PT Symmetry in Quantum Field Theory

The Hamiltonian H specifies the energy levels and the time evolution of a quantum theory. It is an axiom of quantum mechanics that H be Hermitian. The Hermiticity of H guarantees that the energy spectrum is real and that the time evolution is unitary (probability preserving). In this talk we investigate an alternative formulation of quantum mechanics in which the mathematical requirement of Hermiticity is replaced by the more physically transparent condition of space-time reflection (PT) symmetry. We show that if the PT symmetry of a Hamiltonian H is not broken, then the spectrum of H is real. Examples of PT-symmetric non-Hermitian Hamiltonians are H=p ²+ix ³ and H=p ²-x ⁴. The crucial question is whether PT-symmetric Hamiltonians specify physically acceptable quantum theories in which the norms of states are positive and the time evolution is unitary. The answer is that a Hamiltonian that has an unbroken PT symmetry also possesses a physical symmetry that we call C. Using C, we show how to construct an inner product whose associated norm is positive definite. The result is a new class of fully consistent complex quantum theories. Observables exhibit CPT symmetry, probabilities are positive, and the dynamics is governed by unitary time evolution.     

Carbon diffusion between the volume and surface of (100) molybdenum

The diffusion of carbon atoms between the volume and the surface of (100) molybdenum is directly studied at temperatures between 1400 and 2000 K (i.e., at process temperatures) for the first time. The balance of carbon atoms in the system is determined. The difference in the activation energies of carbon dissolution and precipitation, ΔE=E s 1-E1s, is found for the case when the diffusion fluxes of dissolved and precipitated carbon atoms are in equilibrium. This difference defines the enrichment of the surface by carbon relative to the bulk. The experimentally found activation energy of carbon dissolution is Es1=3.9 eV. The activation energy of carbon precipitation is estimated at E 1 s=1.9 eV. The latter value is close to the energy of bulk diffusion of carbon in molybdenum.     

Phase transition studies in polymesomorphic compounds(v): Density studies in N-(p-n-Octyloxy benzylidene)-p-n-butyl aniline

The density, ρ, of N-(p-n-octyloxy benzylidene) p-n-butyl aniline (OBBA) is measured as a function of temperature from the isotropic liquid to the smectic-G phase. The compound is trimorphic, exhibiting three smectic phases, smectic-G, crystal smectic-B, and smectic-A phase. The changes in density across the phase transformations and the calculated thermal expansion coefficients confirm the order of the transitions as first order. Particular importance of the smectic-A to crystal smectic-B transformation, which is of first order, is apparent from the density jump across the transition.     

改进的全矢量有效折射率方法分析光子晶体光纤的色散特性

得到了全矢量有效折射率方法中归一化等效纤芯半径(p/Λ)随归一化空气孔直径(d/Λ)和归一化频率(Λ/λ)的变化关系，修正了p/Λ为固定值的不合理取法，得到了改进的全矢量有效折射率方法(IFVEIM).用IFVEIM计算的基模有效折射率和总色散等模式特性与多极法的结果和试验值相比较都具有很好的一致性，将基模有效折射率的误差减小了2—3个数量级.用IFVEIM详细地分析了光子晶体光纤的色散特性，得到了色散值、波长、孔间距、d/Λ之间的相互变化关系. 关键词： 光子晶体光纤 有效折射率方法 等效纤芯半径 色散     

Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models

The general properties of the factorized S-matrix in two-dimensional space-time are considered. The relation between the factorization property of the scattering theory and the infinite number of conservation laws of the underlying field theory is discussed. The factorization of the total S-matrix is shown to impose hard restrictions on two-particle matrix elements: they should satisfy special identities, the so-called factorization equations. The general solution of the unitarity, crossing and factorization equations is found for the S-matrices having isotopic O(N)-symmetry. The solution turns out to have different properties for the cases N = 2 and N 3. For N = 2 the general solution depends on one parameter (of coupling constant type), whereas the solution for N 3 has no parameters but depends analytically on N. The solution for N = 2 is shown to be an exact soliton S-matrix of the sine-Gordon model (equivalently the massive Thirring model). The total S-matrix of the model is constructed. In the case of N 3 there are two “minimum” solutions, i.e., those having a minimum set of singularities. One of them is shown to be an exact S matrix of the quantum O(N)-symmetric nonlinear σ-model, the other is argued to describe the scattering of elementary particles of the Gross-Neveu model.     

Quantum Lax Operators and Discrete 2+1-Dimensional Integrable Models

A specific quantum Lax operator, forming a quantum U _q (sl n) chain, is suggested. The intertwining R L L relation is proved. The invariant local 2+1-dimensional reformulation of the auxiliary linear problem for the L-operator is discussed.     

The Knudsen Ion Layer Problem in the Theory of the Collisionless Sheath

The interaction of a partially ionized continuum gas with a negatively charged electrode is investigated theoretically. It is supposed that l_d ? 1, where l_d is the Debye length, l is the mean-free-path. The self-consistent solution is given for two cases: l_I ? l and l_I ～ l, l_I is the effective ionisation length. The matched asymptotic expansions method is used. The Bohm sheath criterion is shown to be satisfied automatically in the considered cases.     

250步混沌强度解析混沌特征及其在心率研究中的应用

应用250步混沌强度分析Lorenz系统，分别对3维和x分量进行了计算表明，250步混沌强度与Lorenz系统的参数有明显关系.计算了正常人的窦性心率的250步混沌强度，得到了它与年龄的关系：y=6.4623-0.0496x，相关系数为-0.669，这一结果支持了Goldberger的观点，如果人的250步混沌强度照此规律衰减，将在130岁降到0.     

Phase diagram of the extended hubbard model with pair hopping interaction

A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and pair-hopping interaction W is studied at half-filling using the continuum limit field theory approach. The ground state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin-density wave (SDW) and charge-density wave (CDW) phases for large U and V, respectively, we identify a bond-charge-density-wave (BCDW) phase W < 0, | U - 2V| < | 2W| and a bond-spin-density-wave (BSDW) for W > 0, | U - 2V| < W. The possibility of bond-located ordering results from the site-off-diagonal nature of the pair-hopping term and is a special feature of the half-filled band case. The BCDW phase corresponding to an enhanced Peierls instability in the system. The BdSDW is an unconventional insulating magnetic phase, characterized by a gapless spin excitation spectrum and a staggered magnetization located on bonds between sites. The general ground state phase diagram including insulating, metallic, and superconducting phases is discussed. A transition to the η-superconducting phase at | U - 2V| ≪ 2t?W is briefly discussed. Received 20 February 2002 / Received in final form 11 April 2002 Published online 19 July 2002     

SU(2) q in a Hilbert space of analytic functions

The algebraSU(2) _q is realized in a Hilbert spaceH _q ² of analytic functions; the starting point is the differential realization of operators that satisfyq-algebra in a Hilbert spaceH _q. The Weyl realization ofSU(2) _q is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2×2 linear representation ofSU(2) _q is obtained as consistency conditions for couplingj1=j2=1/2 toj=0, 1; the derivation of Clebsch-Gordan coefficients is sketched and theq-generalization of the rotation matrices is included. The unitary correspondence ofH _q with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann's formalism for the rotation group as closely as possible.     

部分相干平顶光束通过湍流大气传输的等效曲率半径

推导出了部分相干平顶光束在湍流大气中传输的等效曲率半径的解析表达式,详细地研究了湍流对其等效曲率半径的影响.研究表明,湍流使得等效曲率半径R减小,但是只有当湍流足够强时等效曲率半径极小值出现的位置z_min才会改变.在弱湍流中,R随着光束相干长度β的增大而增大;但是在强湍流中,R随着β的增大而减小.R随着光束阶数M(N)的增大而缓慢减小.若β越大、 关键词： 等效曲率半径 湍流 部分相干平顶光束     

Towards a Coherent Theory of Physics and Mathematics: The Theory–Experiment Connection

The problem of how mathematics and physics are related at a foundational level is of interest. The approach taken here is to work towards a coherent theory of physics and mathematics together by examining the theory experiment connection. The role of an implied theory hierarchy and use of computers in comparing theory and experiment is described. The main idea of the paper is to tighten the theory experiment connection by bringing physical theories, as mathematical structures over C, the complex numbers, closer to what is actually done in experimental measurements and computations. The method replaces C by C_n which is the set of pairs, R_n,I_n, of n figure rational numbers in some basis. The properties of these numbers are based on those of numerical measurement outcomes for continuous variables. A model of space and time based on R_n is discussed. The model is scale invariant with regions of constant step size interrupted by exponential jumps. A method of taking the limit n→∞ to obtain locally flat continuum-based space and time is outlined. Also R_n based space is invariant under scale transformations. These correspond to expansion and contraction of space relative to a flat background. The location of the origin, which is a space and time singularity, does not change under these transformations. Some properties of quantum mechanics, based on C_n and on R_n space are briefly investigated.     

The ground state problem in the infinite-U Hubbard model

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ ₀ ⁽¹⁾ (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ _FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M _k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ ₀(n)<ɛ _FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m. Fiz. Tverd. Tela (St. Petersburg) 39, 193–203 (February 1997)     

Two-Parameter Deformation of the Oscillator Algebra and (p,q)–Analog of Two-Dimensional Conformal Field Theory

Abstract

The two-parameter deformation of canonical commutation relations is discussed. The self-adjointness property of the (p, q)-deformed position Q and momentum P operators is investigated. The (p, q)-analog of two-dimensional conformal field theory based on the (p, q)-deformation of the su(1, 1) subalgebra of the Virasoro algebra is presented.     

Enhancement in age hardenability of sintered Ti–5Fe alloy by Zr addition processed by pulsed electric current sintering

The age-hardenable Ti–5Fe–5Zr (wt. %, 5Zr) alloy has been consolidated by pulsed electric current sintering, following a β solution treatment, and the results are compared with a Ti–5Fe (0Zr) alloy. The precipitation sequence measured at 640°C ageing is β?+?athermal ω?→?β?+?isothermal ω?→?β?+?α. At the peak hardness isothermal ω phase forms at 20?s of ageing. The Zr addition retards the precipitation kinetics of the α phase; as a result, the α phase nucleates at latest at 300?s ageing in the overaged state. Fe is partitioned into β, while it is depleted from the α phases. There is Zr enrichment near the α/β interface when the α phase precipitates due to a solute drag effect; the growth rate of the α phase in the 5Zr alloy is significantly reduced compared with that in the 0Zr alloy.     

Phase diagram of the Mott transition in a two-band Hubbard model in infinite dimensions

The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory recently developed by Bulla and Potthoff. The phase boundary of the metal-insulator transition is obtained analytically as a function of the on-site Coulomb interaction at the d-orbital, the charge-transfer energy between the d- and p-orbitals and the hopping integrals between p-d, d-d and p-p orbitals. The result is in good agreement with the numerical results obtained from the exact diagonalization method. Received 5 October 2000 and Received in final form 8 December 2000     

二维颗粒流从稀疏态到密集态的临界转变

研究了斜槽中的二维颗粒流由稀疏到密集转变的临界现象.在二维颗粒槽的入口流量Q₀和出口尺寸d固定的条件下，记录并统计了稀疏流转变为密集流所经历的时间.研究发现，在统计时间内转变不发生的概率C(t)随时间指数衰减，其衰减的特征时间尺度α^-1(d)可以很好地由幂律函数a(d_c-d)^-γ来拟合，其中d_c为临界开口尺寸.此临界尺寸的存在确定了稀疏流到密集流转变的临界现象. 关键词： 颗粒物质 颗粒流 非平衡态相变 几何相变     

The enveloping algebra of a covariant system

In an earlier work, Doplicher, Kastler and Robinson have examined a mathematical structure consisting of a pair (A, G), whereA is aC*-algebra andG is a locally compact automorphism group ofA. We call such a structure a covariant system. The enveloping von Neumann algebraA(A, G) of (A, G) is defined as a *-algebra of operator valued functions (called options) on the space of covariant representations of (A, G). The system (A, G) is canonically embedded in, and in fact generates, the von Neumann algebraA(A, G). Further we show there is a natural one-to-one correspondence between the normal *-representations ofA(A, G) and the proper covariant representations of (A, G). The relation ofA(A, G) to the covarainceC*-algebraC*(A, G) is also examined.     

The variable viscoelasticity oscillator

The complex dynamics of a variable viscoelasticity oscillator is studied using the novel concept of Variable‐Order (VO) Calculus. The damping force in the oscillator varies continuously between the elastic and viscous regimes depending on the position of the mass. The oscillator considered here is composed of a linear spring of stiffness k that inputs a restitutive force F_k = ‐k x, a VO damper of order q(x(t)) that generates a damping force F_q = ‐c_q ??^q(x(t)) x, and a mass m. A modified Runge‐Kutta method is used in conjunction with a trapezoidal numerical integration technique to yield a second‐order accurate method for the solution of the resulting VO Differential Equation (VODE). The VO oscillator is also modelled using a Constant Order (CO) formulation where a number of CO fractional order differentials are weighted to simulate the VO behavior. The CO formulation asymptotically approaches the VO results when a relatively large number of weights is used. For the viscoelastic range of 0 ≤ q ≤ 1, the dynamics of the oscillator is well approximated by the CO formulation when 5 or more fractional terms are included (e.g., 0, 1/4, 1/2, 3/4, and 1).     

Analysis ofJCoupling-Induced Fat Suppression in DIET Imaging

The DIET (ordualintervalechotrain) sequence, a modification of thefastspinecho (FSE) sequence that selectively reduces signal from fat in MR images, has been investigated. The DIET sequence uses an initial echo spacing longer than that of a conventional FSE sequence, thus allowingJcoupling-induced dephasing to take effect. The sequence is evaluated theoretically, and its effectiveness on a hydrocarbon (1-pentene) is demonstrated numerically using density matrix calculations. The sequence is also evaluated experimentally usingin vitrosolutions andin vivoimaging. The efficacy of the sequence is compared for different lipid chemical structures, field strengths, and pulse sequence parameters.