localizations on complex networks we study the structural characteristics of complex networks using the representative eigenvectors of the adjacent matrix the probability distribution function of the components of the representative eigenvectors are proposed to describe the localization on networks where the euclidean distance is invalid several quantities are used to describe the localization properties of the representative states such as the participation ratio the structural entropy and the probability distribution function of the nearest neighbor level spacings for spectra of complex networks whole cell networks in the real world and the watts strogatz small world and barabasi albert scale free networks are considered the networks have nontrivial localization properties due to the nontrivial topological structures it is found that the ascending order ranked series of the occurrence probabilities at the nodes behave generally multifractally this characteristic can be used as a structural measure of complex networks

diffusion in deterministic fractals a model for polymer electrolytes abstract we present simulation results for random walks on a family of sierpinski carpets under a periodically varying bias the diffusivity obtained from these results shows a power law variation of the bias with frequency the exponent depends on details of the carpet generator we discuss applicability of these results to real materials with fractal structure such as polymer electrolytes with different salt concentrations

integrable impurities for an open fermion chain employing the graded versions of the yang baxter equation and the reflection equations we construct two kinds of integrable impurities for a small polaron model with general open boundary conditions a we shift the spectral parameter of the local lax operator at arbitrary sites in the bulk and b we embed the impurity fermion vertex at each boundary of the chain the hamiltonians with different types of impurity terms are given explicitly the bethe ansatz equations as well as the eigenvalues of the hamiltonians are constructed by means of the quantum inverse scattering method in addition we discuss the ground state properties in the thermodynamic limit

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

operator content of the xxz chain the finite size scaling spectra of the xxz heisenberg chain are presented for even and odd numbers of sites respectively the operator content is given for free as well as for toroidal boundary conditions

renormalisation on sierpinski type fractals presents a family of deterministic fractals which generalise the d dimensional sierpinski gaskets and establishes their order of ramification and their fractal and spectral dimensions random walks on these fractals are renormalisable and lead to rational not necessarily polynomial mapping

the modified xxz heisenberg chain conformal invariance and the surface exponents of c 1 systems the authors present the operator content of the xxz chain in the presence of external fields the finite size scaling spectra can be expressed in terms of irreps of shifted u 1 kac moody algebras the shift depending on the external fields using an explicit feigin fuchs construction 1982 they project out from these spectra the operator content of c 1 systems with free fixed and mixed boundary conditions they also show how this projection mechanism works for a finite number of sites

boundary conditions for integrable quantum systems a new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering r matrix method the method proposed allows the author to treat open quantum chains with appropriate boundary terms in the hamiltonian the general considerations are applied to the xxz and xyz models the nonlinear schrodinger equation and toda chain

critical behavior of self avoiding walks on fractals using a new graph counting technique suitable for self similar fractals exact 18th order series expansions for saws on some sierpinski carpets are generated from them the critical fugacityxc and critical exponents saw and saw are obtained the results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied we find for some carpets with low lacunarity that saw saw d for saws on the fractals which are embedded in ad dimensional euclidean space

dilute potts model duality and site bond percolation a number of results are obtained for potts models on an arbitrary planar lattice it is shown that the dual of a dilute potts model is a graph generating function and that the dual of a constrained dilute potts model is an undiluted potts model it is also shown that the dilute potts model generates a correlated site bond percolation for uncorrelated site bond percolations the analysis determines the percolation threshold from a knowledge of the critical point of a potts model this generalises a recent result of kondor 1980 who uses a star triangle transformation to derive this relationship for the honeycomb and triangle lattices

the spin 1 2xxz heisenberg chain the quantum algebra uq sl 2 and duality transformations for minimal models the finite size scaling spectra of the spin 1 2 xxz heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c 1 including the unitary and nonunitary minimal series taking into account the half integer angular momentum sectors which correspond to chains with an odd number of sites in many cases leads to new spinor operators appearing in the projected systems these new sectors in the xxz chain correspond to new types of frustration lines in the projected minimal models the corresponding new boundary conditions in the hamiltonian limit are investigated for the ising model and the 3 state potts model and are shown to be related to duality transformations which are an additional symmetry at their self dual critical point by different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite xxz chain the observed degeneracies in the energy and momentummore spectra are shown to be the consequence of intertwining relations involving u sub q sl 2 quantum algebra transformations 35 refs 3 tabs less

diffusion on complex cellular automata patterns we studied random walks on two dimensional patterns formed by the sequence of configurations of complex elementary cellular automata ca with random initial configurations the walkers are allowed to jump between nearest neighbours or next nearest neighbours 1 sites on patterns of rules 22 54 90 122 126 150 and 182 the diffusion is normal 1 2 on patterns 18 and 146 the diffusion is anomalous with 0 415 0 005 and the spectral dimension is ds 1 25 0 1 from the analysis of the diffusion in the horizontal and vertical directions space and time directions of the ca problem respectively of patterns 18 and 146 we obtained x 0 22 and y 0 42 because they have branches of 1 sites which are long in the vertical direction but narrow in the horizontal direction due to the anisotropic diffusion the results do not satisfy the relation ds 2df dw with dw 1 and fractal dimension df 2 considering that the fractal dimension of the region visited by the walker is equal to the dimension of the substrate df we suggest the new scaling relation ds 2 x y this relation is supported by our numerical results and may be generalized to other structures with anisotropic diffusion

diffusion on regular random fractals we study random walks on structures intermediate to statistical and deterministic fractals called regular random fractals constructed introducing randomness in the distribution of lacunas of sierpinski carpets random walks are simulated on finite stages of these fractals and the scaling properties of the mean square displacement of n step walks are analysed the anomalous diffusion exponents obtained are very near the estimates for the carpets with the same dimension this result motivates a discussion on the influence of some types of lattice irregularity random structure dead ends lacunas on based on results on several fractals we also propose to use these and other regular random fractals as models for real self similar structures and to generalize results for statistical systems on fractals

vector coherent state theory in a group with non commuting raising generators vector coherent state theory is used to give an explicit construction of the irreducible representations of a group with non commuting raising generators the simple example of the compact unitary symplectic group usp 4 contains implies usp 2 usp 2

non analytic finite size corrections for the heisenberg chain in a magnetic field with free and twisted boundary conditions the finite size energy spectrum of the anisotropic heisenberg chain in an external magnetic field is calculated for free and twisted boundary conditions as with periodic boundary conditions it is found that the spectra exhibit non analytical terms which do not fit into the form predicted on the basis of conformal invariance unless extra commensurability conditions between the size of the system and the external field are introduced taking these conditions into account some scaling dimensions for associated models are derived

finite size scaling for random walks on fractals random walks are simulated on finite stages of construction of regular fractal lattices it is proved that the mean square displacement rn2 obeys a finite size scaling hypothesis and the critical exponent nu w is estimated the efficiency of the method is proved when applied to finitely ramified fractals in which the problem is exactly solvable nu w is obtained with good accuracy approximately 1 for a class of infinitely ramified fractals the sierpinski carpets the results correct previous estimates based on simulations which did not use finite size scaling it is shown that nu w decreases when dc decreases with very small corrections due to other geometrical properties such as lacunarity the comparison with estimates of the ideal chain exponent nu c shows that the two problems are not equivalent on these fractals and that in general nu w nu c estimates of nu w with the same accuracy are obtained on two sierpinski pastry shells 2 df 3 where anomalous diffusion is also observed

the coastline and lake shores on a fractal island we compute the fractal dimensions of the hulls or external boundary and the boundaries of the internal cavities in several deterministic as well as random fractal structures our conclusion is that the two fractal dimensions are in fact identical the deterministic fractals we study are sierpinski carpets sc in a two dimensional space and the random fractals are percolation clusters at criticality as an intermediate case we present results on some randomized sc in the random structures statistics of the area and perimeters of all internal cavities or holes are taken and the fractal dimension of the hull borderline is computed two different definitions of the borderline are used considering nearest neighbours as well as nearest and second nearest neighbours as connected the conclusion is valid for both cases

boundary bound states and boundary bootstrap in the sine gordon model with dirichlet boundary conditions we present a complete study of boundary bound states and related boundary s matrices for the sine gordon model with dirichlet boundary conditions our approach is based partly on the bootstrap procedure and partly on the explicit solution of the inhomogeneous xxz model with boundary magnetic field and solution of the boundary thirring model we identify boundary bound states with new boundary strings in the bethe ansatz the boundary energy is also computed

diffusion on a dla cluster in two and three dimensions we present a much improved calculation of the dynamic critical exponents of diffusion dw ds and the combination df dw for the dla diffusion limited aggregate on square and simple cubic lattices using two independent approaches one based on the exact enumeration for the displacement and velocity autocorrelation and the other on the eigenspectrum of random walks on the dla the two methods give consistent results which however clearly rule out the scaling relation ds 2df dw first proposed by alexander and orbach 1982 similarly to the case of the eden tree reported previously

statistical mechanics of random paths on disordered lattices the dependence of the universality class on the statistical weight of unrestricted random paths is explicitly shown both for deterministic and statistical fractals such as the incipient infinite percolation cluster equally weighted paths ideal chain and kinetically generated paths random walks belong in general to different universality classes for deterministic fractals exact renormalization group techniques are used asymptotic behaviors for the end to end distance ranging from power to logarithmic localization laws are observed for the ideal chain in all these cases random walks in the presence of nonperfect traps are shown to be in the same universality class of the ideal chain logarithmic behavior is reflected insingular renormalization group recursions for the disordered case numerical transfer matrix techniques are exploited on percolation clusters in two and three dimensions the two point correlation function scales with critical exponents not obeying standard scaling relations the distribution of the number of chains and the number of chains returning to the starting point are found to be well approximated by a log normal distribution the logmoment of the number of chains is found to have an essential type of singularity consistent with the log normal distribution a non self averaging behavior is argued to occur on the basis of the results

regular random fractals and the n parameter model two models of fractal objects are presented the first model represents a new class of fractals which is intermediate to statistical fractals and exact fractals in that each configuration of the random ensemble has an exact and adjustable fractal dimension the second model has a continuously adjustable backbone dimensions and can be used to directly generate conducting backbones

multiscaling analysis of large scale off lattice dla abstract an improved algorithm has been used to simulate off lattice diffusion limited aggregation dla in two dimensions this enables us to grow clusters of up to 6 106 particles which are the largest such clusters made up to now the density profile in two dimensions is analyzed for the scaling form multiscaling g r r r d d x c x with x r r where r is the radius of gyration and r is the distance from the cluster origin in contrast with previous studies the dimension d x shows no symmetric tendency to drop at values of x but only fluctuates around the global fractal dimension d 1 712 0 003

quenched averages for self avoiding walks and polygons on deterministic fractals we study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index different sites on such lattices are not equivalent and the number of rooted open walks wn s and rooted self avoiding polygons pn s of n steps depend on the root s we use exact recursion equations on the fractal to determine the generating functions for pn s and wn s for an arbitrary point s on the lattice these are used to compute the averages langle p n s rangle langle w n s rangle langle log p n s rangle and langle log w n s rangle over different positions of s we find that the connectivity constant and the radius of gyration exponent nu are the same for the annealed and quenched averages however langle log p n s rangle simeq n log mu alpha q 2 log n and langle log w n s rangle simeq n log mu gamma q 1 log n where the exponents alpha q and gamma q take values different from the annealed case these are expressed as the lyapunov exponents of random product of finite dimensional matrices for the 3 simplex lattice our numerical estimation gives alpha q simeq 0 72837 pm 0 00001 and gamma q simeq 1 37501 pm 0 00003 to be compared with the known annealed values alpha a 0 73421 and gamma q 1 37522

on the closedness of the sum of two closed operators o t t 1 where e g a is the infinitesimal generator of an analytic semigroup in a complex banach space x we find that in general it is false that for every fe lp 0 t x problem 1 has a solution uewi p o t x c lp o t a usually it is necessary to impose some further regularity conditions on f consider for instance the way in which problem 1 is studied in the paper 8 and compare th 3 7 and 3 14 which are applied in w 4 of the same paper to solve problem 1 we find that in general we have only strong solutions while in the hilbert space setting we have strict solutions this corresponds to the fact that in general the operator a b where b u u is only closable while in a hilbert space it is closed this remark suggests that the better result may depend on the nicer geometric properties of a hilbert space with respect to a general banach space and it is natural to ask which conditions should be imposed on the banach space to force the sum of two suitable closed opera tors to be closed the above considerations motivate the manifold aim of the present paper a to find conditions on a banach space x and on closed linear operators a and b acting in x which ensure that a b is closed b to apply the result of a to problem 1 it seems that the convenient property for the banach space x is convexity or otherwise stated the umd condition for information about these equiva lent conditions we refer to 4 in which it is also proved that if x is convex and l p oe then the hilbert transform is continuous from lp r x into lp r x on the other hand it is also known see 2 that if there exists pe 1 oe such that the hilbert transform is continuous from lp r x into itself

anomalous diffusion on random fractal composites stochastic fractals generated from combinations of deterministic fractals have the advantage of being tractable to some extent but also being closer to real materials since they are partially disordered in the present work we focus our attention on the remarkable nonlinear mixing behavior exhibited by fractals generated as random combinations of two different sierpinski carpet generators when patterns with different anomalous diffusion exponents and the same or different fractal dimensions are combined together the effective diffusion exponent cannot in general be expressed as a linear weighted average of the diffusion exponents of the constituents the effective exponent may show a maximum or minimum for certain compositions an explanation of this interesting phenomenon is offered on the basis of details of the carpet generator particularly on the number and position of connection points which determine the connectivity of the fractal composite

random walks of oriented particles on fractals random walks of point particles on fractals exhibit subdiffusive behavior where the anomalous diffusion exponent is smaller than one and the corresponding random walk dimension is larger than two this is due to the limited space available in fractal structures here we endow the particles with an orientation and analyze their dynamics on fractal structures in particular we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation which are modeled using an appropriate move class these interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure a surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum