ShantanuT01/DACTYL-Pretraining huggingface dataset:
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$. For an oscillating string $(0\leq S\leq S_{max})$, the average energy $<E>$ over one oscillation period is expressed as a function of $S_{max}$ as a complete elliptic integral of the third kind.
The collective interaction via the environmental vacuum is investigated for a mixture of two deviating multi-atom ensembles in a moderately intense laser field. Due to the numerous inter-atomic couplings, the laser-dressed system may react sensitively and rapidly with respect to changes in the atomic and laser parameters. We show for weak probe fields that in the absence of absorption both the index of refraction and the group velocity may be modified strongly and rapidly due to the collectivity.
Employing Br\"udern's and Wooley's new complification method, we establish an asymptotic Hasse principle for the number of solutions to a system of r_3 cubic and r_2 quadratic diagonal forms, when the number of cubic equations is at least double the number of quadratic forms. The number of variables required is lower than in earlier work. In particular, we achieve essentially square root cancellation for systems of one quadratic and arbitrarily many cubic equations.
The paper is an extended version of the talk which I gave at the XIX Congresso dell'UMI in Bologna in September 2011. The aim of this paper is twofold: first, to give an overview on the recent development in the classification of surfaces of general type with $p_g=q=2$; second, to point out some of the problems that are still open.
The consequences are explored of an observationally established relation of the star formation rate (SFR) of star-forming galaxies with their stellar mass (M) and cosmic time (t), such that SFR is proportional to M x t^{-2.5}. It is shown, that small systematic differences in SFR dramatically amplify in the course of time: galaxies with above average SFR run into quasi-exponential mass and SFR growth, while galaxies with below average SFR avoid such exponential growth and evolve with moderate mass increase. It is argued that galaxies following the first path would enormously overgrow if keeping to form stars all the way to the present, hence should quench star formation and turn passive. By the same token, those instead avoiding the quasi-exponential growth may keep to form stars up to the present. Thus, it is conjectured that this divergent behaviour can help understanding the origin of the dichotomy between passive, spheroidal galaxies, and star-forming, disk galaxies.
Treating class with a single center may hardly capture data distribution complexities. Using multiple sub-centers is an alternative way to address this problem. However, highly correlated sub-classes, the classifier's parameters grow linearly with the number of classes, and lack of intra-class compactness are three typical issues that need to be addressed in existing multi-subclass methods. To this end, we propose to use Fixed Sub-Center (F-SC), which allows the model to create more discrepant sub-centers while saving memory and cutting computational costs considerably. The F-SC specifically, first samples a class center Ui for each class from a uniform distribution, and then generates a normal distribution for each class, where the mean is equal to Ui. Finally, the sub-centers are sampled based on the normal distribution corresponding to each class, and the sub-centers are fixed during the training process avoiding the overhead of gradient calculation. Moreover, F-SC penalizes the Euclidean distance between the samples and their corresponding sub-centers, it helps remain intra-compactness. The experimental results show that F-SC significantly improves the accuracy of both image classification and fine-grained recognition tasks.
Dijkgraaf and Vafa (DV) have conjectured that the exact superpotential for a large class of N=1 SUSY gauge theories can be extracted from the planar limit of a certain holomorphic matrix integral. We test their proposal against existing knowledge for a family of deformations of N=4 SUSY Yang-Mills theory involving an arbitrary polynomial superpotential for one of the three adjoint chiral superfields. Specifically, we compare the DV prediction for these models with earlier results based on the connection between SUSY gauge theories and integrable systems. We find complete agreement between the two approaches. In particular we show how the DV proposal allows the extraction of the exact eigenvalues of the adjoint scalar in the confining vacuum and hence computes all related condensates of the finite-N gauge theory. We extend these results to include Leigh-Strassler deformations of the N=4 theory.
The spin-boson model, often used in NMR and ESR physics, quantum optics and spintronics, is considered in a solvable limit to model a spin one-half particle interacting with a bosonic thermal bath. By applying external pulses to a non-equilibrium initial state of the spin, work can be extracted from the thermalized bath. It occurs on the timescale $\T_2$ inherent to transversal (`quantum') fluctuations. The work (partly) arises from heat given off by the surrounding bath, while the spin entropy remains constant during a pulse. This presents a violation of the Clausius inequality and the Thomson formulation of the second law (cycles cost work) for the two-level system.   Starting from a fully disordered state, coherence can be induced by employing the bath. Due to this, a gain from a positive-temperature (inversion-free) two-level system is shown to be possible.
Newtonian limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.
We investigate the electronic states and the transport properties of the CoO2 plane in NaxCoO2 on the basis of the two-dimensional triangular lattice 11-band d-p model by using the fluctuation exchange approximation, where we consider the Coulomb interaction between the t2g electrons on a Co site. It is found that all of the effective mass of quasiparticles, the resistivity, the thermoelectric power and the uniform spin susceptibility increase with increasing x for x > 0.6. This implies that the ferromagnetic fluctuations play significant roles on determining the electronic states. These results are qualitatively consistent with the experiments.
We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are the same (or {\it mod} $2\pi$) while the corresponding geometric phases are nontrivial.   We illustrate how this strategy to work in a simple but typical NMR-type qubit system.
We discuss the conservation of angular momentum in nuclear time-dependent Hartree-Fock calculations for a numerical representation of wave functions and potentials on a three-dimensional cartesian grid. Free rotation of a deformed nucleus performs extremely well even for relatively coarse spatial grids. Heavy ion collisions produce a highly excited compound system associated with substantial nucleon emission. These emitted nucleons reach the bounds of the numerical box which leads to a decrease of angular momentum. We discuss strategies to distinguish the physically justified loss from numerical artifacts.
We present infrared K'- (2.1 micron) and L'-band (3.8 micron) high-spatial-resolution (<0.3") imaging observations of 17 nearby (z < 0.17) ultraluminous infrared galaxies (ULIRGs) assisted with the adaptive optics of the Subaru Telescope. We search for compact red K'-L' color emission as the indicator of luminous active galactic nuclei (AGNs) due to AGN-heated hot dust emission. Two luminous dual AGN candidates are revealed. Combining these results with those of our previous study, we can state that the detected fraction of luminous dual AGNs in nearby ULIRGs is much less than unity (<20%), even when infrared wavelengths >2 micron are used that should be sensitive to buried AGNs due to small dust extinction effects. For ULIRGs with resolved multiple nuclear K'-band emission, we estimate the activation of supermassive black holes (SMBHs) at individual galaxy nuclei in the form of AGN luminosity normalized by SMBH mass inferred from host galaxy stellar luminosity. We confirm a trend that more massive SMBHs in K'-band brighter primary galaxy nuclei are generally more active, with higher SMBH-mass-normalized AGN luminosity than less massive SMBHs in K'-band fainter secondary galaxy nuclei, as predicted by numerical simulations of gas-rich major galaxy mergers. In two sources, the presence of even infrared elusive extremely deeply buried AGNs is indicated by comparisons with available (sub)millimeter data. Non-synchronous SMBH activation (i.e., less activation of less massive SMBHs) and the possible presence of such infrared elusive AGNs may be responsible for the small fraction of infrared-detected luminous dual AGNs in nearby merging ULIRGs.
We present a detailed analysis of the intrinsic X-ray absorption in the Seyfert 1 galaxy NGC 4151 using Chandra/HETGS data obtained 2002 May, as part of a program which included simultaneous UV spectra using HST/STIS and FUSE. NGC 4151 was in a relatively low flux state during the observations reported here, although roughly 2.5 times as bright in the 2 --10 keV band as during a Chandra observation in 2000. The soft X-ray band was dominated by emission lines, which show no discernible variation in flux between the two observations. The 2002 data show the presence of a very highly ionized absorber, in the form of H-like and He-like Mg, Si, and S lines, as well as lower ionization gas via the presence of inner-shell absorption lines from lower-ionization species of these elements. The former is too highly ionized to be radiatively accelerated in a sub-Eddington source such as NGC 4151. We find that the lower ionization gas had a column density a factor of ~ 3 higher during the 2000 observation. If due to bulk motion, we estimate that this component must have a velocity of more than 1250 km/sec transverse to our line-of-sight. We suggest that these results are consistent with a magneto-hydrodynamic flow.
It has recently been suggested that the quark-gluon plasma formed in heavy-ion collisions behaves as a nearly ideal fluid. That behavior may be understood if the quark and antiquark mean-free- paths are very small in the system, leading to a "sticky molasses" description of the plasma, as advocated by the Stony Brook group. This behavior may be traced to the fact that there are relatively low-energy $q\bar{q}$ resonance states in the plasma leading to very large scattering lengths for the quarks. These resonances have been found in lattice simulation of QCD using the maximum entropy method (MEM). We have used a chiral quark model, which provides a simple representation of effects due to instanton dynamics, to study the resonances obtained using the MEM scheme. In the present work we use our model to study the optical potential of a quark in the quark-gluon plasma and calculate the quark mean-free-path. Our results represent a specific example of the dynamics of the plasma as described by the Stony Brook group.
We consider the Lagrangian particle model introduced in [hep-th/9612017] for zero mass but nonvanishing second central charge of the planar Galilei group. Extended by a magnetic vortex or a Coulomb potential the model exibits conformal symmetry. In the former case we observe an additional SO(2,1) hidden symmetry. By either a canonical transformation with constraints or by freezing scale and special conformal transformations at $t=0$ we reduce the six-dimensional phase-space to the physically required four dimensions. Then we discuss bound states (bounded solutions) in quantum dynamics (classical mechanics). We show that the Schr\"odinger equation for the pure vortex case may be transformed into the Morse potential problem thus providing us with an explanation of the hidden SO(2,1) symmetry.
In this paper, we present an approach to characterising self-similar fast-reaction limits of systems with nonlinear diffusion. For appropriate initial data, in the fast-reaction limit as k tends to infinithy,spatial segregation results in the two components of the original systems converging to the positive and negative parts of a self-similar limit profile f (n), where n=xt^(1/2) that satisfies one of four ordinary differential systems. The existence of these self-similar solutions of the k tends to infinity limit problems is proved by using shooting methods which focus on a, the position of the free boundary which separates the regions where the solution is positive and where it is negative, and g, the derivative of -phi(f) at n = a. The position of the free boundary gives us intuition about how one substance penetrates into the other, and for specific forms of nonlinear diffusion, the relationship between the given form of the nonlinear diffusion and the position of the free boundary is also studied.
Non-local higher-energy auxiliary states have been successfully used to entangle pairs of qubits in different quantum computing systems. Typically a longer-span non-local state or sequential application of few-qubit entangling gates are needed to produce a non-trivial multiqubit gate. In many cases a single non-local state that span over the entire system is difficult to use due to spectral crowding or impossible to have. At the same time, many multiqubit systems can naturally develop a network of multiple non-local higher-energy states that span over few qubits each. We show that continuous time quantum walks can be used to address this problem by involving multiple such states to perform local and entangling operations concurrently on many qubits. This introduces an alternative approach to multiqubit gate compression based on available physical resources. We formulate general requirements for such walks and discuss configurations of non-local auxiliary states that can emerge in quantum computing architectures based on self-assembled quantum dots, defects in diamond, and superconducting qubits, as examples. Specifically, we discuss a scalable multiqubit quantum register constructed as a single chain with nearest-neighbor interactions. We illustrate how quantum walks can be configured to perform single-, two- and three-qubit gates, including Hadamard, Control-NOT, and Toffoli gates. Continuous time quantum walks on graphs involved in these gates are investigated.
We report on experiments allowing to set an upper limit on the magnitude of the spin Hall effect and the conductance by edge channels in quantum wells of PbTe embedded between PbEuTe barriers. We reexamine previous data obtained for epitaxial microstructures of n-type PbSe and PbTe, in which pronounced nonlocal effects and reproducible magnetoresistance oscillations were found. Here we show that these effects are brought about by a quasi-periodic network of threading dislocations adjacent to the BaF$_2$ substrate, which give rise to a p-type interfacial layer and an associated parasitic parallel conductance. We then present results of transport measurements on microstructures of modulation doped PbTe/(Pb,Eu)Te:Bi heterostructures for which the influence of parasitic parallel conductance is minimized, and for which quantum Hall transport had been observed, on similar samples, previously. These structures are of H-shaped geometry and they are patterned of 12 nm thick strained PbTe quantum wells embedded between Pb$_{0.92}$Eu$_{0.08}$Te barriers. The structures have different lateral sizes corresponding to both diffusive and ballistic electron transport in non-equivalent L valleys. For these structures no nonlocal resistance is detected confirming that PbTe is a trivial insulator. The magnitude of spin Hall angle gamma is estimated to be smaller than 0.02 for PbTe/PbEuTe microstructures in the diffusive regime.
The system of interacting spinless fermions hopping on a two-leg ladder in the presence of an external magnetic field is shown to possess a long range order: the bond density wave or the staggered flux phase. In both cases the elementary excitations are $Z_2$ kinks and carry one half the charge of an electron.
We present measurements on the single molecule magnet Fe8 in the presence of pulsed microwave radiation at 118 GHz. The spin dynamics is studied via time resolved magnetization experiments using a Hall probe magnetometer. We investigate the relaxation behavior of magnetization after the microwave pulse. The analysis of the experimental data is performed in terms of different contributions to the magnetization after-pulse relaxation. We find that the phonon bottleneck with a characteristic relaxation time of 10 to 100 ms strongly affects the magnetization dynamics. In addition, the spatial effect of spin diffusion is evidenced by using samples of different sizes and different ways of the sample's irradiation with microwaves.
We derive a necessary and sufficient condition of linear dynamical stability for inhomogeneous Vlasov stationary states of the Hamiltonian Mean Field (HMF) model. The condition is expressed by an explicit disequality that has to be satisfied by the stationary state, and it generalizes the known disequality for homogeneous stationary states. In addition, we derive analogous disequalities that express necessary and sufficient conditions of formal stability for the stationary states. Their usefulness, from the point of view of linear dynamical stability, is that they are simpler, although they provide only sufficient criteria of linear stability. We show that for homogeneous stationary states the relations become equal, and therefore linear dynamical stability and formal stability become equivalent.
We formulate an approximate relativistic framework for an analysis of the 3He(e,e'p)pn and 3He(e,e'n)pp reactions with polarized electrons and 3He in the initial state. Restricting the rescattering series to one term linear in the two-nucleon t-matrix we incorporate various relativistic features when calculating a nuclear current matrix element. These relativistic ingredients encompass the relativistic 3He wave function based on the concept of the Lorentz boosted nucleon-nucleon potential together with the boosted 2N t-matrix, relativistic kinematics and relativistic single-nucleon current operator. This allows us to estimate the magnitude of relativistic effects not included in the standard nonrelativistic approach.
By Monte Carlo simulations we study critical properties of the mixed spin-1/2 and spin-1 Ising model on a triangular lattice, considering two different ways of the spin-value distributions on the three sublattices: $(1/2,1/2,1)$ and $(1/2,1,1)$. In the former case, we find standard Ising universality class phase transitions between paramagnetic and magnetic phases but no phase transitions between two distinct magnetic phases $(\pm 1/2,\pm 1/2,\pm 1)$ and $(\pm 1/2,\pm 1/2,0)$ at any finite temperature, except for some interesting non-critical anomalies displayed by response functions. On the other hand, the latter case turns out to be a rare (or perhaps the only) example of a two-dimensional mixed spin-1/2 and spin-1 Ising model on a standard lattice that displays tricritical behavior.
According to the Belinskii-Khalatnikov-Lifshitz scenario, a collapsing universe approaching a spacelike singularity can be approximated by homogeneous cosmological dynamics, but only if asymptotically small spatial regions are considered. It is shown here that the relevant small-volume behavior in solvable models of loop quantum cosmology is crucially different from the large-volume behavior exclusively studied so far. While bouncing solutions exist and may even be generic within a given quantum representation, they are not generic if quantization ambiguities such as choices of representations are taken into account. The analysis reveals an interesting interplay between sl(2,R)-representation theory and canonical effective theory.
In this paper an explicit cosmological model which allows cosmological singularities are discussed. The generalized power-law and asymptotic expansions of the baro-tropic fluid index $\omega$ and equivalently the deceleration parameter $q$, in terms of cosmic time $'t'$ are considered. Finally, the strength of the found singularities is discussed.
We investigate the impact of different assumptions in the modeling of one-loop galaxy bias on the recovery of cosmological parameters, as a follow up of the analysis done in the first paper of the series at fixed cosmology. We use three different synthetic galaxy samples whose clustering properties match the ones of the CMASS and LOWZ catalogues of BOSS and the SDSS Main Galaxy Sample. We investigate the relevance of allowing for either short range non-locality or scale-dependent stochasticity by fitting the real-space galaxy auto power spectrum or the combination of galaxy-galaxy and galaxy-matter power spectrum. From a comparison among the goodness-of-fit ($\chi^2$), unbiasedness of cosmological parameters (FoB), and figure-of-merit (FoM), we find that a four-parameter model (linear, quadratic, cubic non-local bias, and constant shot-noise) with fixed quadratic tidal bias provides a robust modelling choice for the auto power spectrum of the three samples, up to $k_{\rm max}=0.3\,h\,\mathrm{Mpc}^{-1}$ and for an effective volume of $6\,h^{-3}\,\mathrm{Gpc}^3$. Instead, a joint analysis of the two observables fails at larger scales, and a model extension with either higher derivatives or scale-dependent shot-noise is necessary to reach a similar $k_{\rm max}$, with the latter providing the most stable results. These findings are obtained with three, either hybrid or perturbative, prescriptions for the matter power spectrum, \texttt{RESPRESSO}, gRPT and EFT. In all cases, the inclusion of scale-dependent shot-noise increases the range of validity of the model in terms of FoB and $\chi^2$. Interestingly, these model extensions with additional free parameters do not necessarily lead to an increase in the maximally achievable FoM for the cosmological parameters $\left(h,\,\Omega_ch^2,\,A_s\right)$, which are generally consistent to those of the simpler model at smaller $k_{\rm max}$.
In this article we investigate a conformal extension of the standard model in which the scalar sector consists of a standard model Higgs doublet, a real gauge singlet and a real $SU(2)_{L}$ triplet. Focusing on the scenario where the Higgs boson found at the LHC is identified as the pseudo-Nambu-Goldstone boson of broken scale invariance, various theoretical and phenomenological features of the model are discussed. In particular, we analyze the decay pattern of the new scalar resonance. We also show that when the mass of this new scalar resonance is far below the $WW$ threshold, the natural regions of the parameter space are reduced by a constraint associated with the symmetry enhancement due to the decoupling of the singlet scalar from the rest of the system.