Quantization of Horizon Entropy and the Thermodynamics of Spacetime

This is a review of my work published in the papers of Skakala (JHEP 1201:144, 2012; JHEP 1206:094, 2012) and Chirenti et al. (Phys. Rev. D 86:124008, 2012; Phys. Rev. D 87:044034, 2013). It offers a more detailed discussion of the results than the accounts in those papers, and it links my results to some conclusions recently reached by other authors. It also offers some new arguments supporting the conclusions in the cited articles. The fundamental idea of this work is that the semiclassical quantization of the black hole entropy, as suggested by Bekenstein (Phys. Rev. D 7:2333–2346, 1973), holds (at least) generically for the spacetime horizons. We support this conclusion by two separate arguments: (1) we generalize Bekenstein’s lower bound on the horizon area transition to a much wider class of horizons than only the black-hole horizon, and (2) we obtain the same entropy spectra via the asymptotic quasi-normal frequencies of some particular spherically symmetric multi-horizon spacetimes (in the way proposed by Maggiore (Phys. Rev. Lett. 100:141301, 2008)). The main result of this paper supports the conclusions derived by Kothawalla et al. (Phys. Rev. D 78:104018, 2008) and Kwon and Nam (Class. Quant. Grav. 28:035007, 2011), on the basis of different arguments.     

Variational Bound States of Screened Potentials

Anumber of years ago, a calculational scheme was introduced by Stubbins [Phys. Rev. A48, 220 (1993)] to compute the energies of both the Hulthén and Yukawa potentials. The method introduces a particular ansatz for solving the Schrödinger equation with screened Coulomb type potentials. In this work, we wish to review the method of Stubbins and to show that it is, in fact, equivalent and a subset of a more systematic (and hence more useful) variational scheme [Zhou et al. Phys. Rev. A51, 3337 (1995)]. This variational approach involves the construction of a basis by taking derivatives of the variational parameters of the system. The eigenvalues of the Hamiltonian matrix are then minimized with respect to these parameters yielding a “best guess” upper bound on the energies.     

On the Li Coefficients for the Hecke L-functions

In this paper, we compute and verify the positivity of the Li coefficients for the Hecke L-functions using an arithmetic formula established in Omar and Mazhouda, J. Number Theory 125(1), 50–58 (2007) and J. Number Theory 130(4), 1098–1108 (2010) and the Serre trace formula. Additional results are presented, including new formulas for the Li coefficients and a formulation of a criterion for the partial Riemann hypothesis. Basing on the numerical computations made below, we conjecture that these coefficients are increasing in n.     

Quantum Teleportation of a Three-qubit State using a Five-qubit Cluster State

Recently Muralidharan and Panigrahi (Phys. Rev. A 78, 062333 2008) had shown that using a five-qubit cluster state as quantum channel, it is possible to teleport an arbitrary single-qubit state and an arbitrary two-qubit state. In this paper, we investigate this channel for the teleportation of a special form of three-qubit state.     

Bidirectional Quantum Controlled Teleportation via a Six-Qubit Entangled State

A new application of six-qubit entangled state introduced by Chen et al. (Phys. Rev. A 74, 032324, 2006) is studied for the bidirectional quantum controlled teleportation. In our scheme, a six-qubit entangled state is shared by Alice, Bob and Charlie, Alice and Bob can transmit simultaneously an arbitrary single-qubit state to each other under the control of the supervisor Charlie.     

On the Power-counting Renormalizability of a Lifshitz-type QFT in Configuration Space

Recently, Ho?ava (Phys. Rev. D. 79, 084008, 2009) proposed a theory of gravity in 3+1 dimensions with anisotropic scaling using the traditional framework of quantum field theory (QFT). Such an anisotropic theory of gravity, characterized by a dynamical critical exponent z, has proven to be power-counting renormalizable at a z=3 Lifshitz Point. In the present article, we develop a mathematically precise version of power-counting theorem in Lorentz violating theories and apply this to the Ho?ava-Lifshitz (scalar field) models in configuration space. The analysis is performed under the light of the systematic use of the concept of extension of homogeneous distributions, a concept tailor-made to address the problem of the ultraviolet renormalization in QFT. This becomes particularly transparent in a Lifshitz-type QFT. In the specific case of the \({\phi _{4}^{4}}\) -theory, we show that is sufficient to take z=3 in order to reach the ultraviolet finiteness of the S-matrix in all orders.     

Bianchi type-II String Cosmological Model with Magnetic Field in Scale-Covariant Theory of Gravitation

The spatially homogeneous and totally anisotropic Bianchi type-II cosmological solutions of massive strings have been investigated in the presence of the magnetic field in the framework of scale-covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39, 429, 1977). With the help of special law of variation for Hubble^’s parameter proposed by Berman (Nuovo Cimento 74, 182, 1983) string cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Neutral kaon production in p+p and p+Nb collisions

The kaon nucleus (KN) interaction in dense nuclear matter is predicted to be repulsive and increasing with density. However, determined values for this potential are not yet consistent with each other (Benabderrahmane et al., Phys Rev Lett 102:182501, 2009; Agakishiev et?al., Phys Rev C 82:044907, 2010; Büscher et?al., Eur Phys J A 22:301–317, 2004). We analyze $K^0_S$ mesons identified with the HADES detector in p+p and p+?⁹³Nb reactions at 3.5?GeV kinetic beam energy. To determine the KN potential at normal nuclear density we propose to compare the $K^0_S$ differential distributions in p+?⁹³Nb and p+p collisions. High statistics of low p _t -kaons (p _t ?<?100?MeV/c) ensure the sensitivity of our measurements to the nuclear matter effects. We present the data analysis method and first results.     

New Two-Mode Canonical Operator Realization of Angular Momentum and Generalized Fractional Fourier Transformation Obtained via Entangled State Representation

By virtue of two mutually conjugate bipartite entangled state representations |η〉 and |ξ〉 (Fan and Klauder, Phys Rev A 49:704, 1994) we find new canonical operator realization (COR) of angular momentum. As its two applications, we point out that the COR helps to develop Schwinger bosonic realization theory, and can generalize the concept of FrFT, i.e., constructing new 2-dimensioanl fractional Fourier transformation with additivity.     

Study of the polarization degree for the p ⃗ p → ppη measurement with WASA

Understanding of the production processes of the η meson will strongly rely on the precise determination of spin observables. So far these observables have been determined only for few excess energies and with low statistics (Winter et al. Eur. Phys. J. A18, 355 2003; Czyzykiewicz et al. Phys. Rev. Lett. 98, 122003 2007; Balestra et al. Phys. Rev. C69, 064003 2004). In the year 2010 WASA detector was used for the measurement of the \(\overrightarrow {p}p\rightarrow pp\eta \) reaction with the polarized proton beam of COSY (Moskal and Hodana J. Phys. Conf. Ser 295, 012080 2011). The measurement was done for the excess energy of Q = 15 MeV and Q = 72 MeV. In total about 10⁶ events corresponding to the \(\overrightarrow {p}p\rightarrow pp\eta \) reaction have been collected.     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

A Complete Proof of the Confinement Limit of One-Dimensional Dirac Particles

The validity of the confinement limit obtain by Unanyan et al. (Phys Rev A 79:044101, 2009) is extended by including non-symmetric vector and scalar potentials. It shows that the confinement limit of one-dimensional Dirac particles in vector and scalar potentials is \(\lambda _C/\sqrt{2}\) , with \(\lambda _C\) being the Compton wavelength.     

Composite and Elementary Components in Hadron Resonances

In hadron resonances different structures of hadronic composite (molecule) and elementary (quark-intrinsic) natures may coexist. We sketch discussions based on our previous publications on the origin of hadron resonances (Hyodo et al. Phys. Rev. C 78:025203, 2008) on exotic ${\bar D (B)}$ meson–nucleons as candidates of hadronic composites (Yamaguchi et al. Phys. Rev. D 84:014032, 2011) and on a ₁ for the coexistence/mixing of the two different natures (Nagahiro et al. Phys. Rev. D 83:111504, 2011).     

Approximate Lifshitz Law for the Zero-Temperature Stochastic Ising Model in any Dimension

We study the Glauber dynamics for the zero-temperature stochastic Ising model in dimension d ≥ 4 with “plus” boundary condition. Let ${\mathcal{T}_+}$ be the time needed for an hypercube of size L entirely filled with “minus” spins to become entirely “plus”. We prove that ${\mathcal{T}_+}$ is O(L ²(log L) ^c ) for some constant c, not depending on the dimension. This brings further rigorous justification for the so-called “Lifshitz law” ${\mathcal{T}_{+} = O(L^{2})}$ (Fischer and Huse in Phys Rev B 35:6841–6848, 1987; Lifshitz in Sov Phys JETP 15:939–942, 1962) conjectured on heuristic grounds. The key point of our proof is to use the detailed knowledge that we have on the three-dimensional problem: results for fluctuation of monotone interfaces at equilibrium and mixing time for monotone interfaces dynamics extracted from Caputo et al. (Comm Pure Appl Math 64:778–831, 2011) to get the result in higher dimension.     

Non-normal tracer diffusion from stirring by swimming microorganisms

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ??(??) with long time behaviour ??(??) ?? ?? ^?1??? and a step size distribution p(??x) ?? (??x)^?2??? . The experimentally observed behaviour that ??x ²?? ?? t is obtained for a one-parameter family of exponents with ?? = 2??. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.      

Linear-Optics-Based Entanglement Concentration of Four-Photon χ-type States for Quantum Communication Network

We present an efficient entanglement concentration protocol (ECP) for partially entangled four-photon χ-type states in the first time with only linear optical elements and single-photon detectors. Without any ancillary particles, the parties in quantum communication network can obtain a subset of four-photon systems in the standard |χ ⁰⁰〉 state from a set of four-photon systems in a partially entangled χ-type state with the parameter-splitting method developed by Ren et al. (Phys. Rev. A 88:012302, 2013). The present ECP has the optimal success probability which is determined by the component with the minimal probability amplitude in the initial state. Moreover, it is easy to implement this ECP in experiment.     

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.     

Bianchi Type-II Dark Energy Model in Scale Covariant Theory of Gravitation

Spatially Homogeneous and anisotropic Bianchi type-II space time with variable equation of state (EoS) parameter and constant deceleration parameter has been investigated in scale covariant theory of gravitation formulated by Canuto et al. (Phys. Rev. Lett. 39:429, 1977). With the help of special law of variation for Hubble’s parameter proposed by Bermann (Nuovo Cimento 74B:182, 1983) a dark energy cosmological model is obtained in this theory. We use the power law relation between scalar field ? and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.     

Time reversal and the neutron

We have measured the triple correlation $D\langle\vec J_n\rangle/J_n\cdot (\vec\beta_e\times\hat p_\nu)$ with a polarized cold-neutron beam (Mumm et al., Phys Rev Lett 107:102301, 2011; Chupp et al., Phys Rev C 86:035505, 2012). A non-zero value of D can arise due to parity-even-time-reversal-odd interactions that imply CP violation. Final-state effects also contribute to D at the level of 10^???5 and can be calculated with precision of 1 % or better. The D coefficient is uniquely sensitive to the imaginary part of the ratio of axial-vector and vector beta-decay amplitudes as well as to scalar and tensor interactions that could arise due to beyond-Standard-Model physics. Over 300 million proton-electron coincidence events were used in a blind analysis with the result D?=?[???0.94±1.89 (stat)±0.97(sys)]×10^???4. Assuming only vector and axial vector interactions in beta decay, our result can be interpreted as a measure of the phase of the axial-vector coupling relative to the vector coupling, $\phi_{\rm AV}= 180.012^\circ \pm 0.028^\circ$ . This result also improves constrains on certain non-VA interactions.     

An Alternative Approach to Understanding the Observed Positron Fraction

Space-based observations by PAMELA (Adriani et al., Nature 458, 607, 2009), Fermi-LAT (Ackerman et al., Phys. Rev. Lett. 105, 01103, 2012), and AMS (Aguilar et al., Phys. Rev. Lett. 110, 141102, 2013) have demonstrated that the positron fraction (e+/total-e) increases with increasing energy above about 10 GeV. According to the propagation model for Galactic cosmic rays in widespread use (Moskalenko & Strong, Astrophys. J. 493, 693, 1998), the production of secondary positrons from interaction of cosmic-ray protons and heavier nuclei with the interstellar medium gives a generally falling positron fraction between 10 and 100 GeV, with secondary positrons accounting for only ～20 % of the observed positron fraction at 100 GeV; so some other physical phenomena have been proposed to explain the data. An alternative approach to interpreting the positron observations is to consider these data as presenting an opportunity for re-examining models of Galactic cosmic-ray propagation. Following release of the PAMELA data, three groups published propagation models (Shaviv, et al., Phys. Rev. Lett. 103, 111302, 2009, Cowsik and Burch, Phys. Rev. D. 82, 023009, 2010, Katz et al., Mon. Not. R. Aston. Soc. 405, 1458 2010) in which the observed positron fraction is explained entirely by secondary positrons produced in the interstellar medium. In May of this year, stimulated by the AMS extension of the positron data to higher energy with excellent statistics, two of those groups presented further development of their calculations (Cowsik et al. 2013, Blum et al. 2013), again concluding that the observed positrons can be understood as secondaries. None of the authors of these five papers was registered for the 33rd International Cosmic Ray Conference (ICRC). Although I am not an author of any of these papers, I have some close familiarity with one of these recent papers, so the conference organizers invited me to bring this alternative approach to the attention of the conference. The present paper is a summary of the material I presented, along with a brief comment about reaction at the conference to this approach.