ShantanuT01/DACTYL-Pretraining huggingface dataset:
Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance also in the context of tensor network algorithms, thus setting the stage for cross-fertilization between these two areas of research.
Tibet AS-gamma collaboration has recently reported detection of gamma-rays with energies up to Peta-electronvolt from parts of the Galactic plane. We notice that the analysis of gamma-ray flux by the Tibet AS-gamma experiment also implies an upper bound on the diffuse gamma-ray flux from high Galactic latitudes(|b|>20 degrees) in the energy range between 100 TeV and 1 PeV. This bound is up to an order-of-magnitude stronger than previously derived bounds from GRAPES3, KASCADE and CASA-MIA experiments. We discuss the new TibetAS-gamma limit on high Galactic latitude gamma-ray flux in the context of possible mechanisms of multi-messenger (gamma-ray and neutrino) emission from nearby cosmic ray sources, dark matter decays and large scale cosmic ray halo of the Milky Way.
The $f(R)$ gravity theory is considered. It is a gravitational theory that generalizes the Einstein-Hilbert action. In this context, a holographic dark energy model is studied. Tsallis non-extensive entropy is used to introduce the dark energy density based on the holographic principle. Then the Friedmann equation, deceleration parameter, and equation of state for this model are investigated.
I consider the problem of generalising the Abelian Coulomb gauge condition to the non-Abelian Yang-Mills theory, with an arbitrary compact and semi-simple gauge group. It is shown that a straightforward generalisation exists, which reduces the Gauss law into a form involving the gauge potentials only, but not their time derivatives. The existence and uniqueness of the generalised Coulomb gauge is shown to depend on an elliptic linear partial differential equation for a Lie-algebra valued quantity, which defines the gauge transform by means of which the generalised Coulomb gauge condition is realised. Thus the Gribov problem is actually non-existent in this case.
We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.
The conception of almost complete revivals has been introduced recently. In a quantum many-body system local observable may exhibit an almost complete revival to its maximal value at the predetermined moment of time. In this paper we extend the original procedure such that the revival may be from an arbitrary point on the Bloch sphere to the arbitrary point. Furthermore in the proposed procedure the reviving and collapsing sites are not necessarily the same. We also demonstrate that for spins $S$ higher than $1/2$ almost complete revivals are suppressed as $1/S$.
SrCuTe$_2$O$_6$ consists of a 3-dimensional arrangement of spin-$\frac{1}{2}$ Cu$^{2+}$ ions. The 1st, 2nd and 3rd neighbor interactions respectively couple Cu$^{2+}$ moments into a network of isolated triangles, a highly frustrated hyperkagome lattice consisting of corner sharing triangles and antiferromagnetic chains. Of these, the chain interaction dominates in SrCuTe$_2$O$_6$ while the other two interactions lead to frustrated inter-chain coupling giving rise to long range magnetic order at suppressed temperatures. In this paper, we investigate the magnetic properties in SrCuTe$_2$O$_6$ using muon relaxation spectroscopy and neutron diffraction and present the low temperature magnetic structure.
Active Galactic Nuclei (AGN) are the most luminous persistent objects in the universe. An excess of X-ray emission below about 2 keV, called soft-excess, is very common in Type 1 AGN spectra. The origin of this feature remains debated. Originally modeled with a blackbody, there are now several possibilities to model the soft-excess, including warm Comptonization and blurred ionized reflection. In this paper, we test ionized-reflection models on Mrk 509, a bright Seyfert 1 galaxy for which we have a unique data set, in order to determine whether it can be responsible for the strong soft-excess. We use ten simultaneous XMM-Newton and INTEGRAL observations performed every four days. We present here the results of the spectral analysis, the evolution of the parameters and the variability properties of the X-ray emission. The application of blurred ionized-reflection models leads to a very strong reflection and an extreme geometry, but fails to reproduce the broad-band spectrum of Mrk 509. Two different scenarios for blurred ionized reflection are discussed: stable geometry and lamp-post configuration. In both cases we find that the model parameters do not follow the expected relations, indicating that the model is fine-tuned to fit the data without physical justification. A large, slow variation of the soft-excess without counterpart in the hard X-rays could be explained by a change in ionization of the reflector. However, such a change does not naturally follow from the assumed geometrical configuration. Warm Comptonization remains the most probable origin of the soft-excess in this object. Nevertheless, it is possible that both ionized reflection and warm Comptonization mechanisms can explain the soft-excess in all objects, one dominating the other one, depending on the physical conditions of the disk and the corona.
In this paper we prove the necessity of the main sufficient condition of Meinardus for sub exponential rate of growth of the number of structures, having multiplicative generating functions of a general form and establish a new necessary and suffcient condition for normal local limit theorem for aforementioned structures. The latter result allows to encompass in our study structures with weights having gaps in their supports.
A theoretical study on low-temperature structural phase transitions is presented, in which both phonon-like and relaxation order-parameter dynamics are contemplated. While the first limiting case has been considered previously, the second one is studied here for the first time. Attention is put on the low-temperature asymptotics of the temperature dependence of the generalized susceptibility. In the relaxation case, it is found $\sim (T^2 - T_c^2)^{-1}$ for temperature-independent relaxation times in a broad region of the temperature-pressure phase diagram. In contrast to the obtained in the phonon-like case, this asymptotics is not modified by long-range interactions (dipolar forces, piezoelectric effect, etc.).
We give necessary and sufficient conditions guaranteeing that the coupling for L\'evy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall-Rogers on couplings of random walks. In particular, we obtain that a L\'{e}vy process admits a successful coupling, if it is a strong Feller process or if the L\'evy (jump) measure has an absolutely continuous component.
A polynomial $A(q)=\sum_{i=0}^n a_iq^i$ is said to be unimodal if $a_0\le a_1\le \cdots \le a_k\ge a_{k+1} \ge \cdots \ge a_n$. We investigate the unimodality of rational $q$-Catalan polynomials, which is defined to be $C_{m,n}(q)= \frac{1}{[n+m]} \left[ m+n \atop n\right]$ for a coprime pair of positive integers $(m,n)$. We conjecture that they are unimodal with respect to parity, or equivalently, $(1+q)C_{m+n}(q)$ is unimodal. By using generating functions and the constant term method, we verify our conjecture for $m\le 5$ in a straightforward way.
We derive a formula for Greenberg's $L$-invariant of Tate twists of the symmetric sixth power of an ordinary non-CM cuspidal newform of weight $\geq4$, under some technical assumptions. This requires a "sufficiently rich" Galois deformation of the symmetric cube which we obtain from the symmetric cube lift to $\GSp(4)_{/\QQ}$ of Ramakrishnan--Shahidi and the Hida theory of this group developed by Tilouine--Urban. The $L$-invariant is expressed in terms of derivatives of Frobenius eigenvalues varying in the Hida family. Our result suggests that one could compute Greenberg's $L$-invariant of all symmetric powers by using appropriate functorial transfers and Hida theory on higher rank groups.
The asymmetry in the energy spectra between mirror nuclei (the Thomas-Ehrman shifts) around $^{16}$O is investigated from a phenomenological viewpoint. The recent data on proton-rich nuclei indicates that the residual nuclear interaction is reduced for the loosely bound s-orbit by as much as 30%, which originates in the broad radial distribution of the proton single-particle wave function.
Photon modes have an important role in characterizing the quantum sources of light. Proper coupling of various photon modes obtained in spontaneous parametric down conversion (SPDC) process in optical fibers is essential to generate an effective source of entangled photons. The two main pre-detection factors affecting the biphoton mode coupling in SPDC are the pump beam focusing parameter and the crystal thickness. We present the numerical and experimental results on the effect of pump focusing on conditional down-converted photon modes for a Type-I BBO crystal. We experimentally verify that biphoton coupling efficiency decreases asymptotically with pump beam focusing parameter. We attribute this behaviour to (a) the asymmetry in the spatial distribution of down-converted photons with the pump beam focusing parameter and (b) the ellipticity of biphoton modes introduced due to the focusing of the pump beam. We also show experimentally the ellipticity as well as quantify the asymmetry with the pump focusing parameter. These results may be useful in selecting optimum conditions in the down-conversion process for generating efficient sources of entangled photons for quantum information applications.
Motivated by the various examples of spatial variability in the power of the acoustic spectrum, we attempted to look for spatial variability in the peak frequency of the spectrum. However, the determination of this peak frequency on a spatial scale of a single pixel (8 arc seconds for the GONG data) is limited by the stochastic variations in the power spectrum presumably caused by the stochastic nature of the excitation process. Averaging over a large number of spectra (100 spectra from a 10 $\times$ 10 pixels area) produced stabler spectra. The peak frequencies of 130 such locations were found to be distributed with a FWHM of about 130 $\mu$Hz. A map of the spatial variation of this peak frequency did not show any strong feature with statistically significant deviation from the mean of the distribution. Likewise, the scatter in the peak frequencies masked the detection of magnetic field induced changes in the peak frequency. On a much larger scale, the N latitudes showed a slightly lower value of the peak frequency as compared to the S latitudes, although the difference (25 $\mu$Hz) is barely larger than the {\it rms} spread (20 $\mu$Hz).
The product-wavefunction renormalization group method, which is a novel numerical renormalization group scheme proposed recently,is applied to one-dimensional quantum spin chains in a magnetic field. We draw the zero-temperature magnetization curve of the spin chains, which excellently agrees with the exact solution in the whole range of the field.
We study tautological vector bundles over the Hilbert scheme of points on surfaces. For each K-trivial surface, we write down a simple criterion ensuring that the tautological bundles are big and nef, and illustrate it by examples. In the K3 case, we extend recent constructions and results of Bini, Boissi\`ere and Flamini from the Hilbert scheme of 2 and 3 points to an arbitrary number of points. Among the K-trivial surfaces, the case of Enriques surfaces is the most involved. Our techniques apply to other smooth projective surfaces, including blowups of K3s and minimal surfaces of general type, as well as to the punctual Quot schemes of curves.
We exploit ALMA 870um observations to measure the star-formation rates (SFRs) of eight X-ray detected Active Galactic Nuclei (AGNs) in a z~3.1 protocluster, four of which reside in extended Ly-alpha haloes (often termed Ly-alpha blobs: LABs). Three of the AGNs are detected by ALMA and have implied SFRs of ~220-410~M_sun/yr; the non detection of the other five AGNs places SFR upper limits of <210 M_sun/yr. The mean SFR of the protocluster AGNs (~110-210 M_sun/yr) is consistent (within a factor of ~0.7-2.3) with that found for co-eval AGNs in the field, implying that galaxy growth is not significantly accelerated in these systems. However, when also considering ALMA data from the literature, we find evidence for elevated mean SFRs (up-to a factor of ~5.9 over the field) for AGNs at the protocluster core, indicating that galaxy growth is significantly accelerated in the central regions of the protocluster. We also show that all of the four protocluster LABs are associated with an ALMA counterpart within the extent of their Ly-alpha emission. The SFRs of the ALMA sources within the LABs (~150-410 M_sun/yr) are consistent with those expected for co-eval massive star-forming galaxies in the field. Furthermore, the two giant LABs (with physical extents of >100 kpc) do not host more luminous star formation than the smaller LABs, despite being an order of magnitude brighter in Ly-alpha emission. We use these results to discuss star formation as the power source of LABs.
Matter in its present form was formed when our   Universe emerged from the quark-gluon phase (QGP) at about 30mus into its evolution. To explore this early period in the laboratory, we study highly excited matter formed in relativistic heavy ion collision experiments: heavy nuclei crash into each other, and form compressed and energetically excited nuclear matter, resembling in its key features the stuff which filled the early Universe. In these experiments we further explore the physics of the vacuum structure of strongly interacting gauge theory, Quantum Chromodynamics (QCD). The common beginning for both, heavy ion collisions, and vacuum structure investigations, is the physics of the quantum electrodynamic (QED) vacuum in the presence of the supercritical external field that is formed when two highly charged heavy ions are brought together near to the Coulomb barrier in a considerably lower reaction energy collision.
The theory of constructing instantaneous equilibrium (ieq) transition under arbitrary time-dependent temperature and potential variation for a Brownian particle is developed. It is shown that it is essential to consider the underdamped dynamics for temperature-changing transitions. The ieq is maintained by a time-dependent auxiliary position and momentum potential, which can be calculated for given time-dependent transition protocols. Explicit analytic results are derived for the work and heat statistics, energy, and entropy changes for harmonic and non-harmonic trapping potential with arbitrary time-dependent potential parameters and temperature protocols. Numerical solutions of the corresponding Langevin dynamics are computed to confirm the theoretical results. Although ieq transition of the reverse process is not the time-reversal of the ieq transition of the forward process due to the odd-parity of controlling parameters, their phase-space distribution functions restore the time-reversal symmetry, and hence the energy and entropy changes of the ieq of the reverse process are simply the negative of that of the forward process. Furthermore, it is shown that it is possible to construct an ieq transition that has zero entropy production at a finite transition rate, i.e., a fast ieq isentropic process, and is further demonstrated by explicit Langevin dynamics simulations. Our theory provides fundamental building blocks for designing controlled microscopic heat engine cycles. Implications for constructing an efficient Brownian heat engine are also discussed.
We use Kneser's neighbor method and isometry testing for lattices due to Plesken and Souveigner to compute systems of Hecke eigenvalues associated to definite forms of classical reductive algebraic groups.
Recently, Wi-Fi has caught tremendous attention for its ubiquity, and, motivated by Wi-Fi's low cost and privacy preservation, researchers have been putting lots of investigation into its potential on action recognition and even person identification. In this paper, we offer an comprehensive overview on these two topics in Wi-Fi. Also, through looking at these two topics from an unprecedented perspective, we could achieve generality instead of designing specific ad-hoc features for each scenario. Observing the great resemblance of Channel State Information (CSI, a fine-grained information captured from the received Wi-Fi signal) to texture, we proposed a brand-new framework based on computer vision methods. To minimize the effect of location dependency embedded in CSI, we propose a novel de-noising method based on Singular Value Decomposition (SVD) to eliminate the background energy and effectively extract the channel information of signals reflected by human bodies. From the experiments conducted, we demonstrate the feasibility and efficacy of the proposed methods. Also, we conclude factors that would affect the performance and highlight a few promising issues that require further deliberation.
We present a low frequency study of the diffuse radio emission in the galaxy cluster A754. We present new 150 MHz image of the galaxy cluster A754 made with the Giant Metrewave Radio Telescope (GMRT) and discuss the detection of 4 diffuse features. We compare the 150 MHz image with the images at 74, 330 and 1363 MHz; one new diffuse feature is detected. The flux density upperlimits at 330 and 1363 MHz imply a synchrotron spectral index, $\alpha > 2$, ($S\propto \nu^{-\alpha}$) for the new feature. The 'west relic' detected at 74 MHz (Kassim et al 2001) is not detected at 150 MHz and is thus consistent with its non-detection at 1363 MHz (Bacchi et al 2003) and 330 MHz(Kassim et al 2001). Integrated spectra of all the diffuse features are presented. The fourth diffuse feature is located along the proposed merger axis (Zabludoff et al 1995) in A754 and 0.7 Mpc away from the peak of X-ray emission. We have made use of the framework of adiabatic compression model (Ensslin & Gopal-Krishna 2001) to obtain spectra. We show that the spectrum of the fourth diffuse feature is consistent with that of a cocoon of a radio galaxy lurking for about $9\times10^{7}$ yr; no shock compression is required. The other three diffuse emission have spectra steeper than 1.5 and could be cocoons lurking for longer time. We discuss other possibilities such as shocks and turbulent reacceleration being responsible for the diffuse emission in A754.
Let $k$ be an even integer and $S_k$ be the space of cusp forms of weight $k$ on $\SL_2(\ZZ)$. Let $S = \oplus_{k\in 2\ZZ} S_k$. For $f, g\in S$, we let $R(f, g) = \{ (a_f(p), a_g(p)) \in \mathbb{P}^1(\CC)\ |\ \text{$p$ is a prime} \}$ be the set of ratios of the Fourier coefficients of $f$ and $g$, where $a_f(n)$ (resp. $a_g(n)$) is the $n$th Fourier coefficient of $f$ (resp. $g$). In this paper, we prove that if $f$ and $g$ are nonzero and $R(f,g)$ is finite, then $f = cg$ for some constant $c$. This result is extended to the space of weakly holomorphic modular forms on $\SL_2(\ZZ)$. We apply it to studying the number of representations of a positive integer by a quadratic form.
We calculate the conductance G of a bipolar junction in a graphene nanoribbon, in the high-magnetic field regime where the Hall conductance in the p-doped and n-doped regions is 2e^2/h. In the absence of intervalley scattering, the result G=(e^2/h)(1-cos Phi) depends only on the angle Phi between the valley isospins (= Bloch vectors representing the spinor of the valley polarization) at the two opposite edges. This plateau in the conductance versus Fermi energy is insensitive to electrostatic disorder, while it is destabilized by the dispersionless edge state which may exist at a zigzag boundary. A strain-induced vector potential shifts the conductance plateau up or down by rotating the valley isospin.
We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar invariant under the group realized by the transformations of stochastic local quantum operations and classical communications (SLOCC). This invariant is offered as a candidate entanglement measure for n-qubit states and discussed in relation to measures of quantum state entanglement for certain important classes of two-qubit and three-qubit systems. This invariant can be directly estimated via a quantum network, obviating the need to perform laborious quantum state tomography. We also show that this invariant directly captures the extent of entanglement purification due to SLOCC filters.
We present a phenomenological solution of the Kondo lattice that is derived from an analysis of the bulk specific heat and spin susceptibility of the heavy electron superconductor CeCoIn5. We find that below a crossover temperature corresponding to the intersite coupling scale, T* ~ 45 K, the Kondo gas (of non-interacting Kondo impurities) partially condenses into a heavy electron "Kondo" liquid that has a temperature independent Wilson ratio = 2.0. The relative fraction, f, of the "condensed" Kondo liquid component plays the role of an order parameter; it increases linearly with decreasing temperature until it saturates at its low temperature value of 0.9. The resistivity is shown to be simply the product of (1-f) and that of an isolated Kondo impurity. The generality of this result is suggested by the corresponding analysis for Ce1-xLaxCoIn5 and CeIrIn5.
By an explicit calculation we demonstrate that the triple gauge-ghost vertices in a general renormalizable ${\cal N}=1$ supersymmetric gauge theory are UV finite in the two-loop approximation. For this purpose we calculate the two-loop divergent contribution to the $\bar c^+ V c$-vertex proportional to $(C_2)^2$ and use the finiteness of the two-loop contribution proportional to $C_2 T(R)$ which has been checked earlier. The theory under consideration is regularized by higher covariant derivatives and quantized in a manifestly ${\cal N}=1$ supersymmetric way with the help of ${\cal N}=1$ superspace. The two-loop finiteness of the vertices with one external line of the quantum gauge superfield and two external lines of the Faddeev--Popov ghosts has been verified for a general $\xi$-gauge. This result agrees with the nonrenormalization theorem proved earlier in all orders, which is an important step for the all-loop derivation of the exact NSVZ $\beta$-function.