Related papers: Pair correlation densities of inhomogeneous quadra…
This paper studies beta ensembles on the real line in a high temperature regime, that is, the regime where $\beta N \to const \in (0, \infty)$, with $N$ the system size and $\beta$ the inverse temperature. In this regime, the convergence to…
Motivated by the growing interest in accessing the spin structure of multi-boson processes and in measuring quantum entanglement at high energies, we study polarisation and spin-correlation coefficients in di-boson systems. We show that…
By doing quantum Monte Carlo ab initio simulations we show that dipolar excitons, which are now under experimental study, actually are strongly correlated systems. Strong correlations manifest in significant deviations of excitation spectra…
Consider a random permutation of $\{1, \ldots, \lfloor n^{t_2}\rfloor\}$ drawn according to the Ewens measure with parameter $t_1$ and let $K(n, t)$ denote the number of its cycles, where $t\equiv (t_1, t_2)\in\mathbb [0, 1]^2$. Next,…
We study the two-point correlation function of density perturbations in a spherically symmetric void universe model which does not employ the Copernican principle. First we solve perturbation equations in the inhomogeneous universe model…
The well-known Heisenberg--Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system.…
Elkies and McMullen [Duke Math.J.~123 (2004) 95--139] have shown that the gaps between the fractional parts of \sqrt n for n=1,\ldots,N, have a limit distribution as N tends to infinity. The limit distribution is non-standard and differs…
Let $\left(a_{n}\right)_{n}$ be a strictly increasing sequence of positive integers, denote by $A_{N}=\left\{ a_{n}:\,n\leq N\right\} $ its truncations, and let $\alpha\in\left[0,1\right]$. We prove that if the additive energy…
We show theoretically that polariton pairs with a high degree of polarization entanglement can be produced through parametric scattering. We demonstrate that it can emerge in coincidence experiments, even at low excitation densities where…
The shape of Bose-Einstein (or HBT) correlation functions is determined for the case when particles are emitted from a stable source, obtained after convolutions of large number of elementary random processes. The two-particle correlation…
We present the Schmidt decomposition for arbitrary wavefunctions of two indistinguishable bosons, extending the recent studies of entanglement or quantum correlations for two fermion systems [J. Schliemann et al., Phys. Rev. B {\bf 63},…
Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected…
Photon indistinguishability is an essential concept to understanding mysterious quantum features from the viewpoint of the wave-particle duality in quantum mechanics. The physics of indistinguishability lies in the manipulation of quantum…
$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of…
We show that pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate. The proof is based on a quantitative…
For a family of second-order parabolic systems with bounded measurable, rapidly oscillating and time-dependent periodic coefficients, we investigate the sharp convergence rates of weak solutions in $L^2$. Both initial-Dirichlet and…
In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…
Within a field theoretical formalism suited to treat inhomogeneous hot quantum systems, we derive the two-particle correlation function for particles having a spectral width gamma in the region of their emission. We find, that this…
We discuss 2-particle correlations which arise in the time evolution of C-odd and C-even meson--antimeson states of flavoured neutral mesons. In order to keep our discussion general, we do not use the Weisskopf -- Wigner approximation.…
It is emphasized that the bunching parameter $\beta=P_B/P_D$ , i.e. the ratio between the probability to measure two bosons and two distinguishable particles at the same state, is a constant of motion and depends only on the overlap between…