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In this paper, we study the Hard Core (HC) model with a countable set $\mathbb Z$ of spin values on a Cayley tree of order $k=2$. This model is defined by a countable set of parameters (that is, the activity function $\lambda_i>0$, $i\in \mathbb Z$). A functional equation is obtained that provides the consistency condition for finite-dimensional Gibbs distributions. Analyzing this equation, the following results are obtained: Let $k\geq 2$ and $\Lambda=\sum_i\lambda_i$. For $\Lambda=+\infty$ there is no translation-invariant Gibbs measure (TIGM); Let $k=2$ and $\Lambda<+\infty$. For the model under constraint such that at $G$-admissible graph the loops are imposed at two vertices of the graph, the uniqueness of TIGM is proved; Let $k=2$ and $\Lambda<+\infty$. For the model under constraint such that at $G$-admissible graph the loops are imposed at three vertices of the graph, the uniqueness and non-uniqueness conditions of TIGMs are found., Comment: arXiv admin note: text overlap with arXiv:2206.06333 by other authors

We consider an accelerated relativistic fluid in four-dimensional (anti-)de Sitter space-time. Analyzing only hydrodynamic equations, we construct the equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a thermal bath in the accelerated frame with a temperature, depending on the acceleration in a flat higher-dimensional (namely, five-dimensional) space, in which curved space-times are embedded. We develop the duality between hydrodynamics and gravity finding a direct relationship between the transport coefficients in flat and curved space-times.

In this paper, we focus on studying non-probability Gibbs measures for a Hard Core (HC) model on a Cayley tree of order $k\geq 2$, where the set of integers $\mathbb Z$ is the set of spin values. It is well-known that each Gibbs measure, whether it be a gradient or non-probability measure, of this model corresponds to a boundary law. A boundary law can be thought of as an infinite-dimensional vector function defined at the vertices of the Cayley tree, which satisfies a nonlinear functional equation. Furthermore, every normalisable boundary law corresponds to a Gibbs measure. However, a non-normalisable boundary law can define gradient or non-probability Gibbs measures. In this paper, we investigate the conditions for uniqueness and non-uniqueness of translation-invariant and periodic non-probability Gibbs measures for the HC-model on a Cayley tree of any order $k\geq 2$., Comment: 19 pages, 2 figures

In this paper, we consider a Hard-Core $(HC)$ model with two spin values on Cayley trees. The conception of alternative Gibbs measure is introduced and translational invariance conditions for alternative Gibbs measures are found. Also, we show that the existence of alternative Gibbs measures which are not translation-invariant. In addition, we study free energy of the model.

In this paper, we study the HC-model with a countable set $\mathbb Z$ of spin values on a Cayley tree of order $k\geq 2$. This model is defined by a countable set of parameters (that is, the activity function $\lambda_i>0$, $i\in \mathbb Z$). A functional equation is obtained that provides the consistency condition for finite-dimensional Gibbs distributions. Analyzing this equation, the following results are obtained: - Let $\Lambda=\sum_i\lambda_i$. For $\Lambda=+\infty$ there are no translation-invariant Gibbs measures (TIGM) and no two-periodic Gibbs measures (TPGM); - For $\Lambda<+\infty$, the uniqueness of TIGM is proved; - Let $\Lambda_{\rm cr}(k)=\frac{k^k}{(k-1)^{k+1}}$. If $0<\Lambda\leq\Lambda_{\rm cr}$, then there is exactly one TPGM that is TIGM; - For $\Lambda>\Lambda_{\rm cr}$, there are exactly three TPGMs, one of which is TIGM., Comment: 15 pages, 1 figure

A complete description of two-periodic Gibbs measures on the Cayley tree of orders two and three for HC model with two states is obtained and using the reconstruction method, the extremality of these measures in the area of their existence is proved., Comment: in Russian

We consider fertile three-state hard core models with the activity parameter on an order-three Cayley tree. It is known that there exist four types of such models: in two of them the regions of extremality of the unique translation-invariant Gibbs measure were found., Comment: 13 pages, in Russian, 7 figures

We consider fertile three-state Hard-Core (HC) models with the activity parameter $\lambda>0$ on a Cayley tree. It is known that there exist four types of such models: wrench, wand, hinge, and pipe. These models arise as simple examples of loss networks with nearest-neighbor exclusion. In the case wand on a Cayley tree of order $k\geq2$, exact critical values $\lambda>0$ are found for which two-periodic Gibbs measures are not unique. Moreover, we study the extremality of the existing two-periodic Gibbs measures on a Cayley tree of order two., Comment: in English

In this paper we study Hard-Core model on a Cayley tree. For a normal divisor of index four new conditions for uniqueness and non-uniqueness of weakly periodic Gibbs measures are found., Comment: in Russian

Work is a continuation of work TMPh, 175(2), 2013. We study the Potts model with zero external field on the Cayley tree. It is shown that for any values of the parameter all periodic Gibbs measures are translation-invariant for the q-state antiferromagnetic Potts model on the Cayley tree of order two and for the q-state ferromagnetic Potts model on the Cayley tree of order k., Comment: in Russian

In this paper we study two and three state HC-model on a Cayley tree. Under some conditions on parameters of the HC-model, in the case of normal divisor of the index four, we prove the existence of the weakly periodic (non periodic) Gibbs measures which are different from the known weakly periodic measures. Moreover, we find some regions for the $\lambda$ parameter ensuring that a extreme measure is not unique.

In this paper we consider translation-invariant Gibbs measures for the Blum-Kapel model on a Cayley tree of order k. An approximate critical temperature T_{cr} is found such that for T\geq T_{cr} there exists a unique translation-invariant Gibbs measure and for 0

In this paper we study the extremality of translation-invariant Gibbs measure for the HC-model on a Cayley tree. It is known that for this model the translation-invariant measure is unique. We give a new proof of this statement and found regions of the extremality of this measure on the Cayley tree of order k., Comment: in Russian

Ghost imaging is a technique -- first realized in quantum optics -- in which the image emerges from cross-correlation between particles in two separate beams. One beam passes through the object to a bucket (single-pixel) detector, while the second beam's spatial profile is measured by a high resolution (multi-pixel) detector but never interacts with the object. Neither detector can reconstruct the image independently. However, until now ghost imaging has only been demonstrated with photons. Here we report the first realisation of ghost imaging of an object using massive particles. In our experiment, the two beams are formed by correlated pairs of ultracold metastable helium atoms, originating from two colliding Bose-Einstein condensates (BECs) via $s$-wave scattering. We use the higher-order Kapitza-Dirac effect to generate the large number of correlated atom pairs required, enabling the creation of a ghost image with good visibility and sub-millimetre resolution. Future extensions could include ghost interference as well as tests of EPR entantlement and Bell's inequalities.

In this paper is studied ferromagnetic three states Potts model on a Cayley tree of order three and we give explicit formulas for translation-invariant Gibbs measures. Furthermore, we show that under some conditions on the parameter of the antiferromagnetic Potts model with q-states with zero external field on the Cayley tree of order $k>2$, there are exactly 2(2^q-1) periodic (non translation-invariant) Gibbs measures., Comment: in Russian

We present the first measurement for helium atoms of the tune-out wavelength at which the atomic polarizability vanishes. We utilise a novel, highly sensitive technique for precisely measuring the effect of variations in the trapping potential of confined metastable ($2^{3}S_{1}$) helium atoms illuminated by a perturbing laser light field. The measured tune-out wavelength of 413.0938($9_{Stat.}$)($20_{Syst.}$) nm compares well with the value predicted by a theoretical calculation (413.02(9) nm) which is sensitive to finite nuclear mass, relativistic, and quantum electro-dynamic (QED) effects. This provides motivation for more detailed theoretical investigations to test QED., Comment: 5 pages, 4 figures

We consider fertile HC-models with four-states and the parametre activity on a Cayley tree. It is known that three types of such models exist. For each of these models we prove uniqueness of the translation-invarinat Gibbs measure on a Cayley tree of order two., Comment: in Russian

In this paper we show that under some conditions on the parameter of the Potts model with three states with zero external field on the Cayley tree of order $k>2$, there are exactly two periodic (non translation-invariant) Gibbs measures., Comment: in Russian

For the $q$-state Potts model on a Cayley tree of order $k\geq 2$ it is well-known that at sufficiently low temperatures there are at least $q+1$ translation-invariant Gibbs measures which are also tree-indexed Markov chains. Such measures are called translation-invariant splitting Gibbs measures (TISGMs). In this paper we find all TISGMs, and show in particular that at sufficiently low temperatures their number is $2^{q}-1$. We prove that there are $[q/2]$ (where $[a]$ is the integer part of $a$) critical temperatures at which the number of TISGMs changes and give the exact number of TISGMs for each intermediate temperature. For the binary tree we give explicit formulae for the critical temperatures and the possible TISGMs. While we show that these measures are never convex combinations of each other, the question which of these measures are extremals in the set of all Gibbs measures will be treated in future work., Comment: 13 pages