Related papers: Difference between standard and quasi-conformal BF…

The momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…

We address a problem of proper definition of momentum density for spatially structured electromagnetic fields. We show that the expressions for the momentum and angular momentum obtained locally are not the same when one uses the canonical…

Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…

Kernel methods serve as powerful tools to capture nonlinear patterns behind data in machine learning. The quantum kernel, integrating kernel theory with quantum computing, has attracted widespread attention. However, existing studies…

We establish a domination principle for positive operators, which provides an upper bound on the essential spectral radius and yields quasi-compactness criteria on weighted supremum spaces with Lyapunov type functions and local domination.…

Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…

We introduce a novel topology, called Kernel Mean Embedding Topology, for stochastic kernels, in a weak and strong form. This topology, defined on the spaces of Bochner integrable functions from a signal space to a space of probability…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

Quantum mechanical models with a minimal length are often described by modifying the commutation relation between position and momentum. Although this represents a small complication when described in momentum space, at least formally, the…

This work provides theoretical foundations for kernel methods in the hyperspherical context. Specifically, we characterise the native spaces (reproducing kernel Hilbert spaces) and the Sobolev spaces associated with kernels defined over…

Using the requirement of M\"{o}bius invariance of ${\cal N}$=4 SYM amplitudes in the Regge limit we restore the conformal NLO BFKL kernel out of the eigenvalues known from the forward NLO BFKL result.

We address the problem of a Coulomb impurity in graphene in the presence of a perpendicular uniform magnetic field. We show that the problem can be solved below the supercritical impurity magnitude within the WKB approximation. Without…

We complete the calculation of the next-to-leading kernel of the BFKL equation, by disentangling its energy-scale dependent part from the impact factor corrections in large-k dijet production. Using the irreducible part previously…

The performance of modern quantum devices in communication, metrology or microscopy relies on the quantum-classical interaction which is generally described by the theory of decoherence. Despite the high relevance for long coherence times…

The initial analyses of the next-to-leading logarithmic corrections to the BFKL kernel were very discouraging. Encouraged by the success of new methods in the analysis of the BFKL equation at full NLL accuracy we demonstrate in this talk…

We explore the relationship between classical quasinormal mode frequencies and black hole quantum mechanics in 2+1 dimensions. Following a suggestion of Hod, we identify the real part of the quasinormal frequencies with the fundamental…

Shortcomings of a momentum-space treatment of strong absorption, as discussed in the previous Comment [nucl-th/9611025], are only of concern at low projectile energies, $\gamma$< 1.5. At intermediate and high energies, for which the…

The most recent development of the quark-meson coupling (QMC) model, in which the effect of the mean scalar field in-medium on the hyperfine interaction is also included self-consistently, is used to compute the properties of finite…

In this work, we study the convergence of the empirical measure of moderately interacting particle systems with singular interaction kernels. First, we prove quantitative convergence of the time marginals of the empirical measure of…