相关论文: Form factor for large quantum graphs: evaluating o…

The spectral theory of quantum graphs is related via an exact trace formula with the spectrum of the lengths of periodic orbits (cycles) on the graphs. The latter is a degenerate spectrum, and understanding its structure (i.e.,finding out…

We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to…

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the…

The quantum strategy (or quantum combs) framework is a useful tool for reasoning about interactions among entities that process and exchange quantum information over the course of multiple turns. We prove a time-reversal property for a…

We use the Hopf algebra structure of the time-ordered algebra of field operators to generate all connected weighted Feynman graphs in a recursive and efficient manner. The algebraic representation of the graphs is such that they can be…

Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…

Many observables in QCD rely upon the resummation of perturbation theory to retain predictive power. Resummation follows after one factorizes the cross section into the rele- vant modes. The class of observables which are sensitive to soft…

We present an on-line algorithm for maintaining a topological order of a directed acyclic graph as arcs are added, and detecting a cycle when one is created. Our algorithm takes O(m^{1/2}) amortized time per arc, where m is the total number…

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…

We present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components…

Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…

Using the methods of the 'form factor program' exact expressions of all matrix elements are obtained for several operators of the quantum sine-Gordon model alias the massive Thirring model. A general formula is presented which provides form…

The calculation of massive three-loop QCD form factors using in particular the large moments method has been successfully applied to quarkonic contributions in [1]. We give a brief review of the different steps of the calculation and report…

In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…

Periodic orbits (equivalence classes of closed paths up to cyclic shifts) play an important role in applications of graph theory. For example, they appear in the definition of the Ihara zeta function and exact trace formulae for the spectra…

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard…

Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…

Higher order calculations in perturbative Quantum Field Theories often produce coupled linear systems of differential equations which factorize to first order. Here we present an algorithm to solve such systems in terms of iterated…

We consider the form factor appearing in QCD resummation formalism for event shape distributions in the two-jet (or Sudakov) region. We present an analytic formula for the inverse transform of the form factor, namely from the conjugate…

We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…