Line intensity measurements of methane’s \nu _3-band using a cw-OPO

We report on absolute line strength measurements of P(1), R(0) and R(1) singlet lines in the \(3.3\,\upmu\hbox {m}\,\nu _{3}\) (C–H stretching) band of methane \(^{12}\hbox {CH}_4\) at reference temperature \(T=296\)  K. Line strength measurements are performed at low pressure \((P \le 1\hbox { Torr})\) using direct absorption spectroscopy technique based on a widely tunable continuous-wave singly resonant optical parametric oscillator. The \(1\sigma \) overall accuracy in line strength determinations ranges between 7 and 8 % mostly limited by pressure and frequency measurements. A comparison with previous reported values is made. Our results show good agreement with the HITRAN 2012 database.     

Nitrogen optical emission during nanosecond laser ablation of metals: prompt electrons or photo-ionization?

Experiments on the interaction of metal targets with a Nd:YAG laser beam ( \(\lambda \)  = 1,064 nm, intensity \(10^{10}\) – \(10^{11}\,\hbox {W/cm}{^2}\) ) are carried out in a finite Nitrogen pressure environment. The observed \(\hbox {N}_2\) spectra are unambiguous evidence of the existence of an ionization and excitation source, arriving at the observation volume prior to the plume. Such a source can be either prompt electrons or VUV radiation. The analysis reveals that the prompt electron interpretation requires energies in excess of 1 keV, incompatible with any acceleration mechanisms relevant for such laser intensities. On the other hand, VUV radiation is sufficiently strong to explain the observed spectra.     

Investigation of conductivity of adhesive layer including indium tin oxide particles for multi-junction solar cells

We report connection conductivity ( \(C_{\rm c}\) ) of adhesive which including \(\hbox {In}_2\hbox {O}_3\) – \(\hbox {SnO}_2\) (ITO) particles developed for fabrication of stacked-type-multi-junction solar cells. The commercial 20- \(\upmu \) m sized ITO particles were heated in vacuum at temperature ranging from 800 to 1,300  \(^{\circ }{\rm C}\) for 10 min to increase \(C_{\rm c}\) . 6.2 wt% ITO particles were dispersed in commercial Cemedine adhesive gel to form 100 samples structured with n-type Si/adhesive/n-type Si (n-Si sample) and p-type Si/adhesive/p-type Si (p-Si sample). Current density as a function of voltage (J–V) characteristics gave \(C_{\rm c}\) . It ranged from 4.3 to 1.0 S/cm \(^2\) for the n-Si sample with 800 \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.59 S/cm \(^2\) . On the other hand, it ranged from 2.0 to 0.6 S/cm \(^2\) for the p-Si sample with 800  \(^{\circ }{\rm C}\) heat-treated ITO particles. Its standard deviation was 0.22 S/cm \(^2\) . The distribution of \(C_{\rm c}\) mainly resulted from contact efficiency of ITO particles to substrate. We theoretically estimated that present \(C_{\rm c}\) achieved a low loss of the power conversion efficiency ( \(E_{\rm ff}\) ) lower than 0.3 % in the application of fabrication of multi-junction solar cell with an intrinsic \(E_{\rm ff}\) of 30 % and an open circuit voltage above 1.9 V.     

Generation of vacuum ultraviolet radiation by intracavity high-harmonic generation toward state detection of single trapped ions

Vacuum ultraviolet (VUV) radiation around 159 nm is obtained toward direct excitation of a single trapped \(^{115}\hbox {In}^{+}\) ion. An efficient fluoride-based VUV output coupler is employed for intracavity high-harmonic generation of a Ti:S oscillator. Using this coupler, where we measured its reflectance to be about 90 %, an average power reaching 6.4  \(\upmu\) W is coupled out from a modest fundamental power of 650 mW. When a single comb component out of 1.9  \(\times\)  10 \(^{5}\) teeth is resonant to the atomic transition, 100s of fluorescence photons per second will be detectable under a realistic condition.     

Misalignment tolerance analysis and fabrication for highly efficient parallel optical-electrical convertor module

A compact, highly efficient, and passively assembled parallel optical-electrical convertor module (POECM) for active optical cable application is proposed. This paper presents our POECM structure, optical design simulation results, fabrication process, and data transmission test results, in sequence. The POECM has a compact size of \(18.5\hbox {mm} \times 10\hbox {mm} \times 2.8\hbox {mm}\) . We confirm a data rate of total throughput at 21.6 Gbps ( \(5.4\hbox {Gbps} \times 4\) channels) with a bit error rate of less than \(10^{-12}\) .     

Antineutrino science in KamLAND

The primary goal of KamLAND is a search for the oscillation of \({\bar{\nu }}_\mathrm{e}\) ’s emitted from distant power reactors. The long baseline, typically 180 km, enables KamLAND to address the oscillation solution of the “solar neutrino problem” with \({\bar{\nu }}_{e} \) ’s under laboratory conditions. KamLAND found fewer reactor \({\bar{\nu }}_{e} \) events than expected from standard assumptions about \(\overline{\nu }_e\) propagation at more than 9 \(\sigma \) confidence level (C.L.). The observed energy spectrum disagrees with the expected spectral shape at more than 5 \(\sigma \) C.L., and prefers the distortion from neutrino oscillation effects. A three-flavor oscillation analysis of the data from KamLAND and KamLAND + solar neutrino experiments with CPT invariance, yields \(\Delta m_{21}^2 \) = [ \(7.54_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) , \(7.53_{-0.18}^{+0.19} \times \) 10 \(^{-5}\) eV \(^{2}\) ], tan \(^{2}\theta _{12}\) = [ \(0.481_{-0.080}^{+0.092} \) , \(0.437_{-0.026}^{+0.029} \) ], and sin \(^{2}\theta _{13}\) = [ \(0.010_{-0.034}^{+0.033} \) , \(0.023_{-0.015}^{+0.015} \) ]. All solutions to the solar neutrino problem except for the large mixing angle region are excluded. KamLAND also demonstrated almost two cycles of the periodic feature expected from neutrino oscillation effects. KamLAND performed the first experimental study of antineutrinos from the Earth’s interior so-called geoneutrinos (geo \({\bar{\nu }}_{e} \) ’s), and succeeded in detecting geo \({\bar{\nu }}_{e} \) ’s produced by the decays of \(^{238}\) U and \(^{232}\) Th within the Earth. Assuming a chondritic Th/U mass ratio, we obtain \(116_{-27}^{+28} {\bar{\nu }}_{e}\) events from \(^{238}\) U and \(^{232}\) Th, corresponding a geo \({\bar{\nu }}_{e}\) flux of \(3.4_{-0.8}^{+0.8}\times \) 10 \(^{6}\) cm \(^{-2}\)  s \(^{-1}\) at the KamLAND location. We evaluate various bulk silicate Earth composition models using the observed geo \({\bar{\nu }}_{e} \) rate.     

Resonant cavity enhanced quantum ring photodetector at 20\,\upmu m wavelength

In this paper, in order to enhance the performance characteristics of photodetector, an InAs/GaAs quantum ring infrared photodetector (QRIP) with resonant cavity structure is proposed. For this purpose, distributed bragg reflectors (DBR) in the bottom of structure are used to reflect the transmitted beam back into the active region. For further confinement of light in the active region, a gold layer is added to structure as top reflector and the performance of structures is compared with and without top reflector. Numerical simulation results show that using resonant cavity structure can improve quantum efficiency and responsivity of photodetector. Furthermore, the specific detectivity of device can increase about one order of magnitude using resonant cavity structure. Results show specific detectivity, $\hbox {D}^{*}$ , about $\sim $ 10 $^{11}\,(\hbox {cm}\,\hbox {Hz}^{1/2}\hbox {/W})$ for conventional QRIP and $\sim $ 10 $^{12}\,(\hbox {cm}\,\hbox {Hz}^{1/2}\hbox {/W})$ for conventional QRIP embedded in resonant cavity. As a result of enhancement in detectivity, the operation temperature of detector can be increased up to about 150 K.     

Third-order nonlinear optical properties of an azobenzene-containing ionic liquid crystalline polymer

The nonlinear optical properties of an azobenzene-containing ionic liquid crystalline polymer were investigated by a single beam Z-scan technique employing 38 ps and 6 ns laser pulses at 532 nm. The polymer film exhibited large nonlinear refraction and negligible nonlinear absorption under both ps and ns pulses excitation. The nonlinear refractive indices of the polymer were in the order of \(10^{-11} \hbox {cm}^{2}/\hbox {W}\) under ps excitation and \(10^{-8}\hbox {cm}^{2}/\hbox {W}\) under ns excitation, respectively. The mechanism accounting for the process of nonlinear refraction was discussed in terms of photoinduced trans-cis transformation and thermal effect.     

Design of spectral crosstalk suppressing structure in two-color HgCdTe infrared focal plane arrays detector

Spectral crosstalk suppressing design of two-color HgCdTe medium-wave/long-wave (MW/LW) \(\hbox {n}^{+}\) – \(\hbox {p}_{1}\) – \(\hbox {P}_{2}\) – \(\hbox {P}_{3}\) – \(\hbox {N}^{+}\) infrared focal plane arrays (IRFPAs) detector functioning in simultaneous mode is carried out in this study, using Crosslight Technology Computer Aided Design (TCAD) software. A compositional barrier of \(\hbox {P}_{2}\) -region sandwiched between LW absorption layer of \(\hbox {p}_{1}\) -region and MW absorption layer of \(\hbox {P}_{3}\) -region is designed to suppress spectral crosstalk. MW-to-LW crosstalk can be significantly suppressed to 2.1 % while LW-to-MW crosstalk can be maintained less than 1 % by integrating an optimized compositional barrier.     

An adaptive Rayleigh noise elimination method in Raman distributed temperature sensors using anti-Stokes signal only

In this paper, an adaptive temperature demodulation method to eliminate Rayleigh noise real-timely in Raman distributed temperature sensors using anti-Stokes light only has been presented. The theoretical model calculating Rayleigh noise is proposed. Based on known parameters, the Rayleigh noise can be calculated and then eliminated simultaneously by the intensity of the signal composed by anti-Stokes light and Rayleigh noise at two different temperatures. In our experiments, two sections of reference fiber I, II are utilized and their temperatures were set at 27 and 40  \(^{\circ }\hbox {C}\) respectively. Experiment results indicate that the temperature errors caused by Rayleigh noise are decreased by 4 and 6  \(^{\circ }\hbox {C}\) at 50 and 70  \(^{\circ }\hbox {C}\) respectively after using this method.     

A flexible scintillation light apparatus for rare event searches

Compelling experimental evidences of neutrino oscillations and their implication that neutrinos are massive particles have given neutrinoless double beta decay ( \(\beta \beta 0\nu \) ) a central role in astroparticle physics. In fact, the discovery of this elusive decay would be a major breakthrough, unveiling that neutrino and antineutrino are the same particle and that the lepton number is not conserved. It would also impact our efforts to establish the absolute neutrino mass scale and, ultimately, understand elementary particle interaction unification. All current experimental programs to search for \(\beta \beta 0\nu \) are facing with the technical and financial challenge of increasing the experimental mass while maintaining incredibly low levels of spurious background. The new concept described in this paper could be the answer which combines all the features of an ideal experiment: energy resolution, low cost mass scalability, isotope choice flexibility and many powerful handles to make the background negligible. The proposed technology is based on the use of arrays of silicon detectors cooled to 120 K to optimize the collection of the scintillation light emitted by ultra-pure crystals. It is shown that with a 54 kg array of natural CaMoO \(_4\) scintillation detectors of this type it is possible to yield a competitive sensitivity on the half-life of the \(\beta \beta 0\nu \) of \(^{100}\) Mo as high as \(\sim \) \(10^{24}\)  years in only 1 year of data taking. The same array made of \(^{40}\) Ca \(^{\mathrm {nat}}\) MoO \(_4\) scintillation detectors (to get rid of the continuous background coming from the two neutrino double beta decay of \(^{48}\) Ca) will instead be capable of achieving the remarkable sensitivity of \(\sim \) \(10^{25}\)  years on the half-life of \(^{100}\) Mo \(\beta \beta 0\nu \) in only 1 year of measurement.     

Effects of cerium dopant concentration on structural properties and photocatalytic activity of electrospun Ce-doped TiO2 nanofibers

Electrospun \(\hbox {TiO}_2\) and Ce-doped \(\hbox {TiO}_2\) nanofibers were prepared with 0.5, 2.0 and 8.0 % weight Ce. The structural properties and phase composition were characterized using high-resolution transmission electron microscopy (HR-TEM), X-ray diffraction and X-ray absorption near edge spectroscopy (XANES) at the Ti K-edge. The undoped nanofibers are composed of an assembly of \(\hbox {TiO}_2\) nanoparticles and their crystal structure is a mixture of anatase and rutile phases with an anatase:rutile volume ratio close to 3:1. As Ce is introduced, the nanoparticles decrease in size and the rutile phase volume decreases. Ce \(\hbox {L}_3\) -edge XANES probed the local structure of Ce dopants. At 0.5 % Ce, most Ce ions are incorporated in the \(\hbox {Ce}^{3+}\) charge state but, at 2 % Ce, the majority are \(\hbox {Ce}^{4+}\) . Visible light absorption indicated that \(\hbox {Ce}^{3+}\) act as shallow acceptors that only participate in absorption of wavelengths below 420 nm but \(\hbox {Ce}^{4+}\) impurity states are associated with absorption of wavelengths up to 550 nm. Photocatalytic performance of the nanofibers was assessed by measuring the degradation of adsorbed Rhodamine B in aqueous solution under visible and ultraviolet light. The 0.5 % Ce-doped \(\hbox {TiO}_2\) nanofiber showed the best visible-light photocatalytic activity, which is probably due to the majority presence of \(\hbox {Ce}^{3+}\) . At higher Ce concentration, the photocatalytic reaction rate was lower than undoped nanofibers, indicating that recombination at the \(\hbox {Ce}^{4+}\) sites is rate limiting.     

Preliminary studies of the Raman spectra of \hbox {Ag}_{2}\hbox {Te}\hbox { and }\hbox {Ag}_{5}\hbox {Te}_{3}

The theoretical calculations indicated that the monoclinic low-temperature phase of silver telluride $(\upbeta \hbox {-Ag}_{2}\hbox {Te})$ is a new binary topological insulator with highly anisotropic single Dirac cone surface. We obtained $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ crystal ingots containing few grains by the Bridgman method. We also deposited thin films of tellurium, $\hbox {Ag}_{5}\hbox {Te}_{3}\hbox { and }(\hbox {Te+Ag}_{5}\hbox {Te}_{3})$ by thermal evaporation method. The Raman spectra of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ were measured at three excitation wave lengths: 633, 515 and 488 nm. The Raman active modes of $\upbeta \hbox {-Ag}_{2}\hbox {Te}$ , tellurium and $\hbox {Ag}_{5}\hbox {Te}_{3}$ are situated at frequencies below 300  $\hbox {cm}^{-1}$ while vibrations of other phases appear at higher frequencies.     

Dirac quasinormal modes of two-dimensional charged dilatonic black holes

Following some recent unexpected hints of neutron production in high-voltage atmospheric discharges, we present a measurement of the neutron flux in plasma discharges in electrolytic cells. We use two different types of neutron detectors, polyallyl diglycol carbonate (PADC, aka CR-39) tracers and indium disks. At 95 % C.L. we provide an upper limit of 1.5 neutrons cm \(^{-2}\)  s \(^{-1}\) for the thermal neutron flux at \({\approx } 5\) cm from the center of the cell. Allowing for a higher energy neutron component, the largest allowed flux is 64 neutrons cm \(^{-2}\)  s \(^{-1}\) . This upper limit is two orders of magnitude smaller than the signal previously claimed in an electrolytic cell plasma discharge experiment. Furthermore the behavior of the CR-39 is discussed to point out possible sources of spurious signals.     

Modeling of HOT (111) HgCdTe MWIR detector for fast response operation

The paper reports on photoelectrical performance of the mid-wave infrared (MWIR) (111) HgCdTe high operating temperature detector for the fast response conditions. Detector structure was simulated with software APSYS by Crosslight Inc. The detailed analysis of the time response as a function of device architecture and applied voltage was performed pointing out optimal working conditions. The time response of the MWIR HgCdTe detector with 50 % cut-off wavelength of \(\lambda _{c} \approx 5.3\, \upmu \hbox {m}\) at \(T = 200\)  K was estimated at the level of \(\tau _{s} \approx \) 2,500 ps for \(V = 100\)  mV and series resistance \(R_{Series} = 510\,\Omega \) . The series resistance’s reduction enables to reach \(\tau _{s}\approx 60\!-\!500\)  ps.     

Polymeric N-stage serial-cascaded four-port optical router with scalable 3N channel wavelengths for wideband signal routing application

Device architecture and design scheme of a universal \(N\) -stage cascaded polymer four-port optical router with scalable 3 \(N\) channel wavelengths are proposed. Basic cross-coupling two-microring resonator routing element based on polymer materials is optimized for single-mode transmission, low optical loss and phase-match between microring waveguide and channel waveguide. Then, a one-stage four-port optical router is constructed using four-group basic routing elements, which has 12 possible I/O routing paths and 3 channel wavelengths. The insertion losses of each channel wavelength along every routing path are within the range of 0.04–0.63 dB, the maximum crosstalk between the on-port along each routing path and other off-ports is less than \(-39\)  dB, and the device footprint size is \(\sim \) 0.13 mm \(^{2}\) . Compared with the previously reported four-port silicon optical routers, this device possesses similar ring radius ( \(\sim \) 10  \(\upmu \) m) and device size ( \(<\) 1 mm \(^{2})\) . Aiming at wideband signal routing applications, we then construct a universal \(N\) -stage cascaded polymer four-port optical router possessing scalable 3 \(N\) channel wavelengths. The proposed routing structure has potential application in photonic networks-on-chip, because of low insertion loss, low crosstalk, small footprint size, and scalable wideband 3 \(N\) routing wavelengths.     

Optimal N-Point Configurations on the Sphere: “Magic” Numbers and Smale’s 7th Problem

This paper inquires into the concavity of the map \(N\mapsto v_s(N)\) from the integers \(N\ge 2\) into the minimal average standardized Riesz pair-energies \(v_s(N)\) of \(N\) -point configurations on the sphere \(\mathbb {S}^2\) for various \(s\in \mathbb {R}\) . The standardized Riesz pair-energy of a pair of points on \(\mathbb {S}^2\) a chordal distance \(r\) apart is \(V_s(r)= s^{-1}\left( r^{-s}-1 \right) \) , \(s \ne 0\) , which becomes \(V_0(r) = \ln \frac{1}{r}\) in the limit \(s\rightarrow 0\) . Averaging it over the \(\left( \begin{array}{c} N\\ 2\end{array}\right) \) distinct pairs in a configuration and minimizing over all possible \(N\) -point configurations defines \(v_s(N)\) . It is known that \(N\mapsto v_s(N)\) is strictly increasing for each \(s\in \mathbb {R}\) , and for \(s<2\) also bounded above, thus “overall concave.” It is (easily) proved that \(N\mapsto v_{-2}^{}(N)\) is even locally strictly concave, and that so is the map \(2n\mapsto v_s(2n)\) for \(s<-2\) . By analyzing computer-experimental data of putatively minimal average Riesz pair-energies \(v_s^x(N)\) for \(s\in \{-1,0,1,2,3\}\) and \(N\in \{2,\ldots ,200\}\) , it is found that the map \(N\mapsto {v}_{-1}^x(N)\) is locally strictly concave, while \(N\mapsto {v}_s^x(N)\) is not always locally strictly concave for \(s\in \{0,1,2,3\}\) : concavity defects occur whenever \(N\in {\mathcal {C}}^{x}_+(s)\) (an \(s\) -specific empirical set of integers). It is found that the empirical map \(s\mapsto {\mathcal {C}}^{x}_+(s),\ s\in \{-2,-1,0,1,2,3\}\) , is set-theoretically increasing; moreover, the percentage of odd numbers in \({\mathcal {C}}^{x}_+(s),\ s\in \{0,1,2,3\}\) is found to increase with \(s\) . The integers in \({\mathcal {C}}^{x}_+(0)\) are few and far between, forming a curious sequence of numbers, reminiscent of the “magic numbers” in nuclear physics. It is conjectured that these new “magic numbers” are associated with optimally symmetric optimal-log-energy \(N\) -point configurations on \(\mathbb {S}^2\) . A list of interesting open problems is extracted from the empirical findings, and some rigorous first steps toward their solutions are presented. It is emphasized how concavity can assist in the solution to Smale’s \(7\) th Problem, which asks for an efficient algorithm to find near-optimal \(N\) -point configurations on \(\mathbb {S}^2\) and higher-dimensional spheres.     

The Isospin Mixing in the X(3872) Decay Spectrum

The large isospin symmetry breaking found in the X(3872) decay is investigated by looking into the transfer strength from the \({{c}\bar{c}}\) quarkonium to the two-meson states: \({c\bar{c} \rightarrow D^{0}\overline{D}^{*0}, D^{+} D^{*-} , J /\psi\omega, {\rm and} \, J /\psi\rho}\) . The widths of the \({\rho}\) and \({\omega}\) mesons are taken into account in the calculation. It is found that very narrow \({J /\psi\omega}\) and \({J /\psi\rho}\) peaks appear at the \({D^{0}\overline{D}^{*0}}\) threshold. These narrow peaks appear provided that the strength of the \({D^{0}\overline{D}^{*0}}\) component is large around the threshold. The large width of the \({\rho}\) meson enhances the isospin-one component in the transfer strength considerably, which reduces the ratio \({{\rm Br}(X \rightarrow J /\psi\omega)/{\rm Br}(X \rightarrow J /\psi\rho)}\) down to 2.5.     

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 $8 \le \mathcal {D} \le 10$ .     

Rejection of randomly coinciding events in ZnMoO_4 scintillating bolometers

Random coincidence of events (particularly from two neutrino double beta decay) could be one of the main sources of background in the search for neutrinoless double beta decay with cryogenic bolometers due to their poor time resolution. Pulse-shape discrimination by using front edge analysis, mean-time and \(\chi ^2\) methods were applied to discriminate randomly coinciding events in ZnMoO \(_4\) cryogenic scintillating bolometers. These events can be effectively rejected at the level of 99 % by the analysis of the heat signals with rise-time of about 14 ms and signal-to-noise ratio of 900, and at the level of 92 % by the analysis of the light signals with rise-time of about 3 ms and signal-to-noise ratio of 30, under the requirement to detect 95 % of single events. These rejection efficiencies are compatible with extremely low background levels in the region of interest of neutrinoless double beta decay of \(^{100}\) Mo for enriched ZnMoO \(_4\) detectors, of the order of \(10^{-4}\)  counts/(y keV kg). Pulse-shape parameters have been chosen on the basis of the performance of a real massive ZnMoO \(_4\) scintillating bolometer. Importance of the signal-to-noise ratio, correct finding of the signal start and choice of an appropriate sampling frequency are discussed.