Related papers: Exact and explicit evaluation of Brezin-Hikami ker…
In this work, we study the Lie-point symmetries of Kepler--Ermakov systems presented by C. Athorne in J. Phys. A24 (1991), L1385--L1389. We determine the forms of arbitrary function H(x,y) in order to find the members of this class…
A nonparametric kernel-based method for realizing Bayes' rule is proposed, based on representations of probabilities in reproducing kernel Hilbert spaces. Probabilities are uniquely characterized by the mean of the canonical map to the…
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH…
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…
Several complete systems of integrability conditions on a spin chain Hamiltonian density matrix are presented. The corresponding formulas for $R$-matrices are also given. The latter is expressed via the local Hamiltonian density in the form…
We consider the quantum expectation value \mathcal{A}=\<\psi|A|\psi\> of an observable A over the state |\psi\> . We derive the exact probability distribution of \mathcal{A} seen as a random variable when |\psi\> varies over the set of all…
The effective Hamiltonian for the linear $E\otimes e$ Jahn-Teller model describes the coupling between two electronic states and two vibrational modes in molecules or bulk crystal impurities. While in the Born-Oppenheimer approximation the…
We compute the spectral statistics of the sum H of two independent complex Wishart matrices, each of which is correlated with a different covariance matrix. Random matrix theory enjoys many applications including sums and products of random…
A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we…
We approximate the heat kernel $h(x,y,t)$ on a compact connected Riemannian manifold $M$ without boundary uniformly in $(x,y,t)\in M\times M\times [a,b]$, $a>0$, by $n$-fold integrals over $M^n$ of the densities of Brownian bridges.…
We consider an ensemble of random density matrices distributed according to the Bures measure. The corresponding joint probability density of eigenvalues is described by the fixed trace Bures-Hall ensemble of random matrices which, in turn,…
An effective formula for the Bergman kernel on $\mathbb{H}_{\gamma} = \{|z_1|^\gamma < |z_2| < 1 \}$ is obtained for rational $\gamma = \frac{m}{n} >1$. The formula depends on arithmetic properties of $\gamma$, which uncovers new symmetries…
Let $G$ be a noncompact semisimple Lie group equipped with a certain invariant Riemannian metric. Then, we can consider a heat kernel function on $G$ associated to the Riemannian metric. We give an explicit formula for the heat kernel when…
We demonstrate that the existence of a Hermitian time-dependent intertwining operator that maps the non-Hermitian time-dependent energy operator to its Hermitian conjugate and its right to its left eigenstates guarantees the reality of the…
We consider the rigid body quantization of Skyrmions with topological charges 1 to 8, as approximated by the rational map ansatz. Novel, general expressions for the elements of the inertia tensors, in terms of the approximating rational…
We study a 2-parametric family of probability measures on the space of countable point configurations on the punctured real line (the points of the random configuration are concentrated near zero). These measures (or, equivalently, point…
Prime numbers are the building blocks of our arithmetic, however, their distribution still poses fundamental questions. Bernhard Riemann showed that the distribution of primes could be given explicitly if one knew the distribution of the…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…