Long-Range Correlations between Observables in a Model with Translational Invariance in Rapidity

We estimate the impact of the fixation of the total number of sources (quark–gluon strings) on the long-range rapidity correlations between different observables. In our approach this condition models the fixation of the collision centrality class, what is the usual practice in modern collider experiments, like Relativistic Heavy Ion Collider (RHIC), Large Hadron Collider (LHC) and so on. The estimates are obtained under the assumption of the translational invariance in rapidity, which is usually assumed in mid-rapidity region at high energies. Based on these assumptions, we are developing a technique for the analytical calculation of various average values of extensive and intense variables at high string densities on the transverse lattice, taking into account the effects of string fusion, leading to the formation of string clusters. Using this technique we calculate the asymptotes of the correlations coefficients both between the multiplicities and between the multiplicity and the event-mean transverse momentum of particles in two separated rapidity intervals. As a result, we found that fixing the total number of strings has a significant effect on the behavior of both types of correlations, especially in the case of a uniform distribution of strings in the transverse plane.

Metastability and avalanche dynamics in strongly correlated gases with long-range interactions

We experimentally study the stability of a bosonic Mott insulator against the formation of a density wave induced by long-range interactions and characterize the intrinsic dynamics between these two states. The Mott insulator is created in a quantum degenerate gas of 87-Rubidium atoms, trapped in a 3D optical lattice. The gas is located inside and globally coupled to an optical cavity. This causes interactions of global range, mediated by photons dispersively scattered between a transverse lattice and the cavity. The scattering comes with an atomic density modulation, which is measured by the photon flux leaking from the cavity. We initialize the system in a Mott-insulating state and then rapidly increase the global coupling strength. We observe that the system falls into either of two distinct final states. One is characterized by a low photon flux, signaling a Mott insulator, and the other is characterized by a high photon flux, which we associate with a density wave. Ramping the global coupling slowly, we observe a hysteresis loop between the two states—a further signature of metastability. A comparison with a theoretical model confirms that the metastability originates in the competition between short- and global-range interactions. From the increasing photon flux monitored during the switching process, we find that several thousand atoms tunnel to a neighboring site on the timescale of the single-particle dynamics. We argue that a density modulation, initially forming in the compressible surface of the trapped gas, triggers an avalanche tunneling process in the Mott-insulating region.

Asymptotes of multiplicity and transverse momentum correlation coefficients at large string density

The multiple hadron production in high energy collisions is studied in the model with string fusion on transverse lattice. In the framework of the model the asymptotes of the correlation coefficients between the mean transverse momentum and the multiplicity and between the mean transverse momenta for realistic case of non-uniform string distribution in transverse plane were calculated. The results were obtained by two different methods using the alternative definitions of the correlation coefficients. It is shown that the asymptotes of the correlation coefficients obtained by these two methods coincide in the leading approximation. The examples with non-uniform string distribution in transverse plane were considered. Strong dependence of the correlation coefficient between the transverse momentum and a multiplicity on non-uniformity in the distribution of the strings was found. In particular it is shown that there are distributions of strings for which this coefficient becomes negative. For the correlation coefficient between transverse momenta its dependence on the scaled variance of the number of particles produced from a single string, which disappears in the case of a homogeneous string distribution, is analyzed. The analytical asymptote for the correlation coefficient between transverse momenta obtained at large string density are compared with the results of the MC numerical calculations of this coefficient.

Crystallographic Features of the Charge-Orbital-Ordered State in the Highly-Correlated Electronic System Ca1-xPrxMnO3

The charge-exchange-type orbital-ordered (CEOO) state accompanying antiferromagnetic ordering has been reported in the highly-correlated electronic system Ca1-xPrxMnO3(CPMO) with the simple perovskite structure. The feature of the CEOO state in CPMO is that the state is present in the wide Pr-content range of 0.30 ≤x≤ 0.70. Although the Zener-polaron model was proposed for the CEOO state atx= 0.60, the detailed features of the CEOO state, particularly for lower Pr contents, have not been understood sufficiently. We have thus investigated the crystallographic features of the CEOO state in CPMO with 0.40 ≤x≤ 0.50, mainly by transmission electron microscopy. It was found that, when the temperature was lowered from the disordered state, incommensurate satellite reflections characterizing the CEOO state appeared in electron diffraction patterns below about 250 K in CPMO. The careful analysis of the reflections indicated that the CEOO state for 0.40 ≤x≤ 0.45 was different from that for 0.45 ≤x≤ 0.50. Concretely, the former CEOO state accompanied only a transverse lattice modulation, while both transverse and longitudinal modulations with different wave vectors appeared in the latter state. This implies that the state for 0.40 ≤x≤ 0.45 can be regarded as an orbital-modulated (OM) state without a charge modulation. It is thus understood that an increase in the Pr content leads to the OM-to-CEOO state change below about 250 K aroundx= 0.45.

Crystallographic Features of the C-Type Orbital-Ordered, and Charge- and Orbital-Ordered States in the Simple Perovskite Manganite Ca1-xLaxMnO3

The C-type orbital-ordered (CTOO), and charge-and orbital-ordered (COO) states are present in the simple perovskite manganite Ca1-xLaxMnO3, which has a three-dimensional highly-correlated electronic system. In this study, the crystallographic features of the CTOO and COO states have been investigated mainly by transmission electron microscopy to understand responses of a lattice system to these orderings. Of these two states, the cooling from the disordered orthorhombic Pnma (DO) state around x = 0.20 resulted in the CTOO state with the monoclinic P21/m symmetry. As a result of the monoclinic distortion as a response of the lattice system, the CTOO state consisted of a banded structure that was characterized by an alternating array of two monoclinic domains with different β values. In 0.30 < x < 0.50, on the other hand, the appearance of the COO state from the DO state on cooling accompanied a transverse lattice modulation with q = []DO as a response to orbital ordering in the COO state. The subsequent cooling in the COO state led to the antiferromagnetic ordering with a large lattice dilatation. In other words, no change in the crystal symmetry occurs in the appearance of the antiferromagnetic ordering.

FEYNMAN PERTURBATION THEORY FOR GAUGE THEORY ON TRANSVERSE LATTICE

Feynman perturbation theory for non-Abelian gauge theory in light-like gauge is investigated. A lattice along two spacelike directions is used as a gauge invariant ultraviolet regularization. For preservation of the polynomiality of action, we use as independent variables arbitrary (nonunitary) matrices related to the link of the lattice. The action of the theory is selected in such a way to preserve as much as possible the rotational invariance, which remains after an introduction of the lattice, as well as to make superfluous degrees of freedom vanish in the limit of removing the regularization. Feynman perturbation theory is constructed and diagrams which does not contain ultraviolet divergences are analyzed. The scheme of renormalization of this theory is discussed.