From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

We propose a new class of cluster growth models where growth sites have a finite lifetime , which contains as special cases the Eden model ( = ) and the kinetic growth walk ( = 1). For finite but large values the growth process can be characterized by a crossover timet _X; for times belowt _X an Eden-type cluster is formed, while for times abovet _X the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with . We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).     

Fluctuations of extensive functions of quenched random couplings

An extensive quantity is a family of functions _v of random parameters, indexed by the finite regionsV (subsets of ^d) over which _v are additive up to corrections satisfying the boundary estimate stated below. It is shown that unless the randomness is nonessential, in the sense that lim _v/|V| has a unique value in the absolute (i.e., not just probabilistic) sense, the variance of such a quantity grows as the volume ofV. Of particular interest is the free energy of a system with random couplings; for such _v bounds are derived also for the generating functionE(e ^t ). In a separate application, variance bounds are used for an inequality concerning the characteristic exponents of directed polymers in a random environment.     

Upper bounds for the energy expectation in time-dependent quantum mechanics

We consider quantum systems driven by Hamiltonians of the formH+W(t), where the spectrum ofH consists of an infinite set of bands andW(t) depends arbitrarily on time. Let H (t) denote the expectation value ofH with respect to the evolution at timet of an initial state . We prove upper bounds of the type H (t)=O(t ), >0, under conditions on the strength ofW(t) with respect toH. Neither growth of the gaps between the bands nor smoothness ofW(t) is required. Similar estimates are shown for the expectation value of functions ofH. Sufficient conditions to have uniformly bounded expectation values are made explicit and the consequences on other approaches to quantum stability are discussed.     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

ИЗОТОПЫ ФТОРА F19 И F21 В МОДЕЛИ НИЛЬССОНА

Energy levels and electromagnetic properties of fluorin isotopes in the Nilsson's model with Coriolis mixing are investigated. Position of the F¹⁹ levels is satisfactorily explained up to the energy of 4·5 MeV. Concerning the F²¹ it seems that the shell model will better correspond to the F²¹ nucleus.

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. , .     

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Degenerate four-wave-mixing spectroscopy in NaH

We performed DFWM spectroscopy on X ^–1+–A ¹⁺ transitions in NaH produced in an indirect photochemical reaction between Na(3p) and H₂ and detected v=1, 2 and 3 ground state vibrational levels of NaH molecules, whereas with resonance enhanced CARS, we observed v=0 levels only. This different sensitivity can be explained by considering the Franck-Condon-factors and the relevant damping coefficients for the corresponding transitions in the NaH molecule. Time resolved DFWM spectroscopy showed that NaH(v=1) molecules effectively live much longer than Na(3p) atoms which merely follow the laser excitation pulse.     

Time-energy uncertainty and relativistic canonical commutation relations in quantum spacetime

It is shown that the time operatorQ ⁰ appearing in the realization of the RCCR's [Q,P^v]=–jhg^v, on Minkowski quantum spacetime is a self adjoint operator on Hilbert space of square integrable functions over _m =×v _m , where is a timelike hyperplane. This result leads to time-energy uncertainty relations that match their space-momentum counterparts. The operators Q appearing in Born's metric operator in quantum spacetime emerge as internal spacetime operators for exciton states, and the condition that the metric operator should possess a ground exciton state assumes the significance of achieving minimal spacetime4-momentum uncertainty in fundamental standards for spacetime measurements.Supported in part by NSERC research grant No. A5206.