Critical point estimation and long-range behavior in the one-dimensional XY model using thermal quantum and total correlations

We investigate the thermal quantum and total correlations in the anisotropic XY spin chain in transverse field. While we adopt concurrence and geometric quantum discord to measure quantum correlations, we use measurement-induced non-locality and an alternative quantity defined in terms of Wigner–Yanase information to quantify total correlations. We show that the ability of these measures to estimate the critical point at finite temperature strongly depend on the anisotropy parameter of the Hamiltonian. We also identify a correlation measure which detects the factorized ground state in this model. Furthermore, we study the effect of temperature on long-range correlations.     

Special facets of diffusion and energy transfer in macromolecular systems

We consider energy transfer in polymers in dilute solutions and model it as a purely incoherent, hopping exciton motion which ends at permanent traps, whose positions along the polymer chain are fixed. The transport involves not only steps along the chain but also steps between sites which are far away along the chain's backbone but near to each other in Euclidean space. This possibility leads to very peculiar features of the excitation’s diffusion along the chain, due to strong correlations between subsequent steps. The process depends strongly on whether the chain is frozen or moves. We show that conformational changes influence trapping strongly, even if they are relatively slow on the time scale of the hopping motion. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997.     

Random Wavelet Series Based on a Tree-Indexed Markov Chain

We study the global and local regularity properties of random wavelet series whose coefficients exhibit correlations given by a tree-indexed Markov chain. We determine the law of the spectrum of singularities of these series, thereby performing their multifractal analysis. We also show that almost every sample path displays an oscillating singularity at almost every point and that the points at which a sample path has at most a given Hölder exponent form a set with large intersection.     

Quantification of entanglement from magnetic susceptibility for a Heisenberg spin 1/2 system

We report temperature and magnetic field dependent magnetization and quantification of entanglement from the experimental data for dichloro (thiazole) copper (II), a Heisenberg spin chain system. The plot of magnetic susceptibility vs. temperature indicates an infinite spin chain. Isothermal magnetization measurements (as functions of magnetic field) were performed at various temperatures below the antiferromagnetic (AFM) ordering, where the AFM correlations persist significantly. These magnetization curves are fitted to the Bonner–Fisher model. Magnetic susceptibility is used as an entanglement witness to quantify the amount of entanglement in the system.     

Sequencing-independent delocalization in a DNA-like double chain with base pairing

The question of whether or not DNA is intrinsically conducting is still a challenge. The ongoing debate on DNA molecules as an electronic material has so far underestimated a key distinction of the system: the role of base pairing in opposition to correlations along each chain. We show that a disordered base paired double chain presents truly or, at least, effectively delocalized states. This effect is irrespective to the sequencing along each chain.     

Off equilibrium dynamics in disordered quantum spin chain

We study the non-equilibrium time evolution of the average transverse magnetisation and end-to-end correlation functions of the random Ising quantum chain. Starting with fully magnetised states, either in the x or z direction, we compute numerically the average quantities. They show similar behaviour to the homogeneous chain, that is an algebraic decay in time toward a stationary state. During the time evolution, the spatial correlations, measured from one end to the other of the chain, are building up and finally at long time they reach a size-dependent constant depending on the distance from criticality. Analytical arguments are given which support the numerical results. Received 11 July 2002 / Received in final form 9 September 2002 Published online 29 October 2002     

Competition of isoscalar and isovector proton-neutron pairing in nuclei

We use shell model techniques in the complete pf shell to study pair correlations in nuclei. Particular attention is paid to the competition of isoscalar and isovector proton-neutron pairing modes which is investigated in the odd-odd N = Z nucleus ⁴⁶V and in the chain of even Fe-isotopes. We confirm the dominance of isovector pairing in the ground states. An inspection of the level density and pair correlation strength in ⁴⁶V, however, shows the increasing relative importance of isoscalar correlations with increasing excitation energy. In the Fe-isotopes we find the expected strong dependence of the proton-neutron isovector pairing strength on the neutron excess, while the dominant J = 1 isoscalar pair correlations scale much more gently with neutron number. We demonstrate that the isoscalar pair correlations depend strongly on the spin-orbit splitting.     

一维长程关联无序系统中的电子态

利用傅里叶滤波法在一维Anderson无序系统中产生了具有幂律谱密度公式s(q)∝q^-p形式的长程关联随机能量序列，并利用传输矩阵方法计算了系统中引入了长程关联后的局域长度，同时应用负本征值理论对系统中的电子态密度进行了分析，并分别把计算结果与系统中不具有长程关联时的局域长度与电子态密度进行了比较.结果表明，长程幂律关联的引入对电子态的性质产生了很大的影响，当关联指数p≥2.0时，在系统能带中心范围内发生了部分局域态向退局域态的转变，而同时电子态密度也发生了很大的变化，出现了六个范霍夫奇点，系统的能带范围也相应地得到展宽. 关键词： 无序系统 长程关联 局域长度 电子态密度     

Entanglement in One-Dimensional Anderson Model with Long-Range Correlated Disorder

By using the measure of concurrence, the entanglement of the ground state in the one-dimensional Anderson model is studied with consideration of the long-range correlations. Three kinds of correlations are discussed. We compare the effects of the long-rang Gaussian and power-law correlations between the site energies on the concurrence, and demonstrate the existence of the band structure of the concurrence in the power-law case. The emergence of the sharp kink on the concurrence curve shown in the intraband or in the interband indicates the position at which the localization extent of the state may have the severe variation. We use the Rudin-Shapiro model to describe the site energy distribution of the nucleotides of the DNA chain： guanine （G）, adenine （A）, cytosine（C）, thymine （T）. This model is a tetradic quasiperiodic sequence and is shown to be long-range correlated. Our results show that correlations between the site energies increase the concurrences.     

Density functional theory for polyelectrolytes near oppositely charged surfaces

We report a nonlocal density functional theory of polyelectrolyte solutions that faithfully accounts for both short- and long-range correlations neglected in a typical mean-field method. It is shown that for systems with strong electrostatic interactions, the long-range correlations are subdued by direct Coulomb attractions, thereby manifesting strong local excluded-volume effects. The theory has also been used to describe the influence of the polyion chain length and small ion valence on charge inversion due to the adsorption of polyelectrolytes at an oppositely charged surface.     

Charge distribution and correlation functions near the boundary of a weakly nonideal plasma

We consider the electric double layer formed near the boundary of a weakly nonideal multicomponent classical plasma as a result of interparticle correlations. On the basis of the generalized plasma uncoupling of the equilibrium chain of BBGKY equations, which correctly takes into account correlations of particles at small distances, we find the two-particle and one-particle correlation functions near the surface of the plasma. The asymptotic form of the two-particle correlation function along the boundary of the plasma falls off as the power law 1/r³. The solution obtained here is qualitatively consistent with earlier results, but it takes into account particle correlations at small distances and hence does not have a singularity at the boundary of the plasma. Therefore in a charge-asymmetric plasma there are two correlation radii, the Debye radius D and the radius /tr2D. The thermodynamic functions of the surface layer are calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 72–77, March, 1989.     

Operator product expansion on a fractal: The short chain expansion for polymer networks

We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show factorization of its partition sum by a short chain factor and a long chain factor in the short chain limit. This corresponds to an expansion for short distance along the fractal perimeter of the polymer chains connecting the network vertices and is related to a large mass expansion of field theory.

The scaling of the second virial coefficient for bimodal solutions is explained. Our method also applies to the correlations of the multifractal measure of harmonic diffusion onto an absorbing polymer. We give a result for expanding these correlations for short distance along the fractal carrier of the measure.     

One-way quantum deficit and quantum coherence in the anisotropic <Emphasis Type="Italic">XY</Emphasis> chain

In this study, we investigate pairwise non-classical correlations measured using a one-way quantum deficit as well as quantum coherence in the XY spin-1/2 chain in a transverse magnetic field for both zero and finite temperatures. The analytical and numerical results of our investigations are presented. In the case when the temperature is zero, it is shown that the one-way quantum deficit can characterize quantum phase transitions as well as quantum coherence. We find that these measures have a clear critical point at λ = 1. When λ ≤ 1, the one-way quantum deficit has an analytical expression that coincides with the relative entropy of coherence. We also study an XX model and an Ising chain at the finite temperatures.     

Transient motions of bi-lattices

We develop formal solutions for the propagation of transient pulses on a variety of bi-lattice models. The lattices are composed of a finite homogeneous chain connected in series with a different semi-infinite homogeneous chain at a common location occupied by a single mass which is different from the masses of both chains. Exact analytic solutions of this general case are not possible. Some analytic solutions are, however, possible for a variety of special cases. The general solutions are illustrated by numerically inverting the Laplace transform functions. The exact solutions are found to correlate very well with the numerical inversion scheme. Such correlations give confidence in the numerical scheme's predictions of the solutions of the more complicated chains.     

海森堡XYZ自旋链系统的热纠缠与局域量子不确定性研究

研究了热平衡温度,自旋交换相互作用,Dzyaloshinskii-Moriya(DM)相互作用及外加非一致性磁场对两比特海森堡XYZ自旋链量子系统的热纠缠与局域量子不确定度的影响,对比分析了并发度量子纠缠与局域量子不确定度描述自旋链系统量子关联的差别.结果表明自旋链系统的量子纠缠在热平衡温度,DM相互作用及外加磁场的非一致性参数的变化情况下均会出现纠缠突然死亡的再生现象,而自旋链系统的局域量子不确定度随着这些参数呈连续变化现象.并且,自旋交换相互作用,DM相互作用及外加横向磁场作用强度较小时,他们的变化对自旋链系统的量子纠缠与局域量子不确定度的影响有着明显的差别.     

Exact asymptotic behavior of correlation functions for disordered spin-1/2 XXZ chains

We consider an XXZ spin-1/2 chain in the presence of several types of disorder that do not break the XY symmetry of the system. We calculate the complete asymptotic form of the spin-correlation functions at zero temperature at the transition between liquid and disordered phase that occurs for a special value of anisotropy in the limit of small disorder. Apart from a universal power law decay of correlations, we find additional logarithmic corrections due to marginally irrelevant operator of disorder.     

Finite-size scaling for correlations of quantum spin chains at criticality

We study the finite-size scaling behavior of two-point correlation functions of translationally invariant many-body systems at criticality. We propose an efficient method for calculating the two-point correlation functions in the thermodynamic limit from numerical data of finite systems. Our method is most effective when applied to a two-dimensional (classical) system which possesses a conformal invariance. By using this method with numerical data obtained from exact diagonalizations and Monte Carlo simulations, we study the spin-spin correlations of the quantum spin-1/2 and-3/2 antifierromagnetic chains. In particular, the logarithmic corrections to power-law decay of the correlation of the spin-1/2 isotropic Heisenberg antiferromagnetic chain are studied thoroughly. We clarify the cause of the discrepancy in previous calculations for the logarithmic corrections. Our result strongly supports the field-theoretic prediction based on the mappings to the Wess-Zumino-Witten nonlinear -model or the sine-Gordon model. We also treat logarithmic corrections and crossover phenomena in the spin-spin correlation of the spin-3/2 isotropic Heisenberg antiferromagnetic chain. Our results are consistent with the Affleck-Haldane prediction that the correlation of the spin-3/2 chain exhibits a crossover to the same asymptotic behavior as in the spin-1/2 chain.     

Harmonic Systems with Bulk Noises

We consider a harmonic chain in contact with thermal reservoirs at different temperatures and subject to bulk noises of different types: velocity flips or self-consistent reservoirs. While both systems have the same covariances in the non-equilibrium stationary state (NESS) the measures are very different. We study hydrodynamical scaling, large deviations, fluctuations, and long range correlations in both systems. Some of our results extend to higher dimensions.     

Quasi-particle properties in a quasi-two-dimensional electron liquid

We consider the quasi-particle properties such as the effective mass and spin susceptibility of quasi-two-dimensional electron systems. The finite quantum well width effects are incorporated into the local-field factors that describe the charge and spin correlations. We employ the Fermi-hypernetted chain formalism in conjunction with fluctuation-dissipation theorem to obtain the local-field factors. Our results are in good agreement with recent experiments.