Specific Heat Anomalies in Solids Described by a Multilevel Model

In the field of condensed matter physics, specific heat measurements can be considered as a pivotal experimental technique for characterizing the fundamental excitations involved in a certain phase transition. Indeed, phase transitions involving spin (de Souza et al. Phys. B Condens. Matter 404, 494 (2009) and Manna et al. Phys. Rev. Lett. 104, 016403 (2010)), charge (Pregelj et al. Phys. Rev. B 82, 144438 (2010)), lattice (Jesche et al. Phys. Rev. B 81, 134525 (2010)) (phonons) and orbital degrees of freedom, the interplay between ferromagnetism and superconductivity (Jesche et al. Phys. Rev. B 86, 020501 (2012)), Schottky-like anomalies in doped compounds (Lagos et al. Phys. C Supercond. 309, 170 (1998)), electronic levels in finite correlated systems (Macedo and Lagos J. Magn. Magn. Mater. 226, 105 (2001)), among other features, can be captured by means of high-resolution calorimetry. Furthermore, the entropy change associated with a first-order phase transition, no matter its nature, can be directly obtained upon integrating the specific heat over T, i.e., C(T)/T, in the temperature range of interest. Here, we report on a detailed analysis of the two-peak specific heat anomalies observed in several materials. Employing a simple multilevel model, varying the spacing between the energy levels Δ_i = (E_i?E₀) and the degeneracy of each energy level g_i, we derive the required conditions for the appearance of such anomalies. Our findings indicate that a ratio of \({\Delta }_{2}/{\Delta }_{1}\thickapprox \) 10 between the energy levels and a high degeneracy of one of the energy levels define the two-peaks regime in the specific heat. Our approach accurately matches recent experimental results. Furthermore, using a mean-field approach, we calculate the specific heat of a degenerate Schottky-like system undergoing a ferromagnetic (FM) phase transition. Our results reveal that as the degeneracy is increased the Schottky maximum in the specific heat becomes narrow while the peak associated with the FM transition remains unaffected.     

A Small and Non-simple Geometric Transition

Following notation introduced in the recent paper (Rossi Int. J. Geom. Methods Mod. Phys. 12(5), 2015), this paper is aimed to present in detail an example of a small geometric transition which is not a simple one i.e. a deformation of a conifold transition. This is realized by means of a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y. Namikawa in Remark 2.8 and Example 1.11 of Namikawa (Topology 41(6), 1219–1237, 2002). The physical interest of this example is presenting a geometric transition which can’t be immediately explained as a massive black hole condensation to a massless one, as described by Strominger (Nucl. Phys. B451, 97–109, 1995).     

A Modified Quantum Search Algorithm

We show that by adding a workspace qubit to Ahmed Younes, et al. algorithm (Younes et al. AIP Conf. Proc. 734:171, 2004, 2008), and applying newly defined partial diffusion operators on subsystems, the algorithm’s performance is improved. We consider an unstructured list of N items and M matches, 1 ≤ M ≤ N.     

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.     

Spinning Earth and its Coriolis effect on the circuital light beams: Verification of the special relativity theory

Bilger et al (1995), Anderson et al (1994) and Michelson–Gale assisted by Pearson (1925) measure / mention Sagnac effect on the circuital light /laser beams on the spinning Earth. But from the consideration of classical electrodynamics, the effect measured /mentioned by those experimenters is the Coriolis effect, not the Sagnac effect. A simple experiment is suggested here that can easily settle the problem.     

Derivation of the Time Dependent Gross-Pitaevskii Equation Without Positivity Condition on the Interaction

Using a new method (Pickl in A simple derivation of mean field limits for quantum systems, 2010) it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies.In this paper we wish to analyze scalings which lead to the Gross-Pitaevskii equation which is usually derived assuming positivity of the interaction (Erdös et al. in Commun. Pure Appl. Math. 59(12):1659–1741, 2006; Invent. Math. 167:515–614, 2007). The new method for dealing with mean field limits presented in Pickl (2010) allows us to relax this condition. The price we have to pay for this relaxation is however that we have to restrict the scaling behavior of the interaction and that we have to assume fast convergence of the reduced one particle marginal density matrix of the initial wave function \(\mu^{\Psi_{0}}\) to a pure state |φ ₀〉〈φ ₀|.     

Survival of Near-Critical Branching Brownian Motion

Consider a system of particles performing branching Brownian motion with negative drift \(\mu= \sqrt{2 - \varepsilon}\) and killed upon hitting zero. Initially there is one particle at x>0. Kesten (Stoch. Process. Appl. 7:9–47, 1978) showed that the process survives with positive probability if and only if ε>0. Here we are interested in the asymptotics as ε→0 of the survival probability Q _μ (x). It is proved that if \(L=\pi/\sqrt{\varepsilon}\) then for all x∈?, lim? _ε→0 Q _μ (L+x)=θ(x)∈(0,1) exists and is a traveling wave solution of the Fisher-KPP equation. Furthermore, we obtain sharp asymptotics of the survival probability when x<L and L?x→∞. The proofs rely on probabilistic methods developed by the authors in (Berestycki et al. in arXiv:1001.2337, 2010). This completes earlier work by Harris, Harris and Kyprianou (Ann. Inst. Henri Poincaré Probab. Stat. 42:125–145, 2006) and confirms predictions made by Derrida and Simon (Europhys. Lett. 78:60006, 2007), which were obtained using nonrigorous PDE methods.     

Time growth rate optimisation of terahertz electromagnetic wave generation by converting occupied plasma region from annular plasma to filled plasma in the core,in an elliptical Cherenkov maser with two energy sources

A theoretical model is described here for studying the effect of temperature on nanomaterials. The thermodynamic equation of state (EoS) proposed by Goyal and Gupta in High Temp.-High Press. 45, 163 (2016); Oriental J. Chem. 32(4), 2193 (2016), is extended in the present study using Qi and Wang model [Mater. Chem. Phys. 88, 280 (2004)]. The thermal expansion coefficient is expressed in terms of shape and size and used to obtain the isobaric EoS of nanomaterials for the change in volume \(V/{V_0}\). The variation in \(V/{V_0}\) with temperature is estimated for spherical nanoparticles, nanowires and nanofilms. It is found that the volume thermal expansivity decreases as size of the nanomaterial increases, whereas \(V/{V_0}\) increases with temperature across nanomaterials of different sizes. The lattice parameter variation with temperature is studied in Zn nanowires, Se and Ag nanoparticles. It is found that lattice constant increases with increase in temperature. Also, bulk modulus is found to increase with temperature in nanomaterials. The results obtained from the present model are compared with the available experimental data. A good consistency between the compared results confirms the suitability of the present model for studying thermal properties of the nanomaterials.     

Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

We consider random walks on the square lattice of the plane along the lines of Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) and den Hollander (J Stat Phys 75:891–918, 1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Two-dimensional anisotropic random walks with anisotropic density conditions á  la Heyde (J Stat Phys 27:721–730, 1982, Stochastic processes, Springer, New York, 1993) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (J Stat Phys 75:891–918, 1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with self-contained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.     

Traces of Intertwiners for Quantum Affine {\mathfrak{sl}}_2 and Felder–Varchenko Functions

We show that the traces of \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder–Varchenko’s hypergeometric solutions to the q-KZB heat equation given in [FV02]. This gives the first proof that such a trace function converges and resolves the first case of the Etingof–Varchenko conjecture of [EV00]. As applications, we prove a symmetry property for traces of intertwiners and prove Felder–Varchenko’s conjecture in [FV04] that their elliptic Macdonald polynomials are related to the affine Macdonald polynomials defined as traces over irreducible integrable \({U_q({\widehat{\mathfrak{sl}}}_2)}\)-modules in [EK95]. In the trigonometric and classical limits, we recover results of [EK94,EV00]. Our method relies on an interplay between the method of coherent states applied to the free field realization of the q-Wakimoto module of [Mat94], convergence properties given by the theta hypergeometric integrals of [FV02], and rationality properties originating from the representation-theoretic definition of the trace function.     

Gravitational Rutherford scattering and Keplerian orbits for electrically charged bodies in heterotic string theory

Properties of the motion of electrically charged particles in the background of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole is presented in this paper. Radial and angular motions are studied analytically for different values of the fundamental parameter. Therefore, gravitational Rutherford scattering and Keplerian orbits are analyzed in detail. Finally, this paper complements previous work by Fernando for null geodesics (Phys Rev D 85:024033, 2012), Olivares and Villanueva (Eur Phys J C 73:2659, 2013) and Blaga (Automat Comp Appl Math 22:41–48, 2013; Serb Astron 190:41, 2015) for time-like geodesics.     

Bell Inequalities and Group Symmetry

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr G?ney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S ₄ is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.     

Synthesis,Optical Investigation and Biological Properties of Europium(III) Complexes with 2-(4-Chlorophenyl)-1-(2-Hydroxy-4-Methoxyphenyl)Ethan-1-one and Ancillary Ligands

Synthesis and photoluminescence behaviour of six novel europium complexes with novel β-hydroxyketone ligand, 2-(4-chlorophenyl)-1-(2-hydroxy-4-methoxyphenyl)ethan-1-one (CHME) and 2,2′-bipyridine (bipy) or neocuproine (neo) or 1,10-phenanthroline (phen) or 5,6-dimethyl-1,10-phenanthroline (dmphen) or bathophenanthroline (bathophen) were reported in solid state. The free ligand CHME and europium complexes, Eu(CHME)₃.2H₂O [1] Eu(CHME)₃.bipy [2], Eu(CHME)₃.neo [3], Eu(CHME)₃.phen [4], Eu(CHME)₃.dmphen [5] and Eu(CHME)₃.bathophen [6]were characterized by elemental analysis, FT-IR and ¹H-NMR. The photoluminescence emission spectra exhibited four characteristic peaks arising from the ⁵D₀ → ⁷F_J (J = 1–4) transitions of the europium ion in the solid state on monitoring excitation at λ_ex = 395 nm. The luminescence decay curves of these europium complexes possess single exponential behaviour indicating the presence of a single luminescent species and having only one site symmetry in the complexes. The luminescence quantum efficiency (η) and the experimental intensity parameters, Ω ₂ and Ω ₄ of europium complexes have also been calculated on the basis of emission spectra and luminescence decay curves. In addition, the antimicrobial and antioxidant activities were also studied of the investigated complexes.     

Shape,size and phonon scattering effect on the thermal conductivity of nanostructures

A phenomological model is described here to study the effect of size, shape and phonon scattering on the thermal conductivity of nanostructures. Using the classical model proposed by Guisbiers et al (Phys. Chem. Chem. Phys. 12, 7203 (2010), J. Phys. Chem. C 112, 4097 (2008)) in terms of the melting temperature of nanostructures, the expression for variation of thermal conductivity is obtained in terms of shape and size parameter. An additional term is included in the expression of thermal conductivity to consider the impact of phonon scattering due to the surface roughness with a decrease in size. The expression of thermal conductivity is obtained for spherical nanosolids, nanowires and nanofilms. The thermal conductivity is found to decrease in nanostructures in comparison with the counterpart bulk material. The values of thermal conductivity obtained from the present model are found to be close to the available experimental data for different values of roughness parameter which verifies the suitability of the model.     

Hypersurface-homogeneous Universe filled with perfect fluid in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) theory of gravity

The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of f(R, T) theory of gravity (Harko et al, Phys. Rev. D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.     

Magnetized anisotropic dark energy models with constant deceleration parameter

In this paper, we have studied the solutions of plane-symmetric Universe with variable ω in the presence and the absence of magnetic field of energy density ρ _B . A special law of variation for Hubble’s parameter proposed by Bermann in Nuovo Cimento B 74, 182 (1983) has been utilized to solve the field equations. Some physical and kinematical properties of the models are also discussed.     

Comments on: “Crystal growth and comparison of vibrational and thermal properties of semi-organic nonlinear optical materials”

In Pramana – J. Phys.75, 683 (2010), Gunasekaran et al reported that they have grown the nonlinear optical crystals, urea thiourea mercuric chloride (UTHC) and urea thiourea mercuric sulphate (UTHS). We argue that UTHC and UTHS are dubious crystals and are not what the authors propose.     

An Efficient and Secure Arbitrary <Emphasis Type="Italic">N</Emphasis>-Party Quantum Key Agreement Protocol Using Bell States

Two quantum key agreement protocols using Bell states and Bell measurement were recently proposed by Shukla et al. (Quantum Inf. Process. 13(11), 2391–2405, 2014). However, Zhu et al. pointed out that there are some security flaws and proposed an improved version (Quantum Inf. Process. 14(11), 4245–4254, 2015). In this study, we will show Zhu et al.’s improvement still exists some security problems, and its efficiency is not high enough. For solving these problems, we utilize four Pauli operations {I, Z, X, Y} to encode two bits instead of the original two operations {I, X} to encode one bit, and then propose an efficient and secure arbitrary N-party quantum key agreement protocol. In the protocol, the channel checking with decoy single photons is introduced to avoid the eavesdropper’s flip attack, and a post-measurement mechanism is used to prevent against the collusion attack. The security analysis shows the present protocol can guarantee the correctness, security, privacy and fairness of quantum key agreement.     

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider N bosons in a finite box Λ=[0,L]³?R ³ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle

$\overline{\lim}_{\rho\to0}\overline{\lim}_{L\to\infty,\,N/L^3\to \rho}\biggl(\frac{e_0(\rho)-4\pi a\rho}{(4\pi a)^{5/2}(\rho)^{3/2}}\biggr )\leq\frac{16}{15\pi^2},$

where a is the scattering length of the potential. Previously, an upper bound of the form C16/15π ² for some constant C>1 was obtained in (Erdös et al. in Phys. Rev. A 78:053627, 2008). Our result proves the upper bound of the prediction by Lee and Yang (Phys. Rev. 105(3):1119–1120, 1957) and Lee et al. (Phys. Rev. 106(6):1135–1145, 1957).

     

Contiguity and Entire Separability of States on von Neumann Algebras

We introduce the notions of the contiguity and entirely separability for two sequences of states on von Neumann algebras. The ultraproducts technique allows us to reduce the study of the contiguity to investigation of the equivalence for two states. Here we apply the Ocneanu ultraproduct and the Groh–Raynaud ultraproduct (see Ocneanu (1985), Groh (J. Operator Theory, 11, 2, 395–404 1984), Raynaud (J. Operator Theory, 48, 1, 41–68, 2002), Ando and Haagerup (J. Funct. Anal., 266, 12, 6842–6913, 2014)), as well as the technique developed in Mushtari and Haliullin (Lobachevskii J. Math., 35, 2, 138–146, 2014).