A renormalization procedure for the correlation function theory of finite Fermi systems

The quasiparticle renormalization of symmetrized correlation functions is treated in the framework of the double-time Green function theory of many body systems. The work is based on the Mori-theory of response functions transcribed for symmetrized correlation functions. For the specific example of finite Fermi systems it is shown that the physical situation assumed in the quasiparticle-quasihole renormalization of the many-time Green function theory allows to define an equivalent renormalization procedure for correlation functions. This procedure uses projection operator techniques and is therefore of purely algebraic nature.     

Correlation functions of infinite system of interacting Brownian particles; Local in time evolution close to equilibrium

The time-dependent correlation functions of infinite nonequilibrium systems of interacting diffusing particles are obtained in the thermodynamic limit in the case when the initial correlation functions coincide with the equilibrium correlation functions of the Gibbs system in an external field.     

中性孤子的关联函数

本文研究了自旋非简并体系的关联函数,用来讨论了中性孤子(孤子能级上只有一个正自旋电子)的带自旋的关联函数,在Hartree-Fock(HF)近似下求得各种自旋关联函数的图象,并讨论了这些关联函数的性质。 关键词：     

Single-site- and single-atom-resolved measurement of correlation functions

Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.     

Uniform upper bounds (and thermodynamic limit) for the correlation functions of symmetric coulomb-type systems

Uniform upper bounds are proven for the correlation functions in the strictly charge-neutral canonical and grand canonical ensembles for charge-symmetric two-component systems. For the grand canonical ensemble the increase of the correlation functions along the thermodynamic-limit sequence is shown as well, implying the existence of the states. The particles have bounded pair interactions of positive type. Both classical and quantum systems with Boltzmann statistics are considered. Coulomb systems with regularized interactions are included as a special case.     

Correlation functions of a lattice system

We deduce an integral equation for the infinite volume correlation functions of a class of lattice systems and we apply it to find results on the analyticity in the interaction potentials of the pressure and of the correlation functions and on the ergodicity of the equilibrium states in the gaseous phase. By similar methods we prove some cluster properties for the correlation functions in the gaseous phase.     

General correlation functions of the Clauser-Horne-Shimony-Holt inequality for arbitrarily high-dimensional systems

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two dimensions. This inequality is optimal in the same sense as the CHSH inequality for two-dimensional systems, namely, the maximal amount by which the inequality is violated consists of the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)]].     

Zur theorie polarer multikomponentsysteme

A fluid mixture consisting of molecules with permanent electric dipole moment and scalar polarizability is described by means of correlation functions. To analyse the two-particle correlation functions we extend the graph-theoretical conception developed by Wertheim in the case of multicomponent systems by using graphs with colored points. In order to carry out a topological reduction of these sets of colored graphs the corresponding functions are found to be matrices or tensors. By the aid of a new connecting formalism the tensor notation preserves the structure of the equations in the analysis of correlation functions. These functions can be separated with respect to the range of interactions involved. Then, in applying the results to the case of a polar multicomponent mixture we can derive equations for the dielectric constant of systems consisting of both rigid and polarizable dipoles. These equations involve a correlation factor matrix which is the multicomponent equivalence of the Kirkwood factor. The dielectric expressions are used to obtain dipolar contributions to the Helmholtz free energy of mixing.     

Soliton contribution to correlations in a system of coupled chains

A model representing a two- or a three-dimensional array of classical harmonic chains withnonlinear coupling between them is investigated. Physically real systems to which this model applies are discussed. The model exhibits soliton-like nonlinear modes. The influence of these nonlinear modes on the static and the dynamic correlation functions is calculated by generalizing techniques developed for strictly one-dimensional systems. In the static correlation functions these modes lead to minor quantitative changes only. In certain dynamic correlation functions, however, a central peak is found to occur due to the nonlinear modes. The total weight and the width of this peak are calculated for a real spin system.     

Electron-proton correlation for hydrogen tunneling systems

Hydrogen tunneling is important for numerous chemical and biological processes. We study this phenomenon with a multiconfigurational nuclear-electronic orbital approach. Our results demonstrate that a single configuration nuclear-electronic wave function is inadequate to describe hydrogen tunneling systems because such wave functions do not include the essential electron-proton correlation. A state-averaged multiconfigurational approach is proposed as a practical method for potentially including sufficient electron-proton correlation to obtain delocalized nuclear-electronic wave functions for these systems.     

Decay of correlations in Fermi systems at nonzero temperature

The locality of correlation functions is considered for Fermi systems at nonzero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at nonzero temperature.     

Mean relaxation time approximation for dynamical correlation functions in stochastic systems near instabilities

We present a simple approximation for dynamical correlation functions in stochastic systems which reproduces the high as well as the low frequency behaviour of the exact correlation functions. The approximation is applied in its lowest order to diffusion in a quartic potential and to autocatalytic chemical reaction systems as described by the Schlögl models. The results are compared to those from the conventional Mori-Zwanzig projection operator approach which reproduces only the short-time relaxation of the systems considered. The new approximation describes correctly slow relaxation processes, e.g. barrier crossing in a quartic potential and the slowing down of dynamic processes in finite autocatalytic systems near first and second order transitions.     

关于光学系统中空间关联函数的位相恢复问题

本文把文献[1]中提出的振幅和位相恢复问题的一般表述用于处理空间关联函数位相的恢复问题,类似于文献[1],得到了一组确定位相的方程,用该方程组和迭代求解法,可以求解空间关联函数的位相,但本文不假定传输矩阵R是幺正的。可以证明,如果R是幺正矩阵,在相干极限下,本文的方程组回到文献[1]中的相应方程。 关键词：     

A statistical test of Anderson localization

Numerical demonstrations of localization in random systems are difficult to obtain and interpret because of statistical fluctuations in the electron probability density. This difficulty can be avoided through the use of correlation functions defined in terms of the electron probability density. The fluctuations can then be eliminated by averaging over a large number of Anderson Hamiltonians. The resulting averaged correlation functions clearly show that electrons are exponentially localized. The localization demonstrated here is sufficient to insure a zero dc conductivity in the limit of large systems.     

Gaussian bounds for correlations in lattice spin systems

In quite generalN-component ferromagnetic spin systems, it is proved that an arbitrary correlation function is bounded by the corresponding correlation function of a Gaussian model. The bound is useful for the analysis of high-temperature behavior of the system. Similar bounds for truncated correlation functions are also obtained for a class of single-component spin systems.     

Effect of short and long range forces on the structure of water. II. Orientational ordering and the dielectric constant

The effects of short and long range interactions on the structure of water, both spatial and orientational, has been studied in detail by computing the full pair correlation function, site-site correlation functions, 2-dimensional site-site correlation functions in the (r _OO, r _OH) and (r _OO, r _HH) planes, dipole-dipole correlation function, radial Kirkwood g factor, and the dielectric constant. Two model potentials, the T1P4P and ST2, and their short range versions have been considered at ambient and elevated temperatures and under supercritical conditions. The Ewald summation under different conditions has been used to investigate also their effect on results. An analysis of the results shows that although all site-site correlation functions for the short and long range systems are similar, the orientational ordering in systems of different range may be considerably different, this evidence being provided mainly by the dipole-dipole correlation function and the radial Kirkwood factor. The orientational ordering is only short range in long range systems, whereas in short range systems the hydrogen bonding gives rise to a damped long range regular pattern of alignment. Nonetheless, the resulting dielectric constants for the short and long range systems coincide within the combined error bars. All findings are more pronounced at low temperatures but otherwise they are only marginally temperature and density dependent.     

Efficient evaluation of partition functions of inhomogeneous many-body spin systems

We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments.     

Correlation inequalities and the thermodynamic limit for classical and quantum continuous systems II. Bose-Einstein and Fermi-Dirac statistics

We study quantum mechanical systems of particles with Bose or Fermi statistics interacting via two-body potentials of positive type in thermal equilibrium. We rewrite partition functions, reduced density matrices (RDMs), and correlation functions in terms of Wiener and Gaussian functional integrals (sine-Gordon transformation). This permits us, e.g., to apply correlation inequalities. Our main results include an analysis of stability versus instability in the grand canonical ensemble and, for charge-conjugation-invariant systems, upper and lower bounds on RDMs, the existence of the thermodynamic limit of pressure, RDMs and correlation functions, an inequality comparing correlations with Fermi statistics to ones with Bose statistics, and inequalities which are important in the study of Bose-Einstein condensation and of superconductivity.This research was done in part during the author's stay at the Department of Physics of Princeton University and was partially supported by the NSF under grant NSF PHY 76-80958.     

Exciton correlations and input–output relations in non-equilibrium exciton superfluids

The photoluminescence (PL) measurements on photons and the transport measurements on excitons are the two types of independent and complementary detection tools to search for possible exciton superfluids in electron–hole semi-conductor bilayer systems. In fact, it was believed that the transport measurements can provide more direct evidences on superfluids than the spectroscopic measurements. It is important to establish the relations between the two kinds of measurements. In this paper, using quantum Heisenberg–Langevin equations, we establish such a connection by calculating various exciton correlation functions in the putative exciton superfluids. These correlation functions include both normal and anomalous greater, lesser, advanced, retarded, and time-ordered exciton Green functions and also various two exciton correlation functions. We also evaluate the corresponding normal and anomalous spectral weights and the Keldysh distribution functions. We stress the violations of the fluctuation and dissipation theorem among these various exciton correlation functions in the non-equilibrium exciton superfluids. We also explore the input–output relations between various exciton correlation functions and those of emitted photons such as the angle resolved photon power spectrum, phase sensitive two mode squeezing spectrum and two photon correlations. Applications to possible superfluids in the exciton–polariton systems are also mentioned. For a comparison, using conventional imaginary time formalism, we also calculate all the exciton correlation functions in an equilibrium dissipative exciton superfluid in the electron–electron coupled semi-conductor bilayers at the quantum Hall regime at the total filling factor ν_T=1${\nu }_T=1$. We stress the analogies and also important differences between the correlations functions in the two exciton superfluid systems.