Stronger-Than-Quantum Correlations

After an elementary derivation of Bell's inequality, classical, quantum mechanical, and stronger-than-quantum correlation functions for 2-particle-systems are discussed. Special functions are investigated which give rise to an extreme violation of Bell's inequality by the value of 4. Referring to a specific quantum system it is shown that under certain conditions such an extreme violation would contradict basic laws of physics.     

Correlations in Werner States

Werner states are paradigmatic examples of quantum states and play an innovative role in quantum information theory. In investigating the correlating capability of Werner states, we find the curious phenomenon that quantum correlations, as quantified by the entanglement of formation, may exceed the total correlations, as measured by the quantum mutual information. Consequently, though the entanglement of formation is so widely used in quantifying entanglement, it cannot be interpreted as a consistent measure of quantum correlations per se if we accept the folklore that total correlations are measured （or rather upper bounded） by the quantum mutual information.     

Correlations in quantum dots

The lowest excitations of a repulsively interacting few particle system are investigated within correlated “pocket state” basis functions. For long range interaction and non-isotropic confining potentials the method becomes exact, in the limit of large mean inter-particle distancesr _s. The multiplet structure of the many-electron energy levels is explained and the ratios δ between the lowest excitation energies, which are related to the electron spin, are determined quantitatively using group theoretical means. The δ are independent of the detailed form of the inter-particle repulsion and of sufficiently larger _s. The obtained δ-values are confirmed by available numerical data. The method is applied to 1D and 2D quantum dots.     

Correlations in nuclear masses

It was recently suggested that the error with respect to experimental data in nuclear mass calculations is due to the presence of chaotic motion. The theory was tested by analyzing the typical error size. A more sensitive quantity, the correlations of the mass error between neighboring nuclei, is studied here. The results provide further support to this physical interpretation.     

Correlations in ternary fission

An experiment investigating correlations in ternary fission of²³³U induced by cold polarized neutrons was performed at the high flux reactor of the ILL in Grenoble (France). With the experimental setup, Left—Right and time reversal symmetry violating and conserving correlations between neutron spin $\hat \sigma $ , neutron momentum $\hat p_n $ , momenta of fission fragments $\hat p_f $ and ternary particles $\hat p_t $ could be investigated.     

Correlations beyond the horizon

It is a fundamental feature of quantum field theory that correlations between observable quantities occur over all spacetime regions. In particular, in cosmological models with horizons, such correlations will be present in regions which lie outside of each other's horizon. Such correlations may play an important role in processes occurring in the early universe.This essay received the first award from the Gravity Research Foundation, 1992—Ed.     

Correlations in hypernuclear matter

We investigate short-range correlations in nuclear and hypernuclear matter. Self-energies due to short-range correlations and their influence on the nucleon and Λ -hyperon spectral functions are described in an approach accounting for a realistic treatment of mean-field dynamics and a self-consistently derived quasi-particle interaction. Landau-Migdal theory is used to derived the short-range interaction from a phenomenological Skyrme energy density functional, subtracting the long-range pionic contributions to the nucleonic spectral functions. We discuss our results for different hyperon-baryon ratios to show the influence of strangeness on the correlations in hypernuclear matter.     

Correlations in commodity markets

In this paper we analyzed dependencies in commodity markets, investigating correlations of future contracts for commodities over the period 1998.09.01-2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The tree provides evidence for sector clusterization of investigated contracts. We also studied dynamical properties of commodity dependencies. It turned out that the market was constantly getting more correlated within the investigated period, although the increase of correlation was distributed non-uniformly among all contracts, and depended on contracts branches.     

Correlations in charged bosons

A new chain diagram formula is derived for many-body systems in such a way that an ideal gas term does not explicitly appear. This form is simpler and more convenient than the previously known expression. The result is applied to a charged boson gas under different conditions. It is found that exponential type decrease of the correlations for large distances changes into 1/r⁸ type decrease at the transition point.     

Correlations in ballistic processes

We investigate a class of reaction processes in which particles move ballistically and react upon colliding. We show that correlations between velocities of colliding particles play a crucial role in the long time behavior. In the reaction-controlled limit when particles undergo mostly elastic collisions and therefore are always near equilibrium, the correlations are accounted analytically. For ballistic aggregation, for instance, the density decays as n approximately t(-xi) with xi=2d/(d+3) in the reaction-controlled limit in d dimensions, in contrast with the well-known mean-field prediction xi=2d/(d+2).     

Correlations in quantum dots

The lowest excitations of a repulsively interacting few particle system are investigated within correlated “pocket state” basis functions. For long range interaction and non-isotropic confining potentials the method becomes exact, in the limit of large mean inter-particle distancesr _s. The multiplet structure of the many-electron energy levels is explained and the ratios δ between the lowest excitation energies, which are related to the electron spin, are determined quantitatively using group theoretical means. The δ are independent of the detailed form of the inter-particle repulsion and of sufficiently larger _s. The obtained δ-values are confirmed by available numerical data. The method is applied to 1D and 2D quantum dots.     

Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently.The authors [Phys.Rev.A 88(2013) 034304] found that for some Bell-diagonal states(BDS)which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics,this phenomenon is known as the sudden change.Here in the present paper,we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs.Then,we find that basis change does not necessary mean sudden change of quantum correlations.     

Correlations Between Zeros and Supersymmetry

In our previous work [BSZ2], we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1 and 2. The purpose of this paper is to compute these universal limits in all dimensions and codimensions. First, we use a supersymmetry method to express the n-point correlations as Berezin integrals. Then we use the Wick method to give a closed formula for the limit pair correlation function for the point case in all dimensions. Received: 13 November 2000 / Accepted: 23 February 2001     

Correlations in inhomogeneous Ising models

We study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant either in horizontal or in diagonal direction, i.e. the models have a layered structure. By using transfer matrix techniques the spin-spin correlations are calculated parallel to the layering and are expressed as Toeplitz determinants. After working out the general methods we discuss two special examples in detail: the fully frustrated square lattice (FFS) and the chessboard model, both having no phase transition. At zero temperature correlations in the chessboard model decay exponentially, while in the FFS model one has algebraic decay with a critical index =1/2, i.e.T=0 is a critical point. At finite temperature we find exponential decay in both models with a correlation length determined by the excitation gap in the fermion spectrum. Due to frustration correlations may develop on oscillatory structure and spins separated by an odd diagonal distance are totally uncorrelated at all temperatures.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köla