comparison with the known ground-state energy of another. A double finite-square-well potential and a finite-square-well/parabolic-well pair are presented as examples. For real-time calculations, a weighted analytical averaging of the exponential in the classical action is performed over a region of paths. This “windowed action” has both real and imaginary components. The imaginary component yields an exponentially decaying probability for selecting paths, thereby providing a basis for the Monte Carlo evaluation of the real-time integral-over-paths. Examples of a wave-packet in a parabolic well and a wave-packet impinging upon a potential barrier are considered.     

Comments on the state densities and the transition rates in the pre-equilibrium exciton model

It is proposed to renormalize the exciton-state densities used in models for precompound decay such that the summed state densities agree with the expressions employed in equilibrium statistical models. In this way a close fit can be guaranteed between preequilibrium model calculations and the results of equilibrium statistical models for the evaporative stage of the reaction. The consequences of this proposal for the internal transition rates of the pre-equilibrium exciton model are analyzed. The matrix element for the residual interaction is obtained not from a phenomenological parametrization, but from the nucleon mean free path in nuclear matter. It is demonstrated that the proposed renormalization, from one-component Fermi-gas formulas to two-fermion expressions for the state densities, leads to strongly improved agreement of the effective exciton-model values for the nucleon mean free path in nuclear matter with realistic estimates. It is proved that the particle-hole state densities for a two-component Fermi gas, summed over the allowed exciton-state numbers, agree with the phenomenological state-density expressions used in statistical Hauser-Feshbach models.     

Local-Entire Cyclic Cocycles for Graded Quantum Field Nets

In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over ${\mathbb{R}}$ , and we carried out a detailed analysis of these objects on certain models of superconformal nets. In the present article, we show that these locally bounded functionals give rise to local-entire cyclic cocycles (generalized JLO cocycles) which are homotopy-invariant for a suitable class of perturbations of the dynamical system. Thus we can associate meaningful noncommutative geometric invariants to those graded quantum dynamical systems.     

Path summation formulation of the master equation

Markovian dynamics, modeled by the kinetic master equation, has wide ranging applications in chemistry, physics, and biology. We derive an exact expression for the probability of a Markovian path in discrete state space for an arbitrary number of states and path length. The total probability of paths repeatedly visiting a set of states can be explicitly summed. The transition probability between states can be expressed as a sum over all possible paths connecting the states. The derived path probabilities satisfy the fluctuation theorem. The paths can be the starting point for a path space Monte Carlo procedure which can serve as an alternative algorithm to analyze pathways in a complex reaction network.     

Characters of Demazure modules and solvable lattice models

We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one-dimensional configurations which we call unrestricted, classically restricted and restricted paths. As an application, characters of Demazure modules are obtained in terms of q-multinomial coefficients for several level-1 modules of classical affine algebras.     

Phase diagram of optimal paths

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.     

一种用于fMRI的嗅觉刺激装置优化与验证

为搭建可用于磁共振环境下的自动控制嗅觉刺激器,本文根据刺激装置搭建的通用要求和实验室已有装置的性能提出了改进需求和系统整体设计方案．刺激装置分为控制系统与气体输送系统两部分．控制系统的软件部分基于LabVIEW平台编程,采用了虚拟仪器方案,提供可输入刺激序列的人机界面,并根据不同的刺激需求来控制电磁阀动作,以切换不同气路．气体输送系统由4条可变支路和1条恒流支路组成,其中的3条可变气路由洁净空气分别通过装有不同气味液体的洗气瓶来产生3种刺激气味．系统搭建完成后,使用霍尼韦尔AWM43600空气流量传感器测量了系统气体流量波动率为0.3%,同时测得不同刺激气路切换时的切换响应时间为1.07 s．最后使用该刺激装置对8名被试进行嗅觉刺激的同时进行功能磁共振成像（fMRI）实验,实验采用了乙醇、吡啶和乙酸异戊酯3种刺激气味,fMRI图像结果显示被试的嗅觉受到刺激后,丘脑、杏仁核、梨状皮质、眶额皮层等嗅觉相关脑区激活．以上实验表明,本文搭建的指标可量化的刺激器更能满足嗅觉fMRI实验的要求．     

Modeling and analysis of the radio wave depolarization in urban environments

Depolarization is herein investigated for urban radio propagation. First, a theoretical study on some fundamental depolarizing mechanisms along one path, involving single and double reflection as well as wedge diffraction, is presented. Significant parameters impacting on XPR (cross polarization ratio) as the oblique incidence angle on walls or streets orientation with regards to the transmitter–receiver axis are studied thanks to simple theoretical models.XPR is also analyzed using deterministic propagation simulations in a realistic typical urban environment. The conclusions drawn in the theoretical study for single phenomena are also observed at the scale of several streets combining several paths: XPR decreases in proportion to these parameters change. These observations have been confirmed by polarimetric measurements conducted in Tokyo which are given in the last part.     

Chern-Simons-Witten invariants of lens spaces and torus bundles,and the semiclassical approximation

We derive explicit formulas for the Chern-Simons-Witten invariants of lens spaces and torus bundles overS ¹, for arbitrary values of the levelk. Most of our results are for the groupG=SU(2), though some are for more general compact groups. We explicitly exhibit agreement of the limiting values of these formulas ask with the semiclassical approximation predicted by the Chern-Simons path integral.Partially supported by an NSF Graduate FellowshipAddress as of September 1, 1991: School of Natural Science, Institute for Advanced Study, Princeton, NJ 08540; USA     

Langevin Dynamics,Large Deviations and Instantons for the Quasi-Geostrophic Model and Two-Dimensional Euler Equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.     

住宅建筑中相邻房间的侧向传声预测

侧向传声作为建筑中声传递的组成部分,对住宅的整体隔声效果具有重要的影响,通过将建筑中相邻房间的各建筑构件划分为若干子系统,应用统计能量分析(Statistical Energy Analysis,SEA)理论,从系统的声功率平衡的角度建立侧向传声的预测模型,在描述各路径的传声规律的同时确定主要传声路径。研究结果表明:当外围护结构为重质结构,且为匀质单一材料构造时,(1)在低频处,全程通过两相邻房间的侧墙或楼板的非通过隔墙的侧向路径成为主要侧向传声路径;(2)在中高频,各侧向路径的声压级差趋于一致,此时的建筑隔声性能取决于通过隔墙的直接路径上的声传递;(3)采用重质隔墙可以缩小侧向传声影响的频率范围。本研究为改善住宅的声环境质量及建筑隔声设计提供了理论依据。      

Global Estimates of Errors in Quantum Computation by the Feynman–Vernon Formalism

The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman–Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere \(S^2\) as in Klauder’s coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators \(\hat{S}_z\). The environment can then be integrated out to give a Feynman–Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev’s toric code interacting with an environment in the same manner.     

The upper bound function of nonadiabatic dynamics in parametric driving quantum systems

The adiabatic control is a powerful technique for many practical applications in quantum state engineering, light-driven chemical reactions and geometrical quantum computations. This paper reveals a speed limit of nonadiabatic transition in a general time-dependent parametric quantum system that leads to an upper bound function which lays down an optimal criteria for the adiabatic controls. The upper bound function of transition rate between instantaneous eigenstates of a time-dependent system is determined by the power fluctuations of the system relative to the minimum gap between the instantaneous levels. In a parametric Hilbert space, the driving power corresponds to the quantum work done by the parametric force multiplying the parametric velocity along the parametric driving path. The general two-state time-dependent models are investigated as examples to calculate the bound functions in some general driving schemes with one and two driving parameters. The calculations show that the upper bound function provides a tighter real-time estimation of nonadiabatic transition and is closely dependent on the driving frequencies and the energy gap of the system. The deviations of the real phase from Berry phase on different closed paths are induced by the nonadiabatic transitions and can be efficiently controlled by the upper bound functions. When the upper bound is adiabatically controlled, the Berry phases of the electronic spin exhibit nonlinear step-like behaviors and it is closely related to topological structures of the complicated parametric paths on Bloch sphere.