generalized directed loop method for quantum monte carlo simulations efficient quantum monte carlo update schemes called directed loops have recently been proposed which improve the efficiency of simulations of quantum lattice models we propose to generalize the detailed balance equations at the local level during the loop construction by accounting for the matrix elements of the operators associated with open world line segments using linear programming techniques to solve the generalized equations we look for optimal construction schemes for directed loops this also allows for an extension of the directed loop scheme to general lattice models such as high spin or bosonic models the resulting algorithms are bounce free in larger regions of parameter space than the original directed loop algorithm the generalized directed loop method is applied to the magnetization process of spin chains in order to compare its efficiency to that of previous directed loop schemes in contrast to general expectations we find that minimizing bounces alone does not always lead to more efficient algorithms in terms of autocorrelations of physical observables because of the nonuniqueness of the bounce free solutions we therefore propose different general strategies to further minimize autocorrelations which can be used as supplementary requirements in any directed loop scheme we show by calculating autocorrelation times for different observables that such strategies indeed lead to improved efficiency however we find that the optimal strategy depends not only on the model parameters but also on the observable of interest

on the fock space representation of functionals of the occupation field and their renormalization on fournit une representation du champ d occupation et de ses puissances renormalisees dans un bon espace de fock

on the critical exponent for random walk intersections the exponent zeta sub d for the probability of nonintersection of 2 random walks starting at the same point is considered it is proved that 1 2 zeta sub 2 3 4 monte carlo simulations are done to suggest zeta sub 2 0 61 hor ellipsis and zeta sub 3 approx 0 29

self intersection gauge for random walks and for brownian motion a class of random fields associated with multiple points of a random walk in the plane is studied it is proved that these fields converge in distribution to analogous fields measuring self intersections of the planar brownian motion the concluding section contains a survey of literature on intersection local times and their renormalizations a brief look through the first pages of this section could provide the reader with additional motivation for the present work

renormalization of a self avoiding brownian motion in two dimensions abstract we obtain a measure defined on the space of continuous sample paths which describes a weakly self avoiding brownian motion in a 2 dimensional euclidean space our method is also applicable to a brownian motion with the dirichlet boundary conditions in a 2 dimensional domain for the new measures an inequality of simon lieb type is also obtained

a renormalization result for the intersection local time of lattice random walks ind 3 dimensions in this paper we derive some general conditions on stable walks inz d under which the central limit theorem holds for their normalized intersection local time in particular we prove that the process given by the normalized intersection local time of the simple random walk inz d withd 3 is weakly convergent to the standard brownian motion

a note on the high temperature expansion of the density matrix for the isotropic heisenberg chain abstract gohmann klumper and seel derived the multiple integral formula of the density matrix of the xxz heisenberg chain at finite temperatures we have applied the high temperature expansion hte method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short range correlation functions for example we have succeeded to obtain the coefficients of the hte of the third neighbor correlation function j z j 3 z for zero magnetic field up to the order of 25 these results expand our previous results on the emptiness formation probability z tsuboi m shiroishi j phys a math gen 38 2005 l363 l370 condmat 0502569 to more general correlation functions

universality of parametric spectral correlations local versus extended perturbing potentials we explore the influence of an arbitrary external potential perturbation v on the spectral properties of a weakly disordered conductor in the framework of a statistical field theory of a nonlinear ensuremath sigma model type we find depending on the range and the profile of the external perturbation two qualitatively different universal regimes of parametric spectral statistics i e cross correlations between the spectra of hamiltonians h and h v we identify the translational invariance of the correlations in the space of hamiltonians as the key indicator of universality and find the connection between the coordinate system in this space which makes the translational invariance manifest and the physically measurable properties of the system in particular in the case of localized perturbations the latter turn out to be the eigenphases of the scattering matrix for scattering off the perturbing potential v they also have a purely statistical interpretation in terms of the moments of the level velocity distribution finally on the basis of this analysis a set of results obtained recently by the authors using random matrix theory methods is shown to be applicable to a much wider class of disordered and chaotic structures

large deviations for renormalized self intersection local times of stable processes we study large deviations for the renormalized self intersection local time of d dimensional stable processes of index 2d 3 d we find a difference between the upper and lower tail in addition we find that the behavior of the lower tail depends critically on whether d or d

proprietes d intersection des marches aleatoires i convergence vers le temps local d intersection we study intersection properties of multi dimensional random walks letx andy be two independent random walks with values in d d 3 satisfying suitable moment assumptions and letin denote the number of common points to the paths ofx andy up to timen the sequence in suitably normalized is shown to converge in distribution towards the intersection local time of two independent brownian motions results are applied to the proof of a central limit theorem for the range of a two dimensional recurrent random walk thus answering a question raised by n c jain and w e pruitt

non intersection exponents for brownian paths letx andy be independent 3 dimensional brownian motions x 0 0 0 0 y 0 1 0 0 and letp r p x 0 r y 0 r then the non intersection exponent mathop lim limits r to infty log p r mathord left vphantom log p r log r right kern nulldelimiterspace log r exists and is equal to a similar non intersection exponent for random walks analogous results hold inr2 and for more than 2 paths

random walks and intersection local time with each random walk on z 2 we associate a functional related to the number of steps which the walk spends in sites occupied at least k times we show that if our random walk is in the domain of attraction of a stable process of order greater than 2 2k 2 2k 1 then our functional converges to the intersection local time of the limiting process

semiclassical universality of parametric spectral correlations we consider quantum systems with a chaotic classical limit that depends on an external parameter and study correlations between the spectra at different parameter values in particular we consider the parametric spectral form factor k x which depends on a scaled parameter difference x for parameter variations that do not change the symmetry of the system we show by using semiclassical periodic orbit expansions that the small expansion of the form factor agrees with random matrix theory for systems with and without time reversal symmetry

engineering local optimality in quantum monte carlo algorithms quantum monte carlo algorithms based on a world line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non frustrated spin models and of bosonic models both algorithms work in the grand canonical ensemble and can have a winding number larger than zero however they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm we let us guide by the rigorous statements on the globally optimal form of markov chain monte carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm we provide numerical examples for the soft core bose hubbard model and various spin s models

spectral statistics in chaotic systems with a point interaction we consider quantum systems with a chaotic classical limit that are perturbed by a point like scatterer the spectral form factor k for these systems is evaluated semiclassically in terms of periodic and diffractive orbits it is shown for order 2 and 3 that off diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits implying that the perturbation by the scatterer does not change the spectral statistic we further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer

an almost sure invariance principle for the range of planar random walks for a symmetric random walk in z 2 with 2 moments we represent r n the cardinality of the range in terms of an expansion involving the renormalized intersection local times of a brownian motion we show that for each k 1 logn k 1 n r n 1 j 1 2 logn c x j j n 0 a s where w t is a brownian motion w n t w nt n j n is the renormalized intersection local time at time 1 for w n and c x is a constant depending on the distribution of the random walk

an extension of a result of burdzy and lawler it is shown that for all mean zero finite variance random walks the critical non intersection exponents are equal to those for brownian motion the method uses the local time of intersection

the scaling limit of loop erased random walk in three dimensions we show that the scaling limit exists and is invariant under dilations and rotations we give some tools that might be useful to show universality

parameter dependent spectral statistics of chaotic quantum graphs neumann versus circular orthogonal ensemble boundary conditions the parameter dependent spectral statistics of totally connected quantum graphs with n 4 30 vertices such as the parametric velocities correlation functions and the distribution of curvatures are studied the inverse participation ratio ipr an important measure of localization effects was also numerically investigated in the calculations we successfully used two different theoretical approaches the first approach was based on the graphs eigenenergies and wave functions calculations while the second one used the eigenphases and the eigenvectors of the bond scattering matrix s k we considered graphs with neumann and circular orthogonal ensemble coe boundary conditions we show that in contrast to large neumann graphs for which the departure of many parameter dependent spectral statistics from the random matrix theory rmt predictions is observed for large coe graphs the spectral statistics and ipr are in good agreement with the rmt predictions

local times on curves and uniform invariance principles sufficient conditions are given for a family of local times l t ofd dimensional brownian motion to be jointly continuous as a function oft and then invariance principles are given for the weak convergence of local times of lattice valued random walks to the local times of brownian motion uniformly over a large family of measures applications included some new results for intersection local times for brownian motions on 2 and 2

wiener sausage and self intersection local times abstract let b bt t 0 be a standard brownian motion in r 2 for every e 0 and every compact subset k of r 2 the wiener sausage of radius e associated with k is defined as the union of the sets bs ek s 0 1 the present paper gives full asymptotic expansions for the area of the wiener sausage when the radius e goes to 0 the kth term of the expansion is of order log e k and involves a random variable which measures the number of k multiple self intersections of the process such random variables are called renormalized self intersection local times and have been recently introduced and studied by e b dynkin a self contained construction of these local times is given together with a number of new approximations

some properties of the fractional ornstein uhlenbeck process we consider the fractional analogue of the ornstein uhlenbeck process i e the solution of the langevin equation driven by a fractional brownian motion in place of the usual brownian motion we establish some properties of these processes we show that the process is local nondeterminism for a two dimensional process we show that its renormalized self intersection local time exists in l2 if and only if

universality in quantum parametric correlations we investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied a general scaling procedure is introduced which makes the theory invariant under reparametrizations under certain general conditions we show that this procedure is unique the approach is illustrated with the particular case of the distribution of eigenvalue curvatures we also derive a semiclassical formula for the nonuniversal scaling factor and give an explicit expression valid for arbitrary deformations of a billiard system

parametric spectral statistics in unitary random matrix ensembles from distribution functions to intra level correlations we establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles for a generic confinement potential tr w h we i find the joint distribution functions of the eigenvalues of h and h h v for an arbitrary fixed v both for finite matrix size n and in the thermodynamic n limit ii derive many point parametric correlation functions of the two sets of eigenvalues and show that they are naturally parametrized by the eigenvalues of the reactance matrix for scattering off the potential v iii prove the universality of the correlation functions in unitary ensembles with non gaussian non invariant confinement potential tr w h v iv establish a general scheme for exact calculation of level number dependent parametric correlation functions and apply the scheme to the calculation of intra level velocity autocorrelation function and the distribution of parametric level shifts