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We study thermal entanglement in some low-dimensional Heisenberg models. It is found that in each model there is a critical temperature above which thermal entanglement is absent.
The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a…
We study an asymptotic expansion of the critical point for the nearest-neighbor oriented percolation on $\mathbb Z^d$ in powers of $d^{-1}$ as $d\rightarrow \infty$. The proof relies heavily on the lace expansion.
We present the first example of a rigorous uncertainty quantification on elastic Nucleus-Nucleus scattering at energies near the Coulomb barrier. Experimental data has been analyzed using an energy dependent effective optical model…
The ability to reason about and predict the outcome of contacts is paramount to the successful execution of many robot tasks. Analytical rigid-body contact models are used extensively in planning and control due to their computational…
In this paper we study the Poisson stick model in two dimensional hyperbolic space $\mathbb{H}^2,$ where the sticks all have length $L.$ Typically, percolation models in hyperbolic space undergo two phase transitions as the intensity…
We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…
In experimental physics, it is essential to understand electromagnetic (EM) wave scattering across EM spectrum, from radio waves to X-rays, and is pivotal in driving photonics innovations. Recent advancements have uncovered phenomena like…
We use the lace expansion to prove an infra-red bound for site percolation on the hypercubic lattice in high dimension. This implies the triangle condition and allows us to derive several critical exponents that characterize mean-field…
The critical temperature of layered Ising models on triangular and honeycomb lattices are calculated in simple, explicit form for arbitrary distribution of the couplings.
Undirected hyperbolic graph models have been extensively used as models of scale-free small-world networks with high clustering coefficient. Here we presented a simple directed hyperbolic model, where nodes randomly distributed on a…
We discuss the status of thermal model descriptions of particle ratios in central nucleus-nucleus collisions at ultra-relativistic energy. An alternative to the ``Cleymans-Redlich'' interpretation of the freeze-out trajectory is given in…
The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum…
Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel…
We investigate the spread of correlations carried by an excitation in a 1-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\propto r^{-\mu}$). The increase…
We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained…
We present a high temperature series expansion for the ferromagnetic Kondo lattice model in the large coupling limit, which is used to model CMR perovskites. Our results show the expected cross-over to Curie-Wei{\ss} behavior at a…
Euclidean branching Brownian motion (BBM) has been intensively studied during many decades by renowned researchers. BBM on hyperbolic space has received less attention. A profound study of Lalley and Sellke (1997) provided insight on the…