The robustness of contextuality and the contextuality cost of empirical models

In this paper, we introduce and discuss the robustness of contextuality (RoC) R_C(e) and the contextuality cost C(e) of an empirical model e. The following properties of them are proved. (i) An empirical model e is contextual if and only if R_C(e) > 0; (ii) the RoC function R_C is convex, lower semi-continuous and un-increasing under an affine mapping on the set EM of all empirical models; (iii) e is non-contextual if and only if C(e) = 0; (iv) e is contextual if and only if C(e) > 0; (v) e is strongly contextual if and only if C(e) = 1. Also, a relationship between R_C(e) and C(e) is obtained. Lastly, the RoC of three empirical models is computed and compared. Especially, the RoC of the PR boxes is obtained and the supremum 0.5 is found for the RoC of all no-signaling type (2, 2, 2) empirical models.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Effects of charge on dynamical instability of spherical collapse in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The effects of charge on stable structure of spherically symmetric collapsing model comprising anisotropic matter distribution are studied in f(R, T) gravity, where R and T correspond to scalar curvature and trace of the energy-momentum tensor, respectively. We construct the field equations, Maxwell equations and dynamical equations in this scenario. We employ linear perturbation scheme on physical variables, metric functions as well as modified terms to establish the evolution or collapse equation for a consistent functional form of f(R, T) gravity. We investigate the limit of instability in Newtonian as well as post Newtonian regimes. It is found that charge plays a fundamental role to slow down the collapse and form a more stable system.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

Gamow Vectors and Borel Summability in a Class of Quantum Systems

We analyze the detailed time dependence of the wave function ψ(x,t) for one dimensional Hamiltonians \(H=-\partial_{x}^{2}+V(x)\) where V (for example modeling barriers or wells) and ψ(x,0) are compactly supported.We show that the dispersive part of ψ(x,t) is the Borel sum of its asymptotic series in powers of t ^?1/2, t→∞. The remainder, the difference between ψ and the Borel sum, i.e., the exponential part of the transseries of ψ, is a convergent expansion of the form \(\sum_{k=0}^{\infty}g_{k}\Gamma_{k}(x)e^{-\gamma_{k} t}\), where Γ _k are the Gamow vectors of H, and iγ _k are the associated resonances; generically, all g _k are nonzero. For large k, γ _k ～const?klog?k+k ² π ² i/4. The effect of the Gamow vectors is visible when time is not very large, and the decomposition defines rigorously resonances and Gamow vectors in a nonperturbative regime, in a physically relevant way.The decomposition allows for calculating ψ for moderate and large t, to any prescribed exponential accuracy, using optimal truncation of power series plus finitely many Gamow vectors contributions.The analytic structure of ψ is perhaps surprising: in general (even in simple examples such as square wells), ψ(x,t) turns out to be C ^∞ in t but nowhere analytic on ?⁺. In fact, ψ is t-analytic in a sector in the lower half plane and has the whole of ?⁺ a natural boundary. In the dual space, we analyze the resurgent structure of ψ.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Hyperfine nuclear interaction at copper lattice sites of high-temperature superconductors studied by <Superscript>61</Superscript>Cu(<Superscript>61</Superscript>Ni) Mössbauer emission spectroscopy

Mössbauer emission spectroscopy on the ⁶¹Cu(⁶¹Ni) isotope has been used to determine the quadrupole coupling constant C(Ni) and magnetic induction B(Ni) for the ⁶¹Ni²⁺ probe at copper sites in Cu₂O, CuO, La_{2 ?x}Ba_xCuO₄, Nd_2?xCe_xCuO₄, RBa₂Cu₃O₆, and RBa₂Cu₃O₇ (R=Y, Nd, Gd, Yb). The compounds containing divalent copper were found to exhibit linear C(Ni) vs. C(Cu) and B(Ni) vs. B(Cu) relations [C(Cu) and B(Cu) are the quadrupole coupling constant and magnetic induction for the ⁶³Cu probe, respectively, found by NMR], which is interpreted as an argument for the copper being in divalent state. The deviation of the data points corresponding to the Cu(1) sites in RBa₂Cu₃O₆ and RBa₂Cu₃O₇ from the C(Ni) vs. C(Cu) straight line may be due either to the copper valence being other than 2+ (in the RBa₂Cu₃O₆ compounds) or to the principal axes of the total and valence electric field gradient being differently oriented (in the RBa₂Cu₃O₇ compounds).     

1<Emphasis Type="Italic">∕</Emphasis><Emphasis Type="Italic">f</Emphasis><Superscript><Emphasis Type="Italic">β</Emphasis></Superscript> noise for scale-invariant processes: how long you wait matters

We study the power spectrum which is estimated from a nonstationary signal. In particular we examine the case when the signal is observed in a measurement time window [t _w , t _w + t _m ], namely the observation started after a waiting time t _w , and t _m is the measurement duration. We introduce a generalized aging Wiener–Khinchin theorem which relates between the spectrum and the time- and ensemble-averaged correlation functions for arbitrary t _m and t _w . Furthermore we provide a general relation between the non-analytical behavior of the scale-invariant correlation function and the aging 1∕f ^β noise. We illustrate our general results with two-state renewal models with sojourn times’ distributions having a broad tail.     

Transient bi-fractional diffusion: space-time coupling inducing the coexistence of two fractional diffusions

Anomalous diffusion is researched within the framework of the coupled continuous time random walk model, in which the space-time coupling is considered through the correlated function g(t) ~ t ^γ , 0 ≤ γ< 2, and the probability density function ω(t) of a particle’s transition time t follows a power law for large t: ω(t) ~ t ^{? (1 + α)},1 <α< 2. The bi-fractional generalized master equation is derived analytically which can be applied to describe the transient bi-fractional diffusion phenomenon which is induced by the space-time coupling and the asymptotic behavior of ω(t). Numerical results show that for the transient bi-fractional diffusion, there is a transition from one fractional diffusion to another one in the diffusive process.     

Control of Quantum Echo and Bell State Swapping of Two Atomic Qubits in the Two-Mode Vacuum Field Environment

We investigate quantum echo control and Bell state swapping for two atomic qubits (TAQs) coupling to two-mode vacuum cavity field (TMVCF) environment via two-photon resonance. We discuss the effect of initial entanglement factor ?? and relative coupling strength R=g₁/g₂ on quantum state fidelity of TAQs, and analyze the relation between three kinds of quantum entanglement(C(ρ_a),C(ρ_f),S(ρ_a)) and quantum state fidelity, then reveal physical essence of quantum echo of TAQs. It is shown that in the identical coupling case R=1, periodic quantum echo of TAQs with π cycle is always produced, and the value of fidelity can be controlled by choosing appropriate ?? and atom-filed interaction time. In the non-identical coupling case R≠1, quantum echoes with periods of π, 2π and 4π can be formed respectively by adjusting R. The characteristics of quantum echo results from the non-Markovianity of TMVCF environment, and then we propose Bell state swapping scheme between TAQs and two-mode cavity field.     

Relaxation of the remanent resistance of granular HTSC Y-Ba-Cu-O + CuO composites after magnetic field treatment

The hysteresis of magnetoresistance R(H) and relaxation of the remanent resistance R _rem with time after magnetic field treatment of HTSC (Y-Ba-Cu-O) + CuO composites are studied. Such a composite constitutes a network of Josephson junctions wherein the nonsuperconducting component (CuO) forms Josephson barriers between HTSC grains. By comparing the experimental R _rem(t) and R(H) dependences, it is shown that the relaxation of the remanent resistance is caused by the decreased magnetic field in the intergrain medium due to relaxation of magnetization. The reason is uncovered for the differences between the published values of pinning potentials determined by measuring the relaxation of magnetization or resistance and fitting them by the Anderson law.     

Cosmological implications of different baryon acoustic oscillation data

In this work, we explore the cosmological implications of different baryon acoustic oscillation(BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering(GC) statistics(hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics(hereafter BAO2). To make a comparison, we also take into account the case without BAO data(hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the ΛCDM, the w CDM, and the Chevallier-Polarski-Linder(CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, including its effects on parameter space, equation of state(Eo S), figure of merit(Fo M), deceleration-acceleration transition redshift,Hubble parameter H(z), deceleration parameter q(z), statefinder hierarchy S_3(1)(z), S_4(1)(z) and cosmic age t(z). We find that:(1)NO BAO data always give a smallest fractional matter density ?_(m0), a largest fractional curvature density ?k0and a largest Hubble constant h; in contrast, BAO1 data always give a largest ?_(m0), a smallest ?_(k0) and a smallest h.(2) For the w CDM and the CPL model, NO BAO data always give a largest Eo S w; in contrast, BAO2 data always give a smallest w.(3) Compared with the case of BAO1, BAO2 data always give a slightly larger Fo M, and thus can give a cosmological constraint with a slightly better accuracy.(4) The impacts of different BAO data on the cosmic evolution and the comic age are very small, and cannot be distinguished by using various dark energy diagnoses and the cosmic age data.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

Limiting rate of secret-key generation in quantum cryptography in spacetime

The fundamental restrictions on the maximum admissible rate of secret-key commitment in quantum cryptography in real time are discussed. It is shown that the maximum rate in a quantum channel with limited transmission band is achieved in a cryptosystem on orthogonal states. The dimensionless rate (the number of bits per unit time frequency band through unit of the channel) is determined by the universal function C(λ₀(ΔkT))/ΔkT [where C(λ₀(ΔkT)) is the transmission capacity of a classical binary channel, Δk is the transmission band width, 1/T is the transmission frequency of quantum states, and λ₀ is the maximum eigenvalue of a certain integral equation].     

The reactions N14(n, α)B11 and N14(n,t)C12 observed with a gridded ionization chamber

The cross sections for the reactions N¹⁴(n, α)B¹¹ and N¹⁴(n, t)C¹² have been measured in the neutron energy range 4.0 to 6.4 MeV and at 2.5 MeV. Mono-energetic neutrons were produced in the D(d, n) He³ reaction using a gas target. The (n, α) and (n, t) disintegrations were detected in a gridded ionization chamber filled with an argonnitrogen mixture. The response of the chamber under different operation conditions is described. The excitation functions, measured with a neutron energy resolution of 40 to 50 keV, are given for theα ₀ group from the N¹⁴(n,α)B¹¹ reaction over the entire neutron energy range and for theα ₁ group and the t₀ group from N¹⁴(n, t) C¹² for neutron energies above 4.3 and 5.6 MeV, respectively.     

Magnetoresistance hysteresis in granular HTSCs as a manifestation of the magnetic flux trapped by superconducting grains in YBCO + CuO composites

Hysterestic behavior of the magnetoresistance of granular HTSCs and its interaction with the magnetic hysteresis are studied by measuring magnetoresistance R(H) and critical current I _c(H) of composites formed by HTSC Y_0.75Lu_0.25Ba₂Cu₃O₇ and CuO. A network of Josephson junctions is formed in such composites, in which the nonsuperconducting component plays the role of barriers between HTSC grains. Hysteretic dependences R(H) of magnetoresistance are studied in a wide range of transport current density j and are analyzed in the framework of the two-level model of a granular superconductor, in which dissipation takes place in the Josephson medium and the magnetic flux can be pinned both in grains and in the Josephson medium. The interrelation between the hysteresis of critical current I _c(H) and the evolution of the hysterestic dependence R(H) of the magnetoresistance upon transport current variation is demonstrated experimentally. The effect of the magnetic past history on the hysteretic behavior of R(H) and the emergence of a segment with a negative magnetoresistance are analyzed. It is shown for the first time that the R(H) dependences are characterized by a parameter that is independent of the transport current, viz., the width of the R(H) hysteresis loop.     

A strongly asymmetric single-electron transistor operating as a zero-biased electrometer

We have studied a strongly asymmetric Al single-electron transistor with R₁ ? R₂ and C₁ ? C₂, where R_{1, 2} and C_{1, 2} are the tunnel resistances and capacitances of the first and second junction respectively. Due to the asymmetry in its electric parameters leading to strong asymmetry of the nonlinear I–V curve at zero bias (V = 0), the transistor demonstrated a remarkable current response to an AC signal at the values of the gate charge Q₀ close to (n + 1/2)e, where n is integer. A rather delicate regime of the transistor operation (V ? e/C_Σ) being important for unperturbed measurements was examined. The measured curves are in good agreement with a model based on the orthodox theory of single electron tunneling. This specific zero bias regime of an asymmetric transistor opens new opportunities for a single-electron transistor as an ultrasensitive charge/field sensor.     

Excitation of the Classical Electromagnetic Field in a Cavity Containing a Thin Slab with a Time-Dependent Conductivity

We derive an exact infinite set of coupled ordinary differential equations describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity containing a thin slab with the time-dependent conductivity σ(t) and dielectric permittivity ε(t) for the dispersion-less media. We analyze this problem in connection with the attempts to simulate the so-called dynamical Casimir effect in three-dimensional electromagnetic cavities containing a thin semiconductor slab periodically illuminated by strong laser pulses. Therefore, we assume that functions σ(t) and δε(t) = ε(t) ? ε(0) are different from zero during short time intervals (pulses) only. Our main goal here is to find the conditions under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). We obtain approximate solutions to the dynamical equations in the cases of “small” and “big” maximal values of the functions σ(t) and δε(t). We show that the single-mode approximation used in the previous studies can be justified in the case of “small” perturbations, but the initially excited field mode cannot be amplified in this case if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximum values of conductivity and the concentration of free carries (the model of an “almost ideal conductor”) created inside the slab under the crucial condition providing the negativity of the function δε(t). This result follows from a simple approximate analytical solution confirmed by exact numerical calculations. However, the evaluation shows that the necessary energy of laser pulses must be, probably, unrealistically high.