Censored Glauber Dynamics for the Mean Field Ising Model

We study Glauber dynamics for the Ising model on the complete graph on n vertices, known as the Curie-Weiss Model. It is well known that at high temperature (β<1) the mixing time is Θ(nlog?n), whereas at low temperature (β>1) it is exp?(Θ(n)). Recently, Levin, Luczak and Peres considered a censored version of this dynamics, which is restricted to non-negative magnetization. They proved that for fixed β>1, the mixing-time of this model is Θ(nlog?n), analogous to the high-temperature regime of the original dynamics. Furthermore, they showed cutoff for the original dynamics for fixed β<1. The question whether the censored dynamics also exhibits cutoff remained unsettled.In a companion paper, we extended the results of Levin et al. into a complete characterization of the mixing-time for the Curie-Weiss model. Namely, we found a scaling window of order \(1/\sqrt{n}\) around the critical temperature β _c =1, beyond which there is cutoff at high temperature. However, determining the behavior of the censored dynamics outside this critical window seemed significantly more challenging.In this work we answer the above question in the affirmative, and establish the cutoff point and its window for the censored dynamics beyond the critical window, thus completing its analogy to the original dynamics at high temperature. Namely, if β=1+δ for some δ>0 with δ ² n→∞, then the mixing-time has order (n/δ)log?(δ ² n). The cutoff constant is (1/2+[2(ζ² β/δ?1)]^?1), where ζ is the unique positive root of g(x)=tanh?(β x)?x, and the cutoff window has order n/δ.     

The electron energy spectrum and superconducting transition temperature of strongly correlated fermions with three-center interactions

The renormalizations of the fermionic spectrum are considered within the framework of the t-J* model taking into account three-center interactions (H₍₃₎) and magnetic fluctuations. Self-consistent spin dynamics equations for strongly correlated fermions with three-center interactions were obtained to calculate quasi-spin correlators. A numerical self-consistent solution to a system of ten equations was obtained to show that, in the nearest-neighbor approximation, simultaneously including H₍₃₎ and magnetic fluctuations at n>n₁ (n₁ ≈ 0.72 for 2t/U = 0.25) caused qualitative changes in the structure of the energy spectrum. A new Van Hove singularity is then induced in the density of states, and an additional maximum appears in the T_c(n) concentration dependence of the temperature of the transition to the superconducting phase with order parameter symmetry of the d _x ²?y² type.     

Hybrids of carbyne and fullerene

A new class of quasi-linear carbon molecules [C₆₀] _n [C _m ]_n?1 consisting of n fullerenes C₆₀ linked by n?1 carbyne-type C _m fragments with a system of conjugated bonds is described. The possible geometric configurations of such molecules and crystals on their base are discussed. The structure optimization by the empirical (MM+), semiempirical (PM3), and ab initio (HF/6-21) methods showed that these molecules are energetically stable.     

Infinitesimal Deformations of a Formal Symplectic Groupoid

Given a formal symplectic groupoid G over a Poisson manifold (M, π ₀), we define a new object, an infinitesimal deformation of G, which can be thought of as a formal symplectic groupoid over the manifold M equipped with an infinitesimal deformation \({\pi_0 + \varepsilon \pi_1}\) of the Poisson bivector field π ₀. To any pair of natural star products \({(\ast,\tilde\ast)}\) having the same formal symplectic groupoid G we relate an infinitesimal deformation of G. We call it the deformation groupoid of the pair \({(\ast,\tilde\ast)}\) . To each star product with separation of variables \({\ast}\) on a Kähler–Poisson manifold M we relate another star product with separation of variables \({\hat\ast}\) on M. We build an algorithm for calculating the principal symbols of the components of the logarithm of the formal Berezin transform of a star product with separation of variables \({\ast}\) . This algorithm is based upon the deformation groupoid of the pair \({(\ast,\hat\ast)}\) .     

Quantum Image Encryption Based on Iterative Framework of Frequency-Spatial Domain Transforms

A novel quantum image encryption and decryption algorithm based on iteration framework of frequency-spatial domain transforms is proposed. In this paper, the images are represented in the flexible representation for quantum images (FRQI). Previous quantum image encryption algorithms are realized by spatial domain transform to scramble the position information of original images and frequency domain transform to encode the color information of images. But there are some problems such as the periodicity of spatial domain transform, which will make it easy to recover the original images. Hence, we present the iterative framework of frequency-spatial domain transforms. Based on the iterative framework, the novel encryption algorithm uses Fibonacci transform and geometric transform for many times to scramble the position information of the original images and double random-phase encoding to encode the color information of the images. The encryption keys include the iterative time t of the Fibonacci transform, the iterative time l of the geometric transform, the geometric transform matrix G i which is n × n matrix, the classical binary sequences K (\(k_{0}k_{1}{\ldots } k_{2^{2n}-1}\)) and \(D(d_{0}d_{1}{\ldots } d_{2^{2n}-1}\)). Here the key space of Fibonacci transform and geometric transform are both estimated to be 2²⁶. The key space of binary sequences is (2 ^n×n ) × (2 ^n×n ). Then the key space of the entire algorithm is about \(2^{2{n^{2}}+52}\). Since all quantum operations are invertible, the quantum image decryption algorithm is the inverse of the encryption algorithm. The results of numerical simulation and analysis indicate that the proposed algorithm has high security and high sensitivity.     

Congratulations to Akusticheskii Zhurnal on the occasion of its 50th anniversary. Vibrations of spherical inclusions in elastic solids

Variational principles are derived for the analysis of dynamical phenomena associated with spherical inclusions embedded in homogeneous isotropic elastic solids. The starting point is Hamilton’s principle, with the material properties assumed to vary only with the radial distance r from the origin. Attention is restricted to disturbances that are symmetric about the polar (z) axis, such that the nonzero displacement components in spherical coordinates, u _r and u_θ, are independent of the polar coordinate φ. The symmetry allows for a decoupling of the polar components, the nth of which is described by U _{r, n} (r, t)P _n (cosθ) and U_{θ, n}(r, t)dP _n /dθ. A variational principle is subsequently derived for the field quantities U _{r, n} and U_{θ, n}. Concepts analogous to those of the theory of matched asymptotic expansions are used to embellish the principle in order to allow for the damping associated with the outward radiation of elastic waves. Examples illustrating the use of the variational principle for formulating plausible lumped-parameter models are given for the cases of n = 0 and n = 1.     

Spin observables in <Emphasis Type="Italic">np</Emphasis> elastic scattering in the energy range 200–600 MeV. Complete experiment

A survey of available experimental data on the measurement of spin observables in neutron-proton (np) elastic scattering in the neutron energy range 200–600 MeV is presented. Sixteen spin observables (the polarization of recoil particles P _0n00, the analyzing power A _00n0, the spin correlation parameters A _00nn , A _00ss , A _00sk , and A _00kk , the spin transfer parameters K _0nn0, K _0ss0, and K _0sk0, the depolarization parameters D _0n0n , D _0s0s , and D _0s0k , and the three-spin parameters N _0nkk , N _0skn , N _0ssn , and N _0sns for energies of 200–590 MeV and scattering angles in the center of mass system of 60°–164°) were studied in experiments using polarized neutron beams and polarized proton targets at the Paul Scherrer Institute. The results of these investigations present a complete set of precision data on np elastic scattering which, along with the complete set of data for proton-proton (pp) elastic scattering obtained earlier, provides a basis for unambiguous determination of the amplitudes of the scattering matrix for nucleon-nucleon (NN) elastic scattering for the channel with the isotopic spin I = 0 and makes it possible to describe NN interaction in a model-independent way.     

Grundzustand eines Fermi-Gases mit hard-sphere-Wechselwirkung

The decomposition of the ground state wave function of a Fermi gas interacting via hard core potentials into cluster functionsS _n leads to a systematic expansion of wave function and energy in powers of the parameterc=P _F r _c (r _c =hard core radius,P _F =Fermi momentum). For instance,S _n has the order of magnitudec ^n-λ-1, if λ=number of Fermion coordinates with distances smaller thanr _c . The first three energy terms agree with the ones given by other authors. Any occurrence of singular terms in the intermediate steps of the derivation can be avoided     

On a Semiclassical Formula for Non-Diagonal Matrix Elements

Let H(?)=?? ²d²/dx ²+V(x) be a Schrödinger operator on the real line, W(x) be a bounded observable depending only on the coordinate and k be a fixed integer. Suppose that an energy level E intersects the potential V(x) in exactly two turning points and lies below V _∞=lim?inf?_|x|→∞ V(x). We consider the semiclassical limit n→∞, ?=? _n →0 and E _n =E where E _n is the nth eigenenergy of H(?). An asymptotic formula for 〈n|W(x)|n+k〉, the non-diagonal matrix elements of W(x) in the eigenbasis of H(?), has been known in the theoretical physics for a long time. Here it is proved in a mathematically rigorous manner.     

Self-consistent expansion of a multicomponent plasma into a vacuum

The problem of the one-dimensional collisionless expansion of a multicomponent plasma into a vacuum is considered. In the hydrodynamic approximation, an approximate analytical solution for an arbitrary set of ion species with masses M₁,..., M_n and charge numbers Z₁e, Z₂e,..., Z_ne is found by using the technique of self-similar variables employed by Gurevich, Pariiskaya, and Pitaevskii for the case of single-species ions. A numerical iterative algorithm is developed in which the analytical solution is used as a first approximation.     

On correlators for high multiplicity events

We present the results of the study of the energy correlators K₂(n) and K₃(n) and their ratio R₃(n) as a function of the hadron multiplicity at the LHC. The PYTHIA generator has been used. PYTHIA predicts that R₃(n) is not dependent on multiplicity. K₂(n), K₃(n), and the R₃(n) ratio can be studied at ATLAS.     

On Probability Domains

Motivated by IF-probability theory (intuitionistic fuzzy), we study n-component probability domains in which each event represents a body of competing components and the range of a state represents a simplex S _n of n-tuples of possible rewards–the sum of the rewards is a number from [0,1]. For n=1 we get fuzzy events, for example a bold algebra, and the corresponding fuzzy probability theory can be developed within the category ID of D-posets (equivalently effect algebras) of fuzzy sets and sequentially continuous D-homomorphisms. For n=2 we get IF-events, i.e., pairs (μ,ν) of fuzzy sets μ,ν∈[0,1] ^X such that μ(x)+ν(x)≤1 for all x∈X, but we order our pairs (events) coordinatewise. Hence the structure of IF-events (where (μ ₁,ν ₁)≤(μ ₂,ν ₂) whenever μ ₁≤μ ₂ and ν ₂≤ν ₁) is different and, consequently, the resulting IF-probability theory models a different principle. The category ID is cogenerated by I=[0,1] (objects of ID are subobjects of powers I ^X ), has nice properties and basic probabilistic notions and constructions are categorical. For example, states are morphisms. We introduce the category S _n D cogenerated by \(S_{n}=\{(x_{1},x_{2},\ldots ,x_{n})\in I^{n};\:\sum_{i=1}^{n}x_{i}\leq 1\}\) carrying the coordinatewise partial order, difference, and sequential convergence and we show how basic probability notions can be defined within S _n D.     

All possible Cayley-Klein contractions of quantum orthogonal groups

Spaces of constant curvature and their motion groups are described most naturally in the Cartesian basis. All these motion groups, also known as CK groups, are obtained from an orthogonal group by contractions and analytical continuations. On the other hand, quantum deformation of orthogonal group SO(N) is most easily performed in the so-called symplectic basis. We reformulate its standard quantum deformation to the Cartesian basis and obtain all possible contractions of quantum orthogonal group SO _q (N) for both untouched and transformed deformation parameters. It turned out that, similar to the undeformed case, all CK contractions of SO _q (N) are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of SO _q (N), N = 3, 4, 5, are regarded as examples.     

Diffraction spectra of order–order transition structural states in titanium monoxide

A new class of M_(n?i)X_(n?i) superstructures (n is an integer constant and i is a rational variable) that are formed after incomplete equilibrium second-order order–order phase transitions in solid solutions and in compounds with atom–vacancy ordering is proposed. New superstructures are superpositions of partially disordered M _n ?X _n superstructures of various symmetries in the matrix of the basic crystal structure. The model parameters affecting the positions and intensities of superstructure reflections on diffraction patterns have been studied by example of the high-temperature ordered phase β-TiO of titanium monoxide. It has been shown that the diffraction spectra of the low-symmetric M_(5-i)X_(5-i) superstructure (space group P1m1) and the high-symmetric M₅X₅ superstructure (space group Pm3?m) at certain parameters are identical in the positions of superstructure reflections.     

Spectra and mean energies of prompt neutrons from <Superscript>238</Superscript>U fission induced by primary neutrons of energy in the region <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript><20 MeV

The time-of-flight technique is used to measure the ratios R(E, E _n )=N(E, E _n )/N_Cf(E) of the normalized (to unity) spectra N(E, E _n ) of neutrons accompanying the neutron-induced fission of ²³⁸U at primary-neutron energies of E _n =6.0 and 7.0 MeV to the spectrum N_Cf(E) neutrons from the spontaneous fission of ²⁵²Cf. These experimental data and the results of their analysis are discussed together with data that were previously obtained for the neutron-induced fission of ²³⁸U at the primary energies of E _n =2.9, 5.0, 13.2, 14.7, 16.0, and 17.7 MeV.     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Low energy frontier: Physics with polarized cold neutrons

Recent developments in investigations of beta decay of the free neutron are discussed. Measurements of the neutron lifetime τ _n and the electron emission asymmetry A _n are a classic source of determination of the Standard Model parameters G _v , G _A and λ _n . Combined with the results of the muon decay experiments, the nuclear superallowed 0→0 transitions and decays of particles containing heavy quarks, they provide tests of the SM assumptions: the unitarity of the CKM matrix, the number of the neutrino families, or the CVC hypothesis. In contrast, more complex correlations between the spins and the momenta of the emitted particles, (e.g. B _n , D _n , R _n or G _n ), are uniquely sensitive to the so called “Physics beyond the Standard Model”. Thus the question of the right handed bosons, the admixture of the scalar or tensor interaction, with or without time reversal violating terms, may be addressed separately in a dedicated, single experiment. Further development of powerful beams of polarized cold neutrons and sources of ultracold neutrons is imperative for progress in these studies.     

The real solution to scalar field equation in 5D black string space

After the nontrivial quantum parameters Ω _n and quantum potentials V _n obtained in our previous research, the circumstance of a real scalar wave in the bulk is studied with the similar method of Brevik and Simonsen (Gen. Rel. Grav. 33:1839, 2001). The equation of a massless scalar field is solved numerically under the boundary conditions near the inner horizon r _e and the outer horizon r _c . Unlike the usual wave function Ψ_ωl in 4D, quantum number n introduces a new functions Ψ_{ωl n} , whose potentials are higher and wider with bigger n. Using the tangent approximation, a full boundary value problem about the Schrödinger-like equation is solved. With a convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients are obtained. If extra dimension does exist and is visible at the neighborhood of black holes, the unique wave function Ψ_{ωl n} may say something to it.     

Inflation of the early cold Universe filled with a nonlinear scalar field and a nonideal relativistic Fermi gas

We consider a possible scenario for the evolution of the early cold Universe born from a fairly large quantum fluctuation in a vacuum with a size a ₀ ? l _P (where l _P is the Planck length) and filled with both a nonlinear scalar field φ, whose potential energy density U(φ) determines the vacuum energy density λ, and a nonideal Fermi gas with short-range repulsion between particles, whose equation of state is characterized by the ratio of pressure P(n _F ) to energy density ε(n _F ) dependent on the number density of fermions n _F . As the early Universe expands, the dimensionless quantity ν(n _F ) = P(n _F )/ε(n _F ) decreases with decreasing n _F from its maximum value ν_max = 1 for n _F → ∞ to zero for n _F → 0. The interaction of the scalar and gravitational fields, which is characterized by a dimensionless constant ξ, is proportional to the scalar curvature of four-dimensional space R = κ[3P(n _F )–ε(n _F )–4λ] (where κ is Einstein’s gravitational constant), and contains terms both quadratic and linear in φ. As a result, the expanding early Universe reaches the point of first-order phase transition in a finite time interval at critical values of the scalar curvature R = R _c =–μ²/ξ and radius a _c ? a ₀. Thereafter, the early closed Universe “rolls down” from the flat inflection point of the potential U(φ) to the zero potential minimum in a finite time. The release of the total potential energy of the scalar field in the entire volume of the expanding Universe as it “rolls down” must be accompanied by the production of a large number of massive particles and antiparticles of various kinds, whose annihilation plays the role of the Big Bang. We also discuss the fundamental nature of Newton’ gravitational constant G _N .     

The effect of non-linear capacitances in the localization properties of aperiodic dual electric transmission lines

This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The V_C,n voltage across each capacitor is selected as a non-linear function of the electric charge q_n, i.e., V_C,n = q_n(1/C_n -ε_n|q_n|²)where C_n is the linear part of the capacitance and ε_n the amplitude of the non-linear term. We follow a binary distribution of values of ε_n, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.