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The R\'{e}nyi statistics is applied for a description of finite size effects in the 1D Ising model. We calculate the internal energy of the spin chain and the system temperature using the R\'{e}nyi distribution and postulate them to be equal to their counterparts, obtained in the microcanonical ensemble. It allows us to self-consistently derive the R\'{e}nyi $q$-index and the Lagrange parameter $T$ to relate them to the physically observed system temperature $T_{\rm ph}$, and to show that the entropic phase transitions are possible in a broad temperature domain. We have also studied the temperature dependence of the internal energy $U(T_{\rm ph})$ at constant $q$ and an influence of the size related effects on the system thermodynamics., Comment: 20 pages, 9 figures (Published version)

The main purpose of this paper is to construct convergent series for the approximate calculation of certain integrals over the Gaussian measure with a nuclear covariance operator, nonlocal propagator, in separable Hilbert space. Such series arise, for example, in the model with the interaction Lagrangian $\sinh^{2(p+1)}\varphi$, where $p \in \mathbb{N}$ and $\varphi$ is the scalar field, although the problem can be solved in general form for a fairly wide class of Lagrangians: an even, strictly convex, continuous, non-negative function with a single zero value for $\varphi=0$ and for $|\varphi|\rightarrow +\infty$ growing faster than $\varphi^{2}$. We strictly define the scattering matrix, $\mathcal{S}$-matrix, at the zero value of the classical field, argument of the $\mathcal{S}$-matrix, of such a theory in terms of the corresponding integral, find the iterated expansion for the integrand (the Gaussian measure doesn't expand) over two orthonormal bases of functions, prove the validity of summation and integration interchange and thus find the expansion of the $\mathcal{S}$-matrix at the zero value of the classical field into the iterated series in powers of the interaction action. The individual terms of the resulting series have the form of a canonical partition function (CPF), and the methods of statistical physics are applicable to them. In particular, we express them in terms of Bell polynomials. It is important to note that such iterated series cannot be reduced to the perturbation theory (PT) series, since in the proposed model the latter diverges as $e^{n^{2}}$, where $n \in \mathbb {N}$ is the PT order. Along the way, we provide detailed mathematical background, including Beppo Levi's monotone convergence theorem (MCT) and Henri Lebesgue's dominated convergence theorem (DCT), without which the presented calculation would be significantly more complex., Comment: Version 1: 35 pages

The main purpose of this paper is to derive a new perturbation theory (PT) that has converging series. Such series arise in the nonlocal scalar quantum field theory (QFT) with fractional power potential. We construct PT for the generating functional (GF) of complete Green functions (including disconnected parts of functions) $\mathcal{Z}\left[j\right]$ as well as for GF of connected Green functions $\mathcal{G}\left[j\right]=\ln \mathcal{Z}\left[j\right]$ in powers of coupling constant $g$. It has infrared (IR)-finite terms. We prove that the obtained series, which has the form of a grand canonical partition function (GCPF), is dominated by a convergent series, in other words, has majorant, which allows to expand beyond the weak coupling $g$ limit. Vacuum energy density in second order in $g$ is calculated and researched for different types of Gaussian part $S_{0}[\phi]$ of the action $S[\phi]$. Further in the paper, using the polynomial expansion, the general calculable series for $\mathcal{G}\left[j\right]$ is derived. We provide, compare and research simplifications in cases of second-degree polynomial and hard-sphere gas (HSG) approximations. The developed formalism allows us to research the physical properties of the considering system across the entire range of coupling constant $g$, in particular, the vacuum energy density., Comment: V1 - raw preprint; V2 - fix of language; V3 - significantly revised preprint, MDPI template

Dualities between quantum field theories have proven to be a powerful tool in various areas of physics. In this paper, we introduce a new perspective for obtaining strong coupling expansions based on a well-known technique -- the Field-space Fourier transform. We discuss the advantages of this approach for a class of Euclidean quantum field theories on a general lattice, with a focus on a self-interacting $\phi^4$ scalar field theory defined on a cubic lattice of arbitrary dimension. We establish a duality between the strong coupling regime of this theory and the weak coupling regime of a corresponding dual theory. Without loss of generality, we choose the original theory to be local and show that its dual action becomes nonlocal. Using standard diagrammatic techniques, we derive expansions for the two-point correlator and the free energy per site in the regime of large and intermediate coupling constants $g$. The obtained expansions remain regular in the limit $g \to 0$ and exhibit rapid numerical convergence in the considered regions. Numerical analysis in dimensions $d = 2$ and $d = 3$ demonstrates good agreement between our analytical results and Monte Carlo simulations. Furthermore, we show that the strong coupling expansions are consistent with traditional weak coupling expansions.

One of the basic concepts of modern physics with a long prehistory is a fluid, which means a substance that flows under an applied shear stress. In this sense fluids form a wide subset of the phases of matter that includes liquids, dense gases, plasmas, and to some extent even plastic solids. Fluidity is one of the main dynamical characteristics that depends strongly on the details of the local structure. And vice versa, dominant details of local structural ordering in the arrangement of particles on some time scales are important for understanding the dynamics of fluids. The orderliness over distances comparable to the inter-particle distances is usually treated as the short-range order, whereas the orderliness repeated over infinitely large distances is called the long-range order. Both are absent in the ideal gas, but liquids and amorphous solids exhibit the short-range order. The physics of crystalline solids with the long-range order is well understood. In fluids, however, the atomic structure is changing with time. How are specific features of structural ordering reflected in the fluid dynamics? In this chapter we try to find answers to some old and new questions that still make the fluid dynamics still very attractive for the theoretical studies., Comment: Chapter submitted to the book: Order, Disorder and Criticality: Advanced Problems of Phase Transition Theory. Ed. by Yu. Holovatch. Vol. 7, 2022, World Scientific, Singapore

The non-Markovian master equation for open quantum systems is obtained by generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath $\varrho_{B}(t)$ and of the system $\varrho_{S}(t)$ are written. Formal solution of the equation for $\varrho_{B}(t)$ in the 2-nd approximation in interaction yields a specific extra term, related to the intrinsic bath dynamics. This term is nonlinear in the reduced density matrix $\varrho_{S}(t)$, and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we apply the generalized ZN projection scheme to a simple dephasing model. We study the obtained kinetic equation both in the Markovian approximation and beyond it (for the term related to the intrinsic bath dynamics) and compare the results with the exact ones., Comment: 19 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1911.12312

Activation cross sections of the $^{nat}$Rb (d,xn)$^{87m,85m,85g,83,82}$Sr, $^{nat}$Rb(d,x)$^{86,84,83,82m}$Rb and $^{nat}$Rb(d,x)$^{85m}$Kr nuclear reactions have been measured for the first time through an activation method combining the stacked foil irradiation technique and gamma-ray spectrometry. The provided cross sections from the present investigation are all new, in such a way contribute to the completeness of the experimental database. The experimental cross sections were compared with the theoretical prediction in the TENDL-2019 TALYS based library and with our calculation using ALICE-D and EMPIRE-D model codes in order the improve their predictivity. Thick target production yields were calculated form the new cross sections for all investigated radioisotopes. Practical applications of the results are shortly discussed.

An IAEA research project was dedicated to the compilation, evaluation and recommendation of cross-section data for the accelerator production of $^{11}$C, $^{13}$N, $^{15}$O, $^{18}$F, $^{64}$Cu, and $^{124}$I positron-emitting radionuclides clinically used for PET imaging, and for the accelerator production of two gamma emitters, $^{81}$Rb and $^{123}$I, used in SPECT imaging. Cross sections for 19 charged-particle induced reactions that can be employed for radionuclide accelerator production were evaluated including uncertainties. The resulting reference cross-section data were obtained from Pad\'e fits to selected and corrected experimental data, and integral thick target yields were subsequently deduced. Uncertainties in the fitted results were estimated via a Pad\'e least-squares method with the addition of a 4\% assessed systematic uncertainty to the estimated experimental uncertainty. Experimental data were also compared with theoretical predictions available from the TENDL library. All of the numerical reference cross-section data with their corresponding uncertainties and deduced integral thick target yields are available on-line at the IAEA-NDS medical portal https://www-nds.iaea.org/medportal/ and also at the IAEA-NDS web page https://www-nds.iaea.org/medical/., Comment: 24 pages, 36 figures, 150 references

The non-Markovian master equation for open quantum systems is obtained by generalization of the ordinary Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath $\varrho_{B}(t)$ and the system $\varrho_{S}(t)$ are written down. A formal solution of the equation for $\varrho_{B}(t)$, having been inserted in the equation for the reduced density matrix of the system, in the 2-nd approximation in interaction yields a very specific extra term in the generalized master equation. This term, being nonlinear in $\varrho_{S}(t)$, is related to the intrinsic bath dynamics and vanishes in the Markovian limit. To verify the consistence and robustness of our approach, we applied the generalized ZN projection scheme to a simple dephasing model. It is shown that consideration of the lowest order in interaction is insufficient to describe time evolution of the system coherence adequately. We explain this fact by analyzing the exact and approximate forms of $\varrho_{B}(t)$ and give some hints how to take the dynamic correlations (which originate from the spin-bath coupling) into account., Comment: 26 pages, 2 figures, 4 appendixes

Velocity autocorrelation functions (VAF) of the fluids are studied on short- and long-time scales within a unified approach. This approach is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the high order memory functions, which have purely kinetic origin. The VAFs obtained within our method are compared with computer simulation data for the liquid Ne at different densities and the results, which follow from the Markovian approximation for the highest order kinetic kernels. It is shown that in all the thermodynamic points and at the chosen level of the hierarchy, our results agree much better with the MD data than those of the Markovian approximation. The density dependence of the transition time, needed for the fluid to attain the hydrodynamic stage of evolution, is evaluated. The common and distinctive features of our method are discussed in their relations to the generalized collective mode (GCM) theory, the mode coupling theory (MCT), and some other theoretical approaches., Comment: 26 pages, 4 figures

In the frame of a systematical study of light ion induced nuclear reactions on hafnium, activation cross sections for proton induced reactions were investigated. Excitation functions were measured in the 38 to 65 MeV energy range for the $^{nat}$Hf(p,xn)$^{180g,177,176,175,173}$Ta, $^{nat}$Hf(p,x)$^{180m,179m,175,173,172,171}$Hf, $^{177g,173,172,171,170,169}$Lu and $^{nat}$Hf(p,x)$^{169}$Yb reactions by using the activation method, combining stacked foil irradiation and off line gamma ray spectroscopy. The experimental results are compared with earlier results in the overlapping energy range, and with the theoretical predictions of the ALICE IPPE and EMPIRE theoretical codes and of the TALYS code reported in the TENDL2015 and TENDL2017 libraries. The production routes of $^{172}$Lu (and its parent $^{172}$Hf) and of $^{169Y}$b are reviewed.

Excitation functions were measured in the 31 - 49.2 MeV energy range for the natPd(d,xn)111,110m,106m,105,104g,103Ag, natPd(d,x) 111m,109,101,100Pd, natPd(d,x), 105,102m,102g,101m,101g,100,99m,99gRh and natPd(d,x)103,97Ru nuclear reactions by using the stacked foil irradiation technique. The experimental results are compared with our previous results and with the theoretical predictions calculated with the ALICE-D, EMPIRE-D and TALYS (TENDL libraries) codes.

Excitation functions were measured for the production of the 101,100Pd, 102m, 102g,101m,101g,100,99m,99gRh and 97Ru radionuclides by bombardment of 103Rh targets with proton beams up to 70 MeV, some of them for the first time. The new results are compared with the earlier experimental data and with the theoretical nuclear model code calculations from ALICE-IPPE, EMPIRE and TALYS 1.6. Thick target yields were deduced and possible application of the new data for production of medically relevant 101m,101gRh and 97Ru are discussed.

Experimental cross sections are presented for the 159Tb(p,xn)153,155,157,159Dy, 152,153,155,156m2,m1,g,158Tb and 153,151Gd nuclear reactions up to 65 MeV. The experimental results are compared with the recently reported experimental data and with the results of the nuclear reaction codes ALICE-IPPE, EMPIRE and TALYS as reported in the TENDL-2015 on-line library. Integral thick-target yields are also derived for the reaction products used in practical applications and production routes are discussed.

Excitation functions were measured for the $^{nat}$Ag(d,x)$^{105,104}$Cd, $^{110m,108m,106m,105g,104g}$Ag and $^{101}$Pd, $^{105,101m}$Rh reactions over the energy range 33 50 MeV by using the stacked foil activation technique and subsequent high-resolution gamma spectrometry. We present the first experimental cross section data above 40 MeV for all of these reactions and the first experimental cross section data for $^{nat}$Ag(d,x)$^{108m,104g}$Ag and $^{105,103}$Rh. The experimental data are compared with results of the model calculations performed with the ALICE D, EMPIRE D theoretical nuclear reaction model codes and with the TALYS code results as available in the TENDL2014 and 2015 on-line libraries.

A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation times of the higher order memory functions, which have a purely kinetic origin. The VAFs obtained within our approach are compared with the results of the Markovian approximation for memory kernels. It is shown that although in the "overdamped" regime both approaches agree to a large extent at the initial and intermediate times of the system evolution, our formalism yields power law relaxation of the VAFs which is not observed at the description with a finite number of the collective modes. Explicit expressions for the transition times from kinetic to hydrodynamic regimes are obtained from the analysis of the singularities of spectral functions in the complex frequency plane., Comment: 14 pages, 2 figures

Activation cross-sections of deuterons induced reactions on Nb targets were determined with the aim of different applications and comparison with theoretical models.

In the frame of a systematic study of excitation functions of deuteron induced reactions the excitation functions of the $^{133}$Cs(d,x)$^{133m,133mg,131mg}$Ba, ${134,132}$Cs and $^{129m}$Xe nuclear reactions were measured up to 40 MeV deuteron energies by using the stacked foil irradiation technique and $\gamma$-ray spectroscopy of activated samples. The results were compared with calculations performed with the theoretical nuclear reaction codes ALICE-IPPE-D, EMPIRE II-D and TALYS calculation listed in the TENDL-2014 library. A moderate agreement was obtained. Based on the integral yields deduced from our measured cross sections, production of $^{131}$Cs via the $^{133}$Cs(d,4n)$^{131}$Ba $\longrightarrow$ $^{131}$Cs reaction and $^{133}$Ba via $^{133}$Cs(d,2n) reactions is discussed in comparison with other charged particle production routes., Comment: 8 journal pages, 12 figures 2 tables

The energy range of our earlier measured activation cross-sections data of longer-lived products of deuteron induced nuclear reactions on indium were extended from 40 MeV up to 50 MeV. The traditional stacked foil irradiation technique and non-destructive gamma spectrometry were used. No experimental data were found in literature for this higher energy range. Experimental cross-sections for the formation of the radionuclides $^{113,110}$Sn, $^{116m,115m,114m,113m,111,110g,109}$In and $^{115}$Cd are reported in the 37-50 MeV energy range, for production of $^{110}$Sn and $^{110g,109}$In these are the first measurements ever. The experimental data were compared with the results of cross section calculations of the ALICE and EMPIRE nuclear model codes and of the TALYS1.6 nuclear model code as listed in the on-line library TENDL-2014.

Evaluation of nuclear data for production routes of $^{110m}$In is in progress in the frame of an IAEA Coordinated Research Project (CRP). New experimental cross section data for the indirect $^{nat}$In(p,x)$^{110}$Sn $\longrightarrow$ $^{110m}$In and for the direct $^{107}$Ag($\alpha$,n)$^{110m}$In and $^{109}$Ag($^{3}$He,2n)$^{110m}$In production routes and for the satellite impurity reactions $^{107}$Ag($\alpha$,xn)$^{110g,109}$In and $^{109}$Ag($^{3}$He,xn)$^{110g,111,109}$In have been measured by using the activation method, stacked foil irradiation technique and gamma-ray spectrometry. Additional data are reported for production of the $^{111}$In diagnostic gamma-emitter via the $^{109}$Ag($\alpha$,2n)$^{111}$In reaction. The earlier experimental data were critically reviewed in order to prepare recommended data and optimal production parameters for the different routes.

Activation cross sections for proton induced reactions on Sm are presented for the first time for $^{nat}$Sm(p,xn)$^{154,152m2,152m1,152g,150m,150g,149,148,147,146,145}$Eu, $^{nat}$Sm(p,x)$^{153,145}$Sm, $^{nat}$Sm(p,x)$^{151,150,149,148g,148m,146,144,143}$Pm and $^{nat}$Sm(p,x)$^{141}$Nd up to 65 MeV. The cross sections were measured via activation method by using a stacked-foil irradiation technique and high resolution gamma ray spectroscopy. The results were compared with results of the nuclear reaction codes ALICE, EMPIRE and TALYS (results taken from TENDL libraries). Integral yields of the activation products were calculated from the excitation functions., Comment: arXiv admin note: text overlap with arXiv:1411.7161

Activation cross-sections data of longer-lived products of proton induced nuclear reactions on dysprosium were extended up to 65 MeV by using stacked foil irradiation and gamma spectrometry experimental methods. Experimental cross-sections data for the formation of the radionuclides $^{159}$Dy, $^{157}$Dy, $^{155}$Dy, $^{161}$Tb, $^{160}$Tb, $^{156}$Tb, $^{155}$Tb, $^{154m2}$Tb, $^{154m1}$Tb, $^{154g}$Tb, $^{153}$Tb, $^{152}$Tb and $^{151}$Tb are reported in the 36-65 MeV energy range, and compared with an old dataset from 1964. The experimental data were also compared with the results of cross section calculations of the ALICE and EMPIRE nuclear model codes and of the TALYS nuclear reaction model code as listed in the latest on-line libraries TENDL 2013., Comment: 16 figures 4 tables. arXiv admin note: text overlap with arXiv:1310.4695

We consider the qubit initial state preparation due to the nonselective measurements on an overcomplete basis, when the number of outcomes $N=3$. To be specific, we have chosen the dephasing model and applied the conditions for a post-measurement state to ensure a gradual coherence enhancement at the initial stage of the system evolution. It is shown that contrary to the von Neumann-L\"uders projection scheme with $N=2$, the most mixed post-measurement state of the qubit in the general case can depend on the bath temperature. This remarkable feature allows one to consider a ``temperature controlled'' initial purification of the open quantum system. We also consider some kinds of the repeated nonselective measurements from the viewpoint of an eventual system purification and analyze the important peculiarities of such schemes., Comment: 12 pages, 1 figure

Due to potential level of energy intensity 178m2Hf is an extremely interesting isomer. One possible way to produce this isomer is irradiation of nat-Ta or nat-W samples with high energy protons. Irradiation of nat-Ta and nat-W samples performed for other purposes provides an opportunity to study the corresponding reactions. This paper pre-sents the 178m2Hf independent production cross sections for both targets measured by the gamma-ray spectrometry method. The reaction excitation functions have been obtained for the proton energies from 40 up to 2600 MeV. The experimental results were compared with calculations by various versions of the intranuclear cascade model in the well-known codes: ISABEL, Bertini, INCL4.5+ABLA07, PHITS, CASCADE07 and CEM03.02. The isomer ratio for the nat-Ta(p,x)178m2Hf reaction is evaluated on the basis of the available data., Comment: 8 pages, 8 figures, 1 table, submitted to Phys. Rev. C

The influence of the initial preparation on dephasing in open quantum dynamics is studied using an exactly solvable model of a two-level system (qubit) interacting with a bosonic bath. It is found that for some classes of non-selective preparation measurements, qubit-bath correlations lead to a significant enhancement of coherence in the qubit at the initial stage of evolution. The time behavior of the qubit purity and entropy in the regime of enhancement of coherence is considered for different temperatures and coupling strengths.