Influence of temperature on the electric,dielectric and AC conductivity properties of nano-crystalline zinc substituted cobalt ferrite synthesized by solution combustion technique

Cobalt–zinc nanoferrites with formulae Co $_{1-x}$ Zn $_{x}$ Fe $_{2}$ O $_{4}$ , where x = 0.0, 0.1, 0.2 and 0.3, have been synthesized by solution combustion technique. The variation of DC resistivity with temperature shows the semiconducting behavior of all nanoferrites. The dielectric properties such as dielectric constant ( $\varepsilon $ ’) and dielectric loss tangent (tan $\delta )$ are investigated as a function of temperature and frequency. Dielectric constant and loss tangent are found to be increasing with an increase in temperature while with an increase in frequency both, $\varepsilon $ ’ and tan $\delta $ , are found to be decreasing. The dielectric properties have been explained on the basis of space charge polarization according to Maxwell–Wagner’s two-layer model and the hopping of charge between Fe $^{2+}$ and Fe $^{3+}$ . Further, a very high value of dielectric constant and a low value of tan $\delta $ are the prime achievements of the present work. The AC electrical conductivity ( $\sigma _\mathrm{AC})$ is studied as a function of temperature as well as frequency and $\sigma _\mathrm{AC}$ is observed to be increasing with the increase in temperature and frequency.     

Asymptotic Quantum Many-Body Localization from Thermal Disorder

We consider a quantum lattice system with infinite-dimensional on-site Hilbert space, very similar to the Bose–Hubbard model. We investigate many-body localization in this model, induced by thermal fluctuations rather than disorder in the Hamiltonian. We provide evidence that the Green–Kubo conductivity κ(β), defined as the time-integrated current autocorrelation function, decays faster than any polynomial in the inverse temperature β as \({\beta \to 0}\) . More precisely, we define approximations \({\kappa_{\tau}(\beta)}\) to κ(β) by integrating the current-current autocorrelation function up to a large but finite time \({\tau}\) and we rigorously show that \({\beta^{-n}\kappa_{\beta^{-m}}(\beta)}\) vanishes as \({\beta \to 0}\) , for any \({n,m \in \mathbb{N}}\) such that m?n is sufficiently large.     

Strong magnetic fields,Dirichlet boundaries,and spectral gaps

We consider magnetic Schrödinger operators $$H(\lambda \vec a) = ( - i\nabla - \lambda \vec a(x))^2$$ inL ₂(R ⁿ ), where $\vec a \in C^1 (R^n ;R^n )$ and λεR. LettingM={x;B(x)=0}, whereB is the magnetic field associated with $\vec a$ , and $M_{\vec a} = \{ x;\vec a(x) = 0\}$ , we prove that $H(\lambda \vec a)$ converges to the (Dirichlet) Laplacian on the closed setM in the strong resolvent sense, as λ→∞,provided the set $M\backslash M_{\vec a}$ has measure zero. In various situations, which include the case of periodic fields, we even obtain norm resolvent convergence (again under the condition that $M\backslash M_{\vec a}$ has measure zero). As a consequence, if we are given a periodic fieldB where the regions withB=0 have non-empty interior and are enclosed by the region withB≠0, magnetic wells will be created when λ is large, opening up gaps in the spectrum of $H(\lambda \vec a)$ . We finally address the question of absolute continuity of $\vec a$ for periodic $H(\vec a)$ .     

Chiral symmetry breaking in the colour dielectric model

Approximating the long-distance gluon dynamics ofSU(3)_colour by colour-dielectric block-spin variables, we obtain an effective QCD theory of a scalar colour-dielectric field and a massive colour-bleached gluon field coupled to light quarks. The massive vector field produces a strong attraction betweenq \(\bar q\) pairs, which leads toq \(\bar q\) condensation when the colour-dielectric field becomes small. We calculate \(\left\langle {\bar \psi \psi } \right\rangle\) and the pion decay constantf _n as a function of the dielectric field expectation value, by evaluating the fermion determinant in a derivative expansion, and integrating out the bosonic variables. We find that the effective quark-gluon coupling,α _s ^eff , including quark effects, is large on the surface of bags, where \(\left\langle {\bar \psi \psi } \right\rangle\) ±0, but decreases inside hadronic bags, where | \(\left\langle {\bar \psi \psi } \right\rangle\) | is decreasing.     

Charmonium rescattering effects in \psi(2S) \rightarrow \gamma \eta_{c}^{} decay

Charmonium rescattering effects in the M1 transition of $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ are investigated by modeling a $ \chi_{{cJ}}^{}$ or J/ $ \psi$ rescattering into a $ \eta_{c}^{}$ final state. The absorptive and dispersive part of the transition amplitudes for the rescattering loops of $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) and $ \gamma$ $ \chi$ ( $ \psi$ ) are separately evaluated. The numerical results show that the contribution from the $ \gamma$ $ \chi$ ( $ \psi$ ) rescattering process is negligible. Compared with the virtual D $ \bar{{D}}$ (D ^*) rescattering processes, the $ \eta$ $ \psi$ ( $ \gamma^{{\ast}}_{}$ ) process may be regarded as the next-leading order of the hadronic loop mechanism, which only offers the partial decay width of ～ 0.045 keV to the $ \psi$ (2S) $ \rightarrow$ $ \gamma$ $ \eta_{c}^{}$ .     

Warm-intermediate inflationary universe model with viscous pressure in high dissipative regime

Warm inflation model with bulk viscous pressure in the context of “intermediate inflation” where the cosmological scale factor expands as $a(t)=a_0\exp (At^f)$ , is studied. The characteristics of this model in slow-roll approximation and in high dissipative regime are presented in two cases: 1—Dissipative parameter $\Gamma $ as a function of scalar field $\phi $ and bulk viscous coefficient $\zeta $ as a function of energy density $\rho $ . 2— $\Gamma $ and $\zeta $ are constant parameters. Scalar, tensor perturbations and spectral indices for this scenario are obtained. The cosmological parameters appearing in the present model are constrained by recent observational data (WMAP7).     

Dielectric properties and microstructural characterization of cubic pyrochlored bismuth magnesium niobates

Cubic bismuth pyrochlores in the $\mathrm{Bi}_{2}\mathrm{O}_{3}$ –MgO– $\mathrm{Nb}_{2}\mathrm{O}_{5}$ system have been investigated as promising dielectric materials due to their high dielectric constant and low dielectric loss. Here, we report on the dielectric properties and microstructures of cubic pyrochlored $\mathrm{Bi}_{1.5}\mathrm{MgNb}_{1.5}\mathrm{O}_{7}$ (BMN) ceramic samples synthesized via solid-state reactions. The dielectric constant (measured at 1 MHz) was measured to be ${\sim}120$ at room temperature, and the dielectric loss was as low as 0.001. X-ray diffraction patterns demonstrated that the BMN samples had a cubic pyrochlored structure, which was also confirmed by selected area electron diffraction (SAED) patterns. Raman spectrum revealed more than six vibrational models predicted for the ideal pyrochlore structure, indicating additional atomic displacements of the A and $\mathrm{O}'$ sites from the ideal atomic positions in the BMN samples. Structural modulations of the pyrochlore structure along the [110] and [121] directions were observed in SAED patterns and high-resolution transmission electron microscopy (HR-TEM) images. In addition, HR-TEM images also revealed that the grain boundaries (GBs) in the BMN samples were much clean, and no segregation or impure phase was observed forming at GBs. The high dielectric constants in the BMN samples were ascribed to the long-range ordered pyrochlore structures since the electric dipoles formed at the superstructural direction could be enhanced. The low dielectric loss was attributed to the existence of noncontaminated GBs in the BMN ceramics.     

Smooth Crossed Products of Rieffel’s Deformations

Assume ${\mathcal{A}}$ is a Fréchet algebra equipped with a smooth isometric action of a vector group V, and consider Rieffel’s deformation ${\mathcal{A}_J}$ of ${\mathcal{A}}$ . We construct an explicit isomorphism between the smooth crossed products ${V\ltimes\mathcal{A}_J}$ and ${V\ltimes\mathcal{A}}$ . When combined with the Elliott–Natsume–Nest isomorphism, this immediately implies that the periodic cyclic cohomology is invariant under deformation. Specializing to the case of smooth subalgebras of C^*-algebras, we also get a simple proof of equivalence of Rieffel’s and Kasprzak’s approaches to deformation.     

Radiative open charm decay of the Y(3940) , Z(3930) , X(4160) resonances

We determine the radiative decay amplitudes for the decay into D^* and $ \bar{{D}}$ $ \gamma$ , or D ^* _s and $ \bar{{D}}_{s}^{}$ $ \gamma$ of some of the charmonium-like states classified as X , Y , Z resonances, plus some other hidden charm states which are dynamically generated from the interaction of vector mesons with charm. The mass distributions as a function of the $ \bar{{D}}$ $ \gamma$ or $ \bar{{D}}_{s}^{}$ $ \gamma$ invariant mass show a peculiar behavior as a consequence of the D ^* $ \bar{{D}}^{*}_{}$ nature of these states. The experimental search of these magnitudes can shed light on the nature of these states.     

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features:

1. The regularizedS ^δ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$
2. The Green positive-frequency functions which determine the operation of multiplication in \(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ?^δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$
3. The operator \(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ₁=δ₂=δ₃=0.
4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

     

|\epsilon|-Near-zero materials in the near-infrared

We consider a mixture of metal-coated quantum dots dispersed in a polymer matrix and, using a modified version of the standard Maxwell-Garnett mixing rule, we prove that the mixture parameters (particles radius, quantum dots gain, etc.) can be chosen so that the effective medium permittivity has an absolute value very close to zero in the near-infrared, i.e. $|{\rm Re}(\epsilon)| \ll 1$ and $|{\rm Im}(\epsilon)| \ll 1$ at the same near-infrared wavelength. Resorting to full-wave simulations, we investigate the accuracy of the effective medium predictions and we relate their discrepancy with rigorous numerical results to the fact that $|\epsilon| \ll 1$ is a critical requirement. We show that a simple method for reducing this discrepancy, and hence for achieving a prescribed and very small value of $|\epsilon|, $ consists in a subsequent fine-tuning of the nanoparticles volume filling fraction.     

Lyapunov Exponents of Random Walks in Small Random Potential: The Lower Bound

We consider the simple random walk on ${\mathbb{Z}^d}$ Z d , d > 3, evolving in a potential of the form β V, where ${(V(x))_{x \in \mathbb{Z}^d}}$ ( V ( x ) ) x ∈ Z d are i.i.d. random variables taking values in [0, + ∞), and β > 0. When the potential is integrable, the asymptotic behaviours as β tends to 0 of the associated quenched and annealed Lyapunov exponents are known (and coincide). Here, we do not assume such integrability, and prove a sharp lower bound on the annealed Lyapunov exponent for small β. The result can be rephrased in terms of the decay of the averaged Green function of the Anderson Hamiltonian ${-\triangle + \beta V}$ - ? + β V .     

On Gravitational Effects in the Schrödinger Equation

The Schrödinger  equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon  equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional  action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski  space–time  , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations  that differ in a curved background  space–time   $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon  action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational  field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational  contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time  coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger  (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional  mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational  Lagrangian   $L_\mathcal{D}$ which contains higher-derivative  terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory  , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski  space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter  space for $8 \le \mathcal {D} \le 10$ .     

Reaction pp \rightarrow pp \pi \pi \pi as a background for hadronic decays of the \eta^{{\prime}}_{} meson

Isospin violating hadronic decays of the $ \eta$ and $ \eta{^\prime}$ mesons into 3 $ \pi$ mesons are driven by a term in the QCD Lagrangian proportional to the mass difference of the d and u quarks. The source giving large yield of the mesons for such decay studies are pp interactions close to the respective kinematical thresholds. The most important physics background for $ \eta$ , $ \eta{^\prime}$ $ \rightarrow$ $ \pi$ $ \pi$ $ \pi$ is coming from direct three-pion production reactions. In case of the $ \eta$ meson the background for the decays is relatively low ( $ \approx$ 10% . The purpose of this article is to provide an estimate of the direct pion production background for the $ \eta{^\prime}$ $ \rightarrow$ 3 $ \pi$ decays. Using the inclusive data from the COSY-11 experiment we have extracted the differential cross-section for the pp $ \rightarrow$ pp -multipion production reactions with the invariant mass of the pions equal to the $ \eta{^\prime}$ meson mass and estimated an upper limit for the signal to background ratio for studies of the $ \eta{^\prime}$ $ \rightarrow$ $ \pi^{+}_{}$ $ \pi^{-}_{}$ $ \pi^{0}_{}$ decay.     

AC conductivity and dielectric studies of (C5H10N)2BiCl5 compound

The bis (3-dimethylammonium-1-propyne) pentachlorobismuthate (III) exhibits a structural phase transition at T₁?=?(337?±?2?K), which has been characterized by differential scanning calorimetric, X-ray powder analysis, AC conductivity and dielectric measurements. The dielectric dispersion yielded the real and imaginary parts of impedance of (C₅H₁₀N)₂BiCl₅ in the form of a semicircle in a complex plane. Besides, a Cole?CCole plot was observed at frequencies ranging from 209?Hz to 5?MHz, whose result was found to fit the theoretical resistor?Ccapacitor parallel circuit model. The temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law. The frequency-dependent conductivity data were fitted in the modified power law: $ \sigma = {\sigma_{dc}} + {B_1}(T){\omega^{{s_1}}} + {B_2}(T){\omega^{{s_2}}} $ . The imaginary part of the permittivity constant is analyzed with the Cole?CCole formalism. With regard to the modulus plot, it can be characterized by full width at half height or in terms of a non-exponential decay function $ \phi (t) = \exp {\left( {\frac{{ - t}}{{{\tau_\sigma }}}} \right)^\beta } $ . Besides, the activation energy responsible for relaxation has been evaluated and found to be close the DC conductivity.     

Reunion Probabilities of N One-Dimensional Random Walkers with Mixed Boundary Conditions

In this work we extend the results of the reunion probability of \(N\) one-dimensional random walkers to include mixed boundary conditions between their trajectories. The level of the mixture is controlled by a parameter \(c\) , which can be varied from \(c=0\) (independent walkers) to \(c\rightarrow \infty \) (vicious walkers). The expressions are derived by using Quantum Mechanics formalism (QMf) which allows us to map this problem into a Lieb-Liniger gas (LLg) of \(N\) one-dimensional particles. We use Bethe ansatz and Gaudin’s conjecture to obtain the normalized wave-functions and use this information to construct the propagator. As it is well-known, depending on the boundary conditions imposed at the endpoints of a line segment, the statistics of the maximum heights of the reunited trajectories have some connections with different ensembles in Random Matrix Theory. Here we seek to extend those results and consider four models: absorbing, periodic, reflecting, and mixed. In all four cases, the probability that the maximum height is less or equal than \(L\) takes the form \(F_N(L)=A_N\sum _{\varvec{k}\in \Omega _{\text {B}}} \mathrm{e}^{-\sum _{j=1}^Nk_j^2}\mathcal {V}_N(\varvec{k})\) , where \(A_N\) is a normalization constant, \(\mathcal {V}_N(\varvec{k})\) contains a deformed and weighted Vandermonde determinant, and \(\Omega _{\text {B}}\) is the solution set of quasi-momenta \(\varvec{k}\) obeying the Bethe equations for that particular boundary condition.     

An Averaging Theorem for FPU in the Thermodynamic Limit

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature $\beta ^{-1}$ . Given a fixed $K$ , we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order $\beta ^{1-a}$ , $a>0$ ) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\beta $ . The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\rightarrow \infty $ , $\beta >0$ .     

Galton–Watson Trees with Vanishing Martingale Limit

We show that an infinite Galton–Watson tree, conditioned on its martingale limit being smaller than  $\varepsilon $ , agrees up to generation $K$ with a regular $\mu $ -ary tree, where $\mu $ is the essential minimum of the offspring distribution and the random variable $K$ is strongly concentrated near an explicit deterministic function growing like a multiple of $\log (1/\varepsilon )$ . More precisely, we show that if $\mu \ge 2$ then with high probability, as $\varepsilon \downarrow 0$ , $K$ takes exactly one or two values. This shows in particular that the conditioned trees converge to the regular $\mu $ -ary tree, providing an example of entropic repulsion where the limit has vanishing entropy. Our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by Fleischmann and Wachtel [11].     

A Strong Central Limit Theorem for a Class of Random Surfaces

This paper is concerned with d = 2 dimensional lattice field models with action ${V(\nabla\phi(\cdot))}$ , where ${V : \mathbf{R}^d \rightarrow \mathbf{R}}$ is a uniformly convex function. The fluctuations of the variable ${\phi(0) - \phi(x)}$ are studied for large |x| via the generating function given by ${g(x, \mu) = \ln \langle e^{\mu(\phi(0) - \phi(x))}\rangle_{A}}$ . In two dimensions ${g'' (x, \mu) = \partial^2g(x, \mu)/\partial\mu^2}$ is proportional to ${\ln\vert x\vert}$ . The main result of this paper is a bound on ${g''' (x, \mu) = \partial^3 g(x, \mu)/\partial \mu^3}$ which is uniform in ${\vert x \vert}$ for a class of convex V. The proof uses integration by parts following Helffer–Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.     

Asymptotic Analysis of the Spatially Homogeneous Boltzmann Equation: Grazing Collisions Limit

In the present work, we consider the asymptotic problem of the spatially homogeneous Boltzmann equation when almost all collisions are grazing, that is, the deviation angle $\theta $ of the collision is limited near zero (i.e., $\theta \le \epsilon $ ). We show that by taking the proper scaling to the cross-section which was used in [37], that is, assuming $$\begin{aligned} B^\epsilon ( v-v_{*},\sigma )=2(1-s)|v-v_*|^{\gamma }\epsilon ^{-3}\sin ^{-1}\theta \left( \frac{\theta }{\epsilon }\right) ^{-1-2s}\mathrm {1}_{\theta \le \epsilon }, \end{aligned}$$ where $\theta = \langle \theta ={\frac{\upsilon -\upsilon _*}{|\upsilon -\upsilon _*|}}.\sigma \rangle , $ the solution $f^\epsilon $ of the Boltzmann equation with initial data $f_0$ can be globally or locally expanded in some weighted Sobolev space as $$\begin{aligned} f^\epsilon = f+ O(\epsilon ), \end{aligned}$$ where the function $f$ is the solution of Landau equation, which is associated with the grazing collisions limit of Boltzmann equation, with the same initial data $f_0$ . This gives the rigorous justification of the Landau approximation in the spatially homogeneous case. In particular, if taking $\gamma =-3$ and $s=1-\epsilon $ in the cross-section $B^\epsilon $ , we show that the above asymptotic formula still holds and in this case $f$ is the solution of Landau equation with the Coulomb potential. Going further, we revisit the well-posedness problem of the Boltzmann equation in the limiting process. We show there exists a common lifespan such that the uniform estimates of high regularities hold for each solution $f^\epsilon $ . Thanks to the weak convergence results on the grazing collisions limit in [37], in other words, we establish a unified framework to establish the well-posedness results for both Boltzmann and Landau equations.