Related papers: Form factor expansion for large graphs: a diagramm…
We prove that in bosonic quantum mechanics the two-point spectral form factor can be obtained as an average of the two-point out-of-time ordered correlation function, with the average taken over the Heisenberg group. In quantum field…
We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the…
The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…
We study a combinatorial model of the quantum scalar field with polynomial potential on a graph. In the first quantization formalism, the value of a Feynman graph is given by a sum over maps from the Feynman graph to the spacetime graph…
The classical quadratic Gauss sum can be thought of as an exponential sum attached to a quadratic form on a cyclic group. We introduce an equivariant version of Gauss sum for arbitrary finite quadratic forms, which is an exponential sum…
In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…
We discuss consequences of a recent observation that the sequence of periodic orbits in a chaotic billiard behaves like a poissonian stochastic process on small scales. This enables the semiclassical form factor $K_{sc}(\tau)$ to agree with…
Quantum graphs have attracted attention from mathematicians for some time. A quantum graph is defined by having a Laplacian on each edge of a metric graph and imposing boundary conditions at the vertices to get an eigenvalue problem. A…
We derive semiclassical periodic orbit expansions for a correlation function of the Wigner time delay. We consider the Fourier transform of the two-point correlation function, the form factor $K(\tau,x,y,M)$, that depends on the number of…
Form factor axioms are derived in two dimensional integrable defect theories for matrix elements of operators localized both in the bulk and on the defect. The form factors of bulk operators are expressed in terms of the bulk form factors…
The electromagnetic form factor of the pion is calculated in the "point-form" of relativistic quantum mechanics using simple, phenomenological wave functions. It is found that the squared charge radius of the pion is predicted one order of…
The spectral form factor (SFF) is a powerful diagnostic of random matrix behavior in quantum many-body systems. We introduce a family of random circuit ensembles whose SFFs can be computed \textit{exactly}. These ensembles describe the…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
A regular factor is a factor algebra of the unitriangular Lie algebra with respect to some regular ideal. In the paper we construct system of generators of the field of invariants for the coadjoint representation of an arbitrary regular…
The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
We perform an analysis of the one- and two-loop massive quark form factor in QED in a region expansion, up to next-to-leading power in the quark mass. This yields an extensive set of regional integrals, categorized into three topologies,…
A general approach is presented that offers exact analytical solutions for the time-evolution of quantum spin systems during parametric waveforms of arbitrary functions of time. The proposed method utilises the \emph{path-sum} method that…
In these lectures, I describe the techniques used within the QCD sum rule approach. The basic concepts of the approach are introduced using a simple model of quantum-mechanical oscillator in 2+1 dimensions. Then I discuss their…