Self-organization of charged particles on a two-dimensional lattice subject to anisotropic Jahn-Teller-type interaction and three-dimensional Coulomb repulsion

2007 ◽  
Vol 76 (5) ◽  
Author(s):  
T. Mertelj ◽  
V. V. Kabanov ◽  
J. Miranda Mena ◽  
D. Mihailovic
Keyword(s):  
Three Dimensional ◽  
Charged Particles ◽  
Coulomb Repulsion ◽  
Self Organization ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Jahn Teller ◽  
Type Interaction

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

Two-dimensional zeolite-like network in the new caesium copper aluminate Cs2CuAl4O8

2015 ◽  
Vol 71 (5) ◽  
pp. 498-506 ◽  
Author(s):  
Larisa Shvanskaya ◽  
Olga Yakubovich ◽  
Werner Massa ◽  
Alexander Vasiliev
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Double Layers ◽  
Two Dimensional ◽  
Magnetic Subsystem ◽  
Jahn Teller ◽  
Copper Aluminate ◽  
Jahn Teller Effect ◽  
Phosphate Flux ◽  
Temperature Crystallization

Monoclinic dicaesium copper tetraaluminate, Cs2CuAl4O8, space groupP21/c,a= 8.4551 (7),b= 10.012 (1),c= 17.073 (2) Å, β = 101.643 (9)°,Z= 6, was obtained by high-temperature crystallization from a phosphate flux. Its microporous crystal structure presents the first example of double layers built from [AlO4] tetrahedra combined in 4-, 6- and 8-rings, topologically similar to those found in theATT-type zeolites and isostructural minerals armstrongite, davanite and dalyite. These layers show a rare arrangement of three [AlO4] tetrahedra sharing one oxygen vertex. The aluminate slabs are further linked by chains of edge-sharing [CuO4] square planes to form a mixed anionic three-dimensional framework with Cs+cations in channels and cavities. An unusually short Cu...Cs distance of 3.166 Å is ascribed to the strong Jahn–Teller effect of Cu2+. The magnetic subsystem demonstrates properties of an alternating antiferromagnetic chain with a gap in the spectrum of magnetic excitations.

A COMPARISON BETWEEN THE TWO-DIMENSIONAL AND THREE-DIMENSIONAL LATTICES

2004 ◽  
Vol 18 (25) ◽  
pp. 1301-1309 ◽  
Author(s):  
ANDREI DOLOCAN ◽  
VOICU OCTAVIAN DOLOCAN ◽  
VOICU DOLOCAN
Keyword(s):  
Lattice Constant ◽  
Cohesive Energy ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Coupling Constant ◽  
Dimensional Lattice ◽  
Analytical Formulae ◽  
Three Dimensional Space

By using a new Hamiltonian of interaction we have calculated the interaction energy for two-dimensional and three-dimensional lattices. We present also, approximate analytical formulae and the analytical formulae for the constant of the elastic force. The obtained results show that in the three-dimensional space, the two-dimensional lattice has the lattice constant and the cohesive energy which are smaller than that of the three-dimensional lattice. For appropriate values of the coupling constants, the two-dimensional lattice in a two-dimensional space has both the lattice constant and the cohesive energy, larger than that of the two-dimensional lattice in a three-dimensional space; this means that if there is a two-dimensional space in the Universe, this should be thinner than the three-dimensional space, while the interaction forces should be stronger. On the other hand, if the coupling constant in the two-dimensional lattice in the two-dimensional space is close to zero, the cohesive energy should be comparable with the cohesive energy from three-dimensional space but this two-dimensional space does not emit but absorbs radiation.

A POSSIBLE PAIRING MECHANISM FOR HTSC: TWO-DIMENSIONAL CONFINEMENT AND COULOMB OVER-SCREENING

1999 ◽  
Vol 13 (29n31) ◽  
pp. 3472-3477 ◽  
Author(s):  
D. ARIOSA ◽  
H. BECK
Keyword(s):  
Mean Field ◽  
Three Dimensional ◽  
Critical Density ◽  
Zero Point ◽  
Coulomb Repulsion ◽  
Two Dimensional ◽  
Pairing Mechanism ◽  
Density Region ◽  
Point Energy ◽  
Localization Energy

Among all the common properties of HTCS cuprates, we build our model on two of them: their high anisotropy, and their extremely low density of charge carriers. The intra-layer pairing mechanism is provided by the two-dimensional over-screening of Coulomb repulsion.1,2 The c-axis zero point energy restricts this pairing to a low carrier density region. Below a critical density, the system behaves as a two-dimensional confined jellium where the energy gain due to charge pairing is larger than the c-axis localization energy. In the high density region, where the pairing energy cannot compensate the localization energy, the system delocalizes and crosses over to a three-dimensional regime. This competition between binding and confinement energies implies a monotonic decrease of mass anisotropy with doping. Pre-formed pairs which exist below a Mean Field (MF) temperature defined by the binding energy, account for pseudo-gap observations.3,4 The superconducting critical temperature T c is given by the Beresinskii–Kosterlitz–Thouless (BKT) transition of the two-dimensional layer, renormalized by quantum phase fluctuations (QPF).5 QPF account for the metal-insulator transition at very low doping.

(TP-EDOT)2PF6—Two-dimensional spin array in a three-dimensional lattice

2006 ◽  
Vol 142 (3-4) ◽  
pp. 285-290
Author(s):  
H. Yamochi ◽  
M. Soeda ◽  
J. Hagiwara ◽  
G. Saito
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Lattice

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1059-1073 ◽  
Author(s):  
G. Knorr ◽  
J. P. Lynov ◽  
H. L. Pécseli
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Self Organization ◽  
Two Dimensional ◽  
Hydrodynamic Turbulence ◽  
Available Energy ◽  
Wave Numbers ◽  
Negative Helicity ◽  
Incompressible Euler

Abstract The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.

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