Related papers: Spectral form factor and semi-circle law in the ti…
We extend a recent analysis of the pion electromagnetic form factor constrained by the conformal symmetry to explore the time-like region. We show explicitly that the time-like form factor obtained by the analytic continuation of the…
We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. Then P is not equal to NP iff fP is a non-regular…
A sum rule relative to a reference measure on R is a relationship between the reversed Kullback-Leibler divergence of a positive measure on R and some non-linear functional built on spectral elements related to this measure (see for example…
We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We give a non-asymptotic bound on the spectral norm of a $d\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\sqrt{\log d}$…
We study an approximation by time-discretized geodesic random walks of a diffusion process associated with a family of time-dependent metrics on manifolds. The condition we assume on the metrics is a natural time-inhomogeneous extension of…
Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low…
An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…
Sum rules for the off-shell isovector form factor pi -> gamma gamma* are given in terms of the pion form factor and the gamma pi ->pi pi experimental data. Similarly the corresponding sum rules for the isoscalar form factor are given in…
This paper delves into the Inverse Stefan problem, specifically focusing on determining the time-dependent source coefficient in the parabolic heat equation governing heat transfer in a semi-infinite rod. The problem entails the intricate…
We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions, in the presence and absence of particle number conservation ($U(1)$) symmetry. We analytically…
In this paper, inspired by Tsallis' probability distribution based on a $q$-deformed Boltzmann factor, we stipulate a new $q$-deformed quantum dynamics by applying the inverse Wick rotation $ \beta \rightarrow i t$ to the Tsallis-deformed…
We study the semigroup of the symmetric $\alpha$-stable process in bounded domains in $\R^2$. We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be…
Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise…
We use three-point function QCD sum rules to calculate the form factor $A_0(q^2)$ appearing in the matrix element of the flavour-changing axial current between the $D (B)$ state and a vector meson state. We describe the role of this form…
A derivation of the cyclic form factor equation from quantum field theoretical principles is given; form factors being the matrix elements of a field operator between scattering states. The scattering states are constructed from Haag-Ruelle…
We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for…