Thouless

H at m energy of 1.2 eV in the center-of-mass frame. By using an atomic orbital basis and a representation of the electronic state of the system in terms of a Thouless determinant and the protons as classical particles, the leading term of the electronic state of the reactants is... 

In many ion-atom and ion-molecule collisions, one is often only interested in the projections on various charge states, which can be given a very simple treahnent. The Thouless determinant at separation of the two product fragments can be expressed as... 

D.J. Thouless, The Quantum Mechanics of Many-Body Systems (Academic Press, New York, 1961) pp. 88-93. 

The roughening transition itself is believed to be of the Kosterlitz-Thouless type , according to which one should expect the following properties ... 

The above results show that the APB undergoes a roughening transition at T j 1490 K, which is below the bulk first-order transition, and this transition is in agreement with the Kosterlitz-Thouless theory. In brief, the APB is flat below T j and, above T j, it develops transverse fluctuations and wanders through the lattice. 

ABBA molecules, 631-633 HCCS radical, 633-640 perturbative handling, 641-646 theoretical principles, 625-633 Hamiltonian equation, 626-628 vibronic problem, 628-631 Thouless determinantal wave function, electron nuclear dynamics (END) ... 

The Thouless determinantal electronic wave function z) = det Xi(xj) in Eq. (21) is an example of such proper parametrization. The dynamical spin orbitals are expressed in terms of atomic spin orbitals centered on the various nuclei... 

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

Kosterlitz-Thouless and commensurate-incommensurate transitions in the triangular lattice gas... 

It is not clear whether in the centered rectangular lattice gas of section 3.2 such a Kosterlitz-Thouless transition occurs, or whether the disordered phase extends, though being incommensurate, down to the commensurate (3x1) phase (then this transition is believed to belong to a new chiral universality class ), or whether there is another disorder line for (3 x 1) correlations. However, Kosterlitz-Thouless type transitions have been found for various two-dimensional models the XY ferromagnet , the Coulomb gas . ... 

Fig. 20. Phase diagram of the triangular lattice gas model with nearest-neighbor repulsion and next-nearest neighbor attraction, for JmJJ = — 1, in the coverage-temperature plane. For fl=0.5 a Kost tz-Thouless transition occurs at Ti and a commensurate-incommensurate transition at Tj. Two commensurate. 3 x 3 phases (with ideal coverages of 1/3 and 2/3, respectively) occur, as well as several two-phase regions, as indicated in the figure. Here l.g. stands for lattice gas and LI for lattice liquid . (From Landau. )...

In the flnite size scaling analysis Eqs. (36)-(38) need modiHcation at Kosterlitz-Thouless transitions the argument (1 — T/T )L or alternatively must be replaced by L/ itself since 1/v = 0, and Eq. (56) must be... 

While the (one-particle) Brillouin condition BCi has been known for a long time, and has played a central role in Hartree-Fock theory and in MC-SCF theory, the generalizations for higher particle rank were only proposed in 1979 [38], although a time-dependent formulation by Thouless [39] from 1961 can be regarded as a precursor. 

D. J. Thouless, The Quantum Mechanics of Many-Body Systems, Academic Press, New York, 1961 P. Nozieres, Le probleme a N corps, Dunod, Paris, 1963 and The Theory of Interacting Fermi Systems, Benjamin, New York, 1964 1. Lindgren and J. Morrison, Atomic Many-Body Theory, Springer, BerUn, 1982. 

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