Two-time correlation functions: stochastic and conventional quantum mechanics

An investigation of two-time correlation functions is reported within the framework of (i) stochastic quantum mechanics and (ii) conventional Heisenberg-Schr?dinger quantum mechanics. The spectral functions associated with the two-time electric dipole moment correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for stochastic and conventional quantum mechanics, differences arise in the two approaches for multiple time correlation functions.     

A cumulant expansion for the two-time correlation functions for linear stochastic differential equations

A cumulant expansion for the two-time correlation functions for linear stochastic differential equations is presented. This extends the work of Kubo and Van Kampen on one-time averages to the case of two-time averages. The resulting equations become exact in the second order approximation in the scalar gaussian case.     

Critical fluctuations in continuous non-equilibrium systems

We treat a continuously extended non-equilibrium system described by a set of space and time dependent variablesq. Theq's are assumed to obey linearized equations of motion with fluctuating forces which areδ-correlated in space and time. We calculate the two-time and two-space-point correlation functions.     

Magnetic Properties of One-Dimensional Ferromagnetic Mixed-Spin Model within Tyablikov Decoupling Approximation

In this paper, we apply the two-time Green's function method, and provide a simple way to study the magnetic properties of one-dimensional spin-(S,s) Heisenberg ferromagnets. The magnetic susceptibility and correlation functions are obtained by using the Tyablikov decoupling approximation. Our results show that the magnetic susceptibility and correlation length are amonotonically decreasing function of temperature regardless of the mixed spins. It is found that in the case of S=s, our results of one-dimensional mixed-spin model is reduced to be those of the isotropic ferromagnetic Heisenberg chain in the whole temperature region. Our results for the susceptibility are in agreement with those obtained by other theoretical approaches.     

Real-time kadanoff-baym approach to plasma oscillations in a correlated electron Gas

A nonequilibrium Green's functions approach to the collective response of correlated Coulomb systems at finite temperatures is presented. It is shown that solving Kadanoff-Baym-type equations of motion for the two-time correlation functions including the external perturbing field allows one to compute the plasmon spectrum with collision effects in a systematic and consistent way. The scheme has a "built-in" sum-rule preservation and is simpler to implement numerically than the equivalent equilibrium approach based on the Bethe-Salpeter equation.     

The poisson representation. II Two-time correlation functions

Basic formulas for the two-time correlation functions are derived using the Poisson representation method. The formulas for the chemical system in thermodynamic equilibrium are shown to relate directly to the fluctuationdissipation theorems, which may be derived from equilibrium statistical mechanical considerations. For nonequilibrium systems, the formulas are shown to be generalizations of these fluctuation-dissipation theorems, but containing an extra term which arises entirely from the nonequilibrium nature of the system. These formulas are applied to two representative examples of equilibrium reactions (without spatial diffusion) and to a nonequilibrium chemical reaction model (including the process of spatial diffusion) for which the first two terms in a systematic expansion for the two-time correlation functions are calculated. The relation between the Poisson representation method and Glauber-SudarshanP-representation used in quantum optics is discussed.     

Superaging and Subaging Phenomena in a Nonequilibrium Critical Behavior of the Structurally Disordered Two-Dimensional XY Model

A Monte Carlo numerical simulation of the specific features of nonequilibrium critical behavior is carried out for the two-dimensional structurally disordered XY model during its evolution from a low-temperature initial state. On the basis of the analysis of the two-time dependence of autocorrelation functions and dynamic susceptibility for systems with spin concentrations of p = 1.0, 0.9, and 0.6, aging phenomena characterized by a slowing down of the relaxation system with increasing waiting time and the violation of the fluctuation–dissipation theorem (FDT) are revealed. The values of the universal limiting fluctuation–dissipation ratio (FDR) are obtained for the systems considered. As a result of the analysis of the two-time scaling dependence for spin–spin and connected spin autocorrelation functions, it is found that structural defects lead to subaging phenomena in the behavior of the spin–spin autocorrelation function and superaging phenomena in the behavior of the connected spin autocorrelation function.     

On the possibility of pair condensation in the Hubbard model with strong repulsion

The phonon-free mechanism of superconductivity at infinite Hubbard energy is discussed. The temperature of superconducting transition (T_c) depending on the rate of non-fulfilling (x) of the lower Hubbard subband has been calculated.     

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

The non-equilibrium dynamics of the kinetic spherical model with a non-conserved order-parameter, quenched to T≤T_c from a fully disordered initial state, is studied at its upper critical dimension d=d^*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t)∼t^1/2.     

A cumulant expansion for the time correlation functions of solutions to linear stochastic differential equations

It is shown that the cumulant expansion for linear stochastic differential equations, hitherto used to compute one-time averages of the solution process, is also capable of yielding the two-time correlation and probability density functions. The general case with a coefficient matrix, an inhomogeneous part and an initial condition which are all random and mutually correlated, is discussed. Two examples are given, the latter of which treats the harmonic oscillator with stochastic frequency and driving term studied before. Finally we investigate the relation of our method with the so-called smoothing method.     

Resemblances and differences in mechanisms of noise-induced resonance

Systems showing stochastic resonance (SR) or coherent resonance (CR) share some features, in particular, the nearly periodic character of the signal. We show that in spite of this resemblance the different underlying dynamics can be detected in experimental data by studying the histogram of the inter-spikes times and some statistical properties like two-time correlation functions. We discuss its possible relevance for climate modeling.     

Controllable precision of the projective truncation approximation for Green's functions

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions(Fan et al., Phys. Rev. B 97, 165140(2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.     

Dissociation of adsorbed diatomic molecules: Combined effects of the surface magnetic field,a laser and the phonon continuum

Effects of the surface magnetic field (SMF), a laser and admolecule-phonon coupling on the dissociation of adsorbed diatomic molecules are studied theoretically. It is observed that the laser photon-dressing and the SMF-splitting of the molecular states give rise to a multiwell configuration, and the dissociation rate of a particular vibrational state in this configuration is altered as compared to the gas-phase laser-induced process. The presence of the phonon continuum also affects dissociation by dampening local transition probabilities at avoided crossings. Dissociation rates as function of laser power densities for a few specific systems are derived with a phonon-free situation and also with the presence of the phonon continuum, and the extent of phonon effects are analyzed.     

激光束准直检测仪：原理,功能与精度

根据先前曾提出的单楔板旋转原理与实验研究,一种定量检测光学系统离焦量及激光发散度的仪器已经研制成功.本文概括地介绍了该仪器原理、主要功能、测试方法及精度评价等.由于本仪器具有一系列优点,已成为激光实验、光学教学及光学工程必备的仪器     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Single-lobed Near Diffraction-limited Beam from 1W Laser Diode Array with an External Cavity

Abstract　An external cavity for the laser diode array with a conventional mirror in what we call two-time self-injection operation is presented. The external cavity consists of two lenses, a flat external mirror(EM) in the image plane of the array and a prism that is used as an output coupler. The single-lobed near diffraction-limited far field beam of a 1 W 10-stripe gain-guided LD array lies at 6.4°～9° with the external cavity operation in two-time self-injection mode, whereas at 2.5°～3.0° for its normal feedback operation. The width of the far field beam (FWHM) is 0.43° and 0.63° at driving current of 2 and 3.2 ×Ithr, respectively, much narrower than that in normal feedback operation, but at the expense of lower output power. The output of the system is very stable and insensitive to the tilt and position of the EM.     

Single-lobed Near Diffraction-limited Beam from 1W Laser Diode Array with an External Cavity

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On the theory of NMR spin echoes in solids

A general expression in terms of two-time correlation functions is derived for the spin echo responses to 90°-τ-β⁰_φ pulse sequences of quadrupolar spins coupled through dipolar interactions. The second moments of the correlation function are calculated for a system of spin one nuclei and shown to be in accordance with the experimental observations. Furthermore, results are presented for the fourth moments.     

Aging in the glass phase of a two-dimensional random periodic elastic system

Using the renormalization group method we investigate the nonequilibrium relaxation of the (Cardy-Ostlund) 2D random sine-Gordon model, which describes pinned arrays of lines. Its statics exhibit a marginal (theta = 0) glass phase for T < Tg described by a line of fixed points. We obtain the universal scaling functions for two-time dynamical response and correlations near Tg for various initial conditions, as well as the autocorrelation exponent. The fluctuation dissipation ratio is found to be nontrivial and continuously dependent on T.     

A theoretical study of the long-range-disorder mixed-spin antiferromagnet L2BaNiO5

In this paper, we introduce a quasi-one-dimensional S = 1 antiferromagnet Heisenberg model, and some physical properties of antiferromagnet L₂BaNiO₅ without antiferromagnet long-range-order above the Néel temperature are analyzed based on the frame of two-time Green’s function theory. In a high temperature region, we calculate the correlation functions, and obtain excitation spectrum along Ni chains and the Haldane gap in this spectrum versus temperature. We find that the short-range correlation still exists at high temperature, which leads to the existence of Haldane gap in excitation spectrum. The increment of excitation energy in the spectrum along the Ni chain is found to be induced by the AF interaction between spins of rare-earth and Ni ions. Additionally, we also find that Haldane gap goes up with temperature increasing.