Quantum-chemical study of the interface formed by carboxylic species on TiO<Subscript>2</Subscript> nanoparticles. 1. Nanoparticle surface

The current paper presents results of a quantum-chemical study of the surface structure of nanoparticles of both rutile and anatase crystallographic modifications. Different stages of the surface relaxation are discussed. Water adsorption is considered. The calculations were performed in the spd-basis by using semi-empirical quantum-chemical codes, both sequential and parallel. The results are mainly addressed to the study of the interface formed by titania nanoparticles and a set of carboxylated species, namely, benzoic, bi-isonicotinic acids as well as tris-(2,2′-dcbipyridine) Fe(II) complex placed on the surface of either rutile or anatase polymorphs.This revised version was published online in August 2005 with a corrected issue number.     

The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

Ergodic Properties of the Quantum Geodesic Flow on Tori

We study ergodic averages for a class of pseudodifferential operators on the flatN-dimensional torus with respect to the Schrödinger evolution. The later can be consider a quantization of the geodesic flow on . We prove that, up to semi-classically negligible corrections, such ergodic averages are translationally invariant operators.Mathematics Subject Classifications (2000) 58J50, 58J40, 81S10.     

Freeze-out volume in multifragmentation --Dynamical simulations

Stochastic mean-field simulations for multifragmenting sources at the same excitation energy per nucleon have been performed. The freeze-out volume, a concept which needs to be precisely defined in this dynamical approach, was shown to increase as a function of three parameters: freeze-out instant, fragment multiplicity and system size.     

Implementation of a multiple round quantum dense coding using nuclear magnetic resonance

~~Implementation of a multiple round quantum dense coding using nuclear magnetic resonance1. Bennett, C. H., Wiesner, S. J., Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 1992, 69(20): 2881-2884. 2. Mattle, K., Weinfurter, H., Kwiat, P. G. et al., Dense coding in experimental quantum communication, Phys. Rev. Lett., 1996, 76(25): 4656-4659. 3. Fang, X. M., Zhu, X. W., Feng, M. et al., Experimental implementation of dens…     

Homoclinic Bifurcations in Symmetric Unfoldings of a Singularity with Three-fold Zero Eigenvalue

In this paper we study the singularity at the origin with three-fold zero eigenvalue forsymmetric vector fields with nilpotent linear part and 3-jet C^∞-equivalent to y δ/δx zδ/δy ax^2yδ/δz with a≠0. We first obtain several subfamilies of the symmetric versal unfoldings of this singularityby using the normal form and blow-up methods under some conditions, and derive the local and global bifurcation behavior, then prove analytically the existence of the Sil‘nikov homoclinic bifurcation for some subfamilies of the symmetric versal unfoldings of this singularity, by using the generalized Mel‘nikov methods of a homoclinic orbit to a hyperbolic or non-hyperbolic equilibrium in a highdimensional space.     

Noncommutative Dynamics of Random Operators

We continue our program of unifying general relativity and quantum mechanics in terms of a noncommutative algebra А on a transformation groupoid Γ = E × G where E is the total space of a principal fibre bundle over spacetime, and G a suitable group acting on Γ . We show that every a ∊ А defines a random operator, and we study the dynamics of such operators. In the noncommutative regime, there is no usual time but, on the strength of the Tomita–Takesaki theorem, there exists a one-parameter group of automorphisms of the algebra А which can be used to define a state dependent dynamics; i.e., the pair (А, ϕ), where ϕ is a state on А, is a “dynamic object.” Only if certain additional conditions are satisfied, the Connes–Nikodym–Radon theorem can be applied and the dependence on ϕ disappears. In these cases, the usual unitary quantum mechanical evolution is recovered. We also notice that the same pair (А, ϕ) defines the so-called free probability calculus, as developed by Voiculescu and others, with the state ϕ playing the role of the noncommutative probability measure. This shows that in the noncommutative regime dynamics and probability are unified. This also explains probabilistic properties of the usual quantum mechanics.     

Information and Distinguishability of Ensembles of Identical Quantum States

We consider a fixed quantum measurement performed over n identical copies of quantum states. Using a rigorous notion of distinguishability based on Shannon’s 12th theorem, we show that in the case of a single qubit, the number of distinguishable states is , where (α₁,α₂) is the angle interval from which the states are chosen. In the general case of an N-dimensional Hilbert space and an area Ω of the domain on the unit sphere from which the states are chosen, the number of distinguishable states is . The optimal distribution is uniform over the domain in Cartesian coordinates.     

Evolution of Orbits and Quantum Correlation Functions by Quadratic Hamiltonians

Quantum systems with quadratic Hamiltonians are considered. Some results about the time evolution of homogeneous polynomials and of quantum correlation functions are given. The image of arbitrary orbit of Weyl–Heisenberg group under this time evolution is shown to be again an orbit of this group. For quantum free particle it is shown that its time evolution intersects arbitrary such orbit at most once. A result about existence of more orbits having the same dispersion of some quantum position is presented.PACS: 02.20.Qs, 02.30.Sa