Asymptotic behavior of the Schrödinger–Debye system with refractive index of quadratic wave amplitude

We obtain local well-posedness for the one-dimensional Schrödinger–Debye interactions in nonlinear optics in the spaces \(L^2\times L^p,\; 1\le p < \infty \). When \(p=1\) we show that the local solutions extend globally. In the focusing regime, we consider a family of solutions \(\{(u_{\tau }, v_{\tau })\}_{\tau >0}\) in \( H^1\times H^1\) associated to an initial data family \(\{(u_{\tau _0},v_{\tau _0})\}_{\tau >0}\) uniformly bounded in \(H^1\times L^2\), where \(\tau \) is a small response time parameter. We prove that \(\left( u_{\tau }, v_{\tau }\right) \) converges to \(\left( u, -|u|^2\right) \) in the space \(L^{\infty }_{[0, T]}L^2_x\times L^1_{[0, T]}L^2_x\) whenever \(u_{\tau _0}\) converges to \(u_0\) in \(H^1\) as long as \(\tau \) tends to 0, where u is the solution of the one-dimensional cubic nonlinear Schrödinger equation with the initial data \(u_0\). The convergence of \(v_{\tau }\) for \(-|u|^2\) in the space \(L^{\infty }_{[0, T]}L^2_x\) is shown under compatibility conditions of the initial data. For non-compatible data, we prove convergence except for a corrector term which looks like an initial layer phenomenon.     

Coexistence of attractors in autonomous Van der Pol–Duffing jerk oscillator: Analysis,chaos control and synchronisation in its fractional-order form

Dynamics at infinity and a Hopf bifurcation for a Sprott E system with a very small perturbation constant are studied in this paper. By using Poincaré compactification of polynomial vector fields in \(R^3\), the dynamics near infinity of the singularities is obtained. Furthermore, in accordance with the centre manifold theorem, the subcritical Hopf bifurcation is analysed and obtained. Numerical simulations demonstrate the correctness of the dynamical and bifurcation analyses. Moreover, by choosing appropriate parameters, this perturbed system can exhibit chaotic, quasiperiodic and periodic dynamics, as well as some coexisting attractors, such as a chaotic attractor coexisting with a periodic attractor for \(a>0\), and a chaotic attractor coexisting with a quasiperiodic attractor for \(a=0\). Coexisting attractors are not associated with an unstable equilibrium and thus often go undiscovered because they may occur in a small region of parameter space, with a small basin of attraction in the space of initial conditions.     

Search of the neutrino-less double beta decay of $$^{}$$Se into the excited states of $$^{}$$Kr with CUPID-0

The CUPID-0 experiment searches for double beta decay using cryogenic calorimeters with double (heat and light) read-out. The detector, consisting of 24 ZnSe crystals 95\(\%\) enriched in \(^{82}\)Se and two natural ZnSe crystals, started data-taking in 2017 at Laboratori Nazionali del Gran Sasso. We present the search for the neutrino-less double beta decay of \(^{82}\)Se into the 0\(_1^+\), 2\(_1^+\) and 2\(_2^+\) excited states of \(^{82}\)Kr with an exposure of 5.74 kg\(\cdot \)yr (2.24\(\times \)10\(^{25}\) emitters\(\cdot \)yr). We found no evidence of the decays and set the most stringent limits on the widths of these processes: \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{0_1^+}\))8.55\(\times \)10\(^{-24}\) yr\(^{-1}\), \(\varGamma \) (\(^{82}\) Se \(\rightarrow ^{82}\) Kr \(_{2_1^+}\))\(\,{<}\,6.25 \,{\times }\,10^{-24}\) yr\(^{-1}\), \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{2_2^+}\))8.25\(\times \)10\(^{-24}\) yr\(^{-1}\) (90\(\%\) credible interval).     

Electron-Spin Relaxation Measurements of Biological [2Fe-2S] Cluster System in View of Electron Spin Quantum Bits

At 20 K, as long as \(T_m\sim 800-1000\) ns were measured for the [2Fe-2S] cluster in its intrinsic protein environment. Such relaxations are a relatively long coherence time for the low-spin \(S=1/2\) system. For this biological cluster, the phase memory time was found significantly affected by the nuclear hyperfine interactions of \(^{14}\)N with \(I=1\). When labeling the surrounding ligands with the \(^{15}\)N isotope uniformly, \(T_m\) are enhanced between \({\sim }1.1-1.4~\upmu\)s at the canonical orientations. This is already an order of magnitude longer than the duration of a single-spin qubit manipulation \({\sim }10-100\) ns. While \(T_1\) are of the order of \({\sim }130\) \(\upmu\)s at the canonical orientations, the transient nutation experiments reflect on the coherent manipulation of the electron spin.     

Asymptotic Equivalence of Probability Measures and Stochastic Processes

Let \(P_n\) and \(Q_n\) be two probability measures representing two different probabilistic models of some system (e.g., an n-particle equilibrium system, a set of random graphs with n vertices, or a stochastic process evolving over a time n) and let \(M_n\) be a random variable representing a “macrostate” or “global observable” of that system. We provide sufficient conditions, based on the Radon–Nikodym derivative of \(P_n\) and \(Q_n\), for the set of typical values of \(M_n\) obtained relative to \(P_n\) to be the same as the set of typical values obtained relative to \(Q_n\) in the limit \(n\rightarrow \infty \). This extends to general probability measures and stochastic processes the well-known thermodynamic-limit equivalence of the microcanonical and canonical ensembles, related mathematically to the asymptotic equivalence of conditional and exponentially-tilted measures. In this more general sense, two probability measures that are asymptotically equivalent predict the same typical or macroscopic properties of the system they are meant to model.     

Observational constraints on the jerk parameter with the data of the Hubble parameter

We study the accelerated expansion phase of the universe by using the kinematic approach. In particular, the deceleration parameter q is parametrized in a model-independent way. Considering a generalized parametrization for q, we first obtain the jerk parameter j (a dimensionless third time derivative of the scale factor) and then confront it with cosmic observations. We use the latest observational dataset of the Hubble parameter H(z) consisting of 41 data points in the redshift range of \(0.07 \le z \le 2.36\), larger than the redshift range that covered by the Type Ia supernova. We also acquire the current values of the deceleration parameter \(q_0\), jerk parameter \(j_0\) and transition redshift \(z_t\) (at which the expansion of the universe switches from being decelerated to accelerated) with \(1\sigma \) errors (\(68.3\%\) confidence level). As a result, it is demonstrate that the universe is indeed undergoing an accelerated expansion phase following the decelerated one. This is consistent with the present observations. Moreover, we find the departure for the present model from the standard \(\Lambda \)CDM model according to the evolution of j. Furthermore, the evolution of the normalized Hubble parameter is shown for the present model and it is compared with the dataset of H(z).     

Kaonic production of $ \Lambda$(1405) off deuteron target in chiral dynamics

The K^--induced production of \( \Lambda\)(1405) is investigated in K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions based on coupled-channels chiral dynamics, in order to discuss the resonance position of the \( \Lambda\)(1405) in the \( \bar{{K}}\) N channel. We find that the K ^- d \( \rightarrow\) \( \Lambda\)(1405)n process favors the production of \( \Lambda\)(1405) initiated by the \( \bar{{K}}\) N channel. The present approach indicates that the \( \Lambda\)(1405) -resonance position is 1420MeV rather than 1405MeV in the \( \pi\) \( \Sigma\) invariant-mass spectra of K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions. This is consistent with an observed spectrum of the K ^- d \( \rightarrow\) \( \pi^{{+}}_{}\) \( \Sigma^{{-}}_{}\) n with 686-844MeV/c incident K^- by bubble chamber experiments done in the 70s. Our model also reproduces the measured \( \Lambda\)(1405) production cross-section.     

Higgs–photon resonances

We study models that produce a Higgs boson plus photon (\(h^0\gamma \)) resonance at the LHC. When the resonance is a \(Z'\) boson, decays to \(h^0\gamma \) occur at one loop. If the \(Z'\) boson couples at tree level to quarks, then the \(h^0\gamma \) branching fraction is typically of order \(10^{-5}\) or smaller. Nevertheless, there are models that would allow the observation of \(Z'\rightarrow \,h^0\gamma \) at \(\sqrt{s}=13\) TeV with a cross section times branching fraction larger than 1 fb for a \(Z'\) mass in the 200–450 GeV range, and larger than 0.1 fb for a mass up to 800 GeV. The one-loop decay of the \(Z'\) into lepton pairs competes with \(h^0\gamma \), even if the \(Z'\) couplings to leptons vanish at tree level. We also present a model in which a \(Z'\) boson decays into a Higgs boson and a pair of collimated photons, mimicking an \(h^0\gamma \) resonance. In this model, the \(h^0\gamma \) resonance search would be the discovery mode for a \(Z'\) as heavy as 2 TeV. When the resonance is a scalar, although decay to \(h^0\gamma \) is forbidden by angular momentum conservation, the \(h^0\) plus collimated photons channel is allowed. We comment on prospects of observing an \(h^0\gamma \) resonance through different Higgs decays, on constraints from related searches, and on models where \(h^0\) is replaced by a nonstandard Higgs boson.     

Warm modified Chaplygin gas shaft inflation

In this paper, we examine the possible realization of a new inflation family called “shaft inflation” by assuming the modified Chaplygin gas model and a tachyon scalar field. We also consider the special form of the dissipative coefficient \(\Gamma ={a_0}\frac{T^{3}}{\phi ^{2 }}\) and calculate the various inflationary parameters in the scenario of strong and weak dissipative regimes. In order to examine the behavior of inflationary parameters, the \(n_s \)–\( \phi ,\, n_s \)–r, and \(n_s \)–\( \alpha _s\) planes (where \(n_s,\, \alpha _s,\, r\), and \(\phi \) represent the spectral index, its running, tensor-to-scalar ratio, and scalar field, respectively) are being developed, which lead to the constraints \(r< 0.11\), \(n_s=0.96 \pm 0.025\), and \(\alpha _s =-0.019 \pm 0.025\). It is quite interesting that these results of the inflationary parameters are compatible with BICEP2, WMAP \((7+9)\) and recent Planck data.     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ decay in the aligned two-Higgs-doublet model

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^-\) transitions. It is found that, when the model parameter \(\left| \varsigma _{u}\right| \) is much smaller than \(\left| \varsigma _{d}\right| \), the charged scalar contributes mainly to chirality-flipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left| \varsigma _{d}\right| ^2\). Numerically, the charged-scalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left| \varsigma _{u}\right| \), small \(\left| \varsigma _{d}\right| \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left| \varsigma _{u}\right| \), large \(\left| \varsigma _{d}\right| \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest model-independent global analysis of \(b\rightarrow s\ell ^+\ell ^-\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.     

Lifshits Tails for Randomly Twisted Quantum Waveguides

We consider the Dirichlet Laplacian \(H_\gamma \) on a 3D twisted waveguide with random Anderson-type twisting \(\gamma \). We introduce the integrated density of states \(N_\gamma \) for the operator \(H_\gamma \), and investigate the Lifshits tails of \(N_\gamma \), i.e. the asymptotic behavior of \(N_\gamma (E)\) as \(E \downarrow \inf \mathrm{supp}\, dN_\gamma \). In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.     

Critical Two-Point Function for Long-Range <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) Models Below the Upper Critical Dimension

We consider the n-component \(|\varphi |^4\) lattice spin model (\(n \ge 1\)) and the weakly self-avoiding walk (\(n=0\)) on \(\mathbb Z^d\), in dimensions \(d=1,2,3\). We study long-range models based on the fractional Laplacian, with spin-spin interactions or walk step probabilities decaying with distance r as \(r^{-(d+\alpha )}\) with \(\alpha \in (0,2)\). The upper critical dimension is \(d_c=2\alpha \). For \(\varepsilon >0\), and \(\alpha = \frac{1}{2} (d+\varepsilon )\), the dimension \(d=d_c-\varepsilon \) is below the upper critical dimension. For small \(\varepsilon \), weak coupling, and all integers \(n \ge 0\), we prove that the two-point function at the critical point decays with distance as \(r^{-(d-\alpha )}\). This “sticking” of the critical exponent at its mean-field value was first predicted in the physics literature in 1972. Our proof is based on a rigorous renormalisation group method. The treatment of observables differs from that used in recent work on the nearest-neighbour 4-dimensional case, via our use of a cluster expansion.     

Supersymmetric deformations of 3D SCFTs from tri-Sasakian truncation

We holographically study supersymmetric deformations of \(N=3\) and \(N=1\) superconformal field theories in three dimensions using four-dimensional \(N=4\) gauged supergravity coupled to three-vector multiplets with non-semisimple \(SO(3)\ltimes (\mathbf {T}^3,\hat{\mathbf {T}}^3)\) gauge group. This gauged supergravity can be obtained from a truncation of 11-dimensional supergravity on a tri-Sasakian manifold and admits both \(N=1,3\) supersymmetric and stable non-supersymmetric \(AdS_4\) critical points. We analyze the BPS equations for SO(3) singlet scalars in detail and study possible supersymmetric solutions. A number of RG flows to non-conformal field theories and half-supersymmetric domain walls are found, and many of them can be given analytically. Apart from these “flat” domain walls, we also consider \(AdS_3\)-sliced domain wall solutions describing two-dimensional conformal defects with \(N=(1,0)\) supersymmetry within the dual \(N=1\) field theory while this type of solutions does not exist in the \(N=3\) case.     

Charmed hadrons from coalescence plus fragmentation in relativistic nucleus-nucleus collisions at RHIC and LHC

In a coalescence plus fragmentation approach we calculate the heavy baryon/meson ratio and the \(p_T\) spectra of charmed hadrons \(D^{0}\), \(D_{s}\) and \(\varLambda _{c}^{+}\) in a wide range of transverse momentum from low \(p_T\) up to about 10 GeV and discuss their ratios from RHIC to LHC energies without any change of the coalescence parameters. We have included the contribution from decays of heavy hadron resonances and also the one due to fragmentation of heavy quarks which do not undergo the coalescence process. The coalescence process is tuned to have all charm quarks hadronizing in the \(p_T\rightarrow 0\) limit and at finite \(p_T\) charm quarks not undergoing coalescence are hadronized by independent fragmentation. The \(p_T\) dependence of the baryon/meson ratios are found to be sensitive to the masses of coalescing quarks, in particular the \(\varLambda _{c}/D^{0}\) can reach values of about \(\mathrm 1\div 1.5 \) at \(p_T \approx \, 3\) GeV, or larger, similarly to the light baryon/meson ratio like \(p/\pi \) and \(\varLambda /K\), however a marked difference is a quite weak \(p_T\) dependence with respect to the light case, such that a larger value at intermediate \(p_T\) implies a relatively large value also for the integrated yields. A comparison with other coalescence model and with the prediction of thermal model is discussed.     

The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

Two-Higgs-doublet type-II and -III models and $$t\rightarrow c h$$ at the LHC

We study the constraints of the generic two-Higgs-doublet model (2HDM) type-III and the impacts of the new Yukawa couplings. For comparisons, we revisit the analysis in the 2HDM type-II. To understand the influence of all involving free parameters and to realize their correlations, we employ a \(\chi \)-square fitting approach by including theoretical and experimental constraints, such as the S, T, and U oblique parameters, the production of standard model Higgs and its decay to \(\gamma \gamma \), \(WW^*/ZZ^*\), \(\tau ^+\tau ^-\), etc. The errors of the analysis are taken at 68, 95.5, and \(99.7~\%\) confidence levels. Due to the new Yukawa couplings being associated with \(\cos (\beta -\alpha )\) and \(\sin (\beta -\alpha )\), we find that the allowed regions for \(\sin \alpha \) and \(\tan \beta \) in the type-III model can be broader when the dictated parameter \(\chi _F\) is positive; however, for negative \(\chi _F\), the limits are stricter than those in the type-II model. By using the constrained parameters, we find that the deviation from the SM in \(h\rightarrow Z\gamma \) can be of \(\mathcal{O}(10~\%)\). Additionally, we also study the top-quark flavor-changing processes induced at the tree level in the type-III model and find that when all current experimental data are considered, we get \(Br(t\rightarrow c(h, H) )< 10^{-3}\) for \(m_h=125.36\) and \(m_H=150\) GeV, and \(Br(t\rightarrow cA)\) slightly exceeds \(10^{-3}\) for \(m_A =130\) GeV.     

Strong homotopy Lie algebras,homotopy Poisson manifolds and Courant algebroids

We study Maurer–Cartan elements on homotopy Poisson manifolds of degree n. They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as twisted Poisson manifolds, quasi-Poisson \(\mathfrak g\)-manifolds, and twisted Courant algebroids. Using the fact that the dual of an n-term \(L_\infty \)-algebra is a homotopy Poisson manifold of degree \(n-1\), we obtain a Courant algebroid from a 2-term \(L_\infty \)-algebra \(\mathfrak g\) via the degree 2 symplectic NQ-manifold \(T^*[2]\mathfrak g^*[1]\). By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid from a 2-term \(L_\infty \)-algebra, which is proposed to be the geometric structure on the dual of a Lie 2-algebra. These results lead to a construction of a new 2-term \(L_\infty \)-algebra from a given one, which could produce many interesting examples.     

A Mysterious Cluster Expansion Associated to the Expectation Value of the Permanent of 0–1 Matrices

We consider two ensembles of \(0-1\) \(n\times n\) matrices. The first is the set of all \(n\times n\) matrices with entries zeroes and ones such that all column sums and all row sums equal r, uniformly weighted. The second is the set of \(n \times n\) matrices with zero and one entries where the probability that any given entry is one is r / n, the probabilities of the set of individual entries being i.i.d.’s. Calling the two expectation values E and \(E_B\) respectively, we develop a formal relation

$$\begin{aligned} E({{\mathrm{perm}}}(A)) = E_B({{\mathrm{perm}}}(A)) e^{\sum _2 T_i}.\quad \quad \quad \quad \mathrm{(A1)} \end{aligned}$$

We use two well-known approximating ensembles to E, \(E_1\) and \(E_2\). Replacing E by either \(E_1\) or \(E_2\) we can evaluate all terms in (A1). For either \(E_1\) or \(E_2\) the terms \(T_i\) have amazing properties. We conjecture that all these properties hold also for E. We carry through a similar development treating \(E({{\mathrm{perm}}}_m(A))\), with m proportional to n, in place of \(E({{\mathrm{perm}}}(A))\).

     

Virtual depth by active background suppression: revisiting the cosmic muon induced background of <Emphasis Type="SmallCaps">Gerda</Emphasis> Phase II

In-situ production of radioisotopes by cosmic muon interactions may generate a non-negligible background for deep underground rare event searches. Previous Monte Carlo studies for the Gerda experiment at Lngs identified the delayed decays of \(^{77}\)Ge and its metastable state \(^{77m}\)Ge as dominant cosmogenic background in the search for neutrinoless double beta decay of \(^{76}\)Ge. This might limit the sensitivity of next generation experiments aiming for increased \(^{76}\)Ge mass at background-free conditions and thereby define a minimum depth requirement. A re-evaluation of the \(^{77(m)}\)Ge background for the Gerda experiment has been carried out by a set of Monte Carlo simulations. The obtained \(^{77(m)}\)Ge production rate is (\(0.21\pm 0.01\)) nuclei/(kg\(\cdot \)year). After application of state-of-the-art active background suppression techniques and simple delayed coincidence cuts this corresponds to a background contribution of \((2.7\pm 0.3)\times 10^{-6}\) cts/(keV\(\cdot \)kg\(\cdot \)year). The suppression achieved by this strategy equals an effective muon flux reduction of more than one order of magnitude. This virtual depth increase opens the way for next generation rare event searches.     

Exotic tetraquark states with the $$qq\bar{Q}\bar{Q}$$ configuration

In this work, we study systematically the mass splittings of the \(qq\bar{Q}\bar{Q}\) (\(q=u\), d, s and \(Q=c\), b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the \(J^P=0^+\) states and possible stable tetraquarks exist in the \(nn\bar{Q}\bar{Q}\) (\(n=u\), d) and \(ns\bar{Q}\bar{Q}\) systems either with \(J=0\) or with \(J=1\). Possible decay patterns of the tetraquarks are briefly discussed.