ShantanuT01/DACTYL-Pretraining huggingface dataset:
The low energy behavior of a huge variety of one-dimensional interacting spinful fermionic systems exhibits spin-charge separation, described in the continuum limit by two sine-Gordon models decoupled in the charge and spin channels. Interaction is known to induce, besides the gapless Luttinger liquid phase, eight possible gapped phases, among which are the Mott, Haldane, charge-/spin-density, and bond-ordered wave insulators, and the Luther Emery liquid. Here we prove that some of these physically distinct phases have nontrivial topological properties, notably the presence of degenerate protected edge modes with fractionalized charge/spin. Moreover, we show that the eight gapped phases are in one-to-one correspondence with the symmetry-protected topological (SPT) phases classified by group cohomology theory in the presence of particle-hole symmetry P. The latter result is also exploited to characterize SPT phases by measurable nonlocal order parameters which follow the system evolution to the quantum phase transition. The implications on the appearance of exotic orders in the class of microscopic Hubbard Hamiltonians, possibly without P symmetry at higher energies, are discussed.
For $x\in End(K^n)$ satisfying $x^2 = 0$ let $F_x$ be the variety of full flags stable under the action of $x$ (Springer fiber over $x$). The full classification of the components of $F_x$ according to their smoothness was provided in a paper of Fresse-Melnikov in terms of both Young tableaux and link patterns. Moreover in a paper of Fresse the purely combinatorial algorithm to compute the singular locus of a singular components of $F_x$ is provided. However this algorithm involves the computation of the graph of the component, and the complexity of computations grows very quickly, so that in practice it is impossible to use it. In this paper, we construct another algorithm, derived from the algorithm of Fresse, providing all the components of the singular locus of a singular component of $F_x$ in terms of link patterns constructed straightforwardly from its link pattern.
A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a non-zero value of the packing fraction. The zero-temperature constraint of force-balance plays a crucial role in determining the nature of the transition. Two order parameters, <z>, the deviation of the average number of contacts from the isostatic value and, <F>, the average magnitude of the force per contact, characterize the transition from the jammed (high packing fraction) to the unjammed (low packing fraction state). The critical point has a mixed character with the order parameters showing a jump discontinuity but with fluctuations of the contact force diverging. At the critical point, the distribution of F shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces. Implications for finite temperature dynamics and generalizations to frictional packings and higher dimensions are discussed
We consider the following problem posed by Volkmann in 2007: How close to regular must a c-partite tournament be, to secure a strongly connected subtournament of order $c$? We give sufficient conditions on the regularity of balanced $c$-partite tournaments to assure the existence of strong maximal subtournament with minimum degree at least $\left\lfloor \frac{c-2}{4}\right\rfloor+1$. We obtain this result as an application of counting the number of subtournaments of order $c$ for which a vertex has minimum out-degree (resp. in-degree) at most $q\geq 0$.
In the late 80's, Ou and Mandel experimentally observed signal beatings by performing a non-time resolved coincidence detection of two photons having interfered in a balanced beam splitter [Phys. Rev. Lett 61, 54 (1988)]. In this work, we provide a new interpretation of the fringe pattern observed in this experiment as the direct measurement of the chronocyclic Wigner distribution of a frequency Schr\"odinger cat-like state produced by local spectral filtering. Based on this analysis, we also study time-resolved HOM experiment to measure such frequency state.
This paper will present some intuitive interpretation of the adjugate transformations of arbitrary Latin square. With this trick, we can generate the adjugates of arbitrary Latin square directly from the original one without generating the orthogonal array. The relations of isotopisms and adjugate transformations in composition will also be shown. It will solve the problem that when F1*I1=I2*F2 how can we obtain I2 and F2 from I1 and F1, where I1 and I2 are isotopisms while F1 and F2 are adjugate transformations and "{*}" is the composition of transformations. These methods could distinctly simplify the computation on a computer for the issues related to main classes of Latin squares. This will improve the efficiency apparently in computation for some related problems.
Using a geometric realization of the $SU(2)_R$ symmetry and a procedure of factorisation of the gauge and $SU(2)_R$ charges, we study the small instanton singularities of the Higgs branch of supersymmetric $U(1)^r$ gauge theories with eight supercharges. We derive new solutions for the moduli space of vacua preserving manifestly the eight supercharges. In particular, we obtain an extension of the ordinary ADE singularities for hyperKahler manifolds and show that the classical moduli space of vacua is in general given by cotangent bundles of compact weighted projective spaces.
One way to define the concentration of measure phenomenon is via Talagrand inequalities, also called transportation-information inequalities. That is, a comparison of the Wasserstein distance from the given measure to any other absolutely continuous measure with finite relative entropy. Such transportation-information inequalities were recently established for some stochastic differential equations. Here, we develop a similar theory for some stochastic partial differential equations.
Motivated by the significant overdensity of background bright quasars recently detected behind the foreground clusters of galaxies on scale of $10$ arcminutes, we have investigated the possibility of attributing the quasar-cluster associations to gravitational lensing by large-scale matter inhomogeneities. Based on the conventional lensing models, we have shown that the reported quasar overdensity is unlikely to be generated by cluster matter alone. The situation does not change even if all the clusters of galaxies which follow their spatial two-point correlation function are taken into account, while matter clumps on scale of $>20$ Mpc are also found to be unable to provide the required mass surface density since their density contrast is strictly limited by the anisotropy measurements of the cosmic background radiation. Moreover, we have pointed out that the influence of a nonzero cosmological constant on the quasar-cluster associations is very minor. We conclude that either the observed quasar number counts have been seriously contaminated by the magnification bias of matter inhomogeneities of the universe or there should exists some intercluster matter on scale of less than $\sim20$ Mpc, e.g. from cluster-galaxy correlation, whose mean cosmic density is about an order of magnitude higher than that of clusters of galaxies.
Quantum states can in a sense be thought of as generalizations of classical probability distributions, but are more powerful than probability distributions when used for computation or communication. Quantum speedup therefore requires some feature of quantum states that classical probability distributions lack. One such feature is interference. We quantify interference and show that there can be no quantum speedup due to a small number of operations incapable of generating large amounts of interference (although large numbers of such operations can in fact lead to quantum speedup). Low-interference operations include sparse unitaries, Grover reflections, short time/low energy Hamiltonian evolutions, and the Haar wavelet transform. Circuits built from such operations can be classically simulated via a Monte Carlo technique making use of a convex combination of two Markov chains. Applications to query complexity, communication complexity, and the Wigner representation are discussed.
In this paper we study the multiplicities and the asymptotic behaviour of the numbers of totients in the strata given by 2-adic valuation.
The Galactic bulge is now considered to be the inner three-dimensional part of the Milky Way's bar. It has a peanut shape and is characterized by cylindrical rotation. In N-body simulations, box/peanut bulges arise from disks through bar and buckling instabilities. Models of this kind explain much of the structure and kinematics of the Galactic bulge and, in principle, also its vertical metallicity gradient. Cosmological disk galaxy formation models with high resolution and improved feedback models are now able to generate late-type disk galaxies with disk-like or barred bulges. These bulges often contain an early collapse stellar population and a population driven by later disk instabilities. Due to the inside-out disk formation, these bulges can be predominantly old, similar to the Milky Way bulge.
We study the flavour changing neutral Higgs boson decays that can be induced from genuine supersymmetric particles at the one-loop level and within the context of the Minimal Supersymmetric Standard Model. We consider all the possible flavour changing decay channels of the three neutral Higgs bosons into second and third generation quarks, and focus on the Supersymmetric-QCD corrections from squark-gluino loops which are expected to provide the dominant contributions. We assume here the more general hypothesis for flavour mixing, where there is misalignment between the quark and squark sectors, leading to a flavour non-diagonal squark mass matrix. The form factors involved, and the corresponding Higgs partial decay widths and branching ratios, are computed both analytically and numerically, and their behaviour with the parameters of the Minimal Supersymmetric Standard Model and with the squark mass mixing are analyzed in full detail. The large rates found, are explained in terms of the non-decoupling behaviour of these squark-gluino loop corrections in the scenario with very large supersymmetric mass parameters. Our results show that if these decays are seen in future colliders they could provide clear indirect signals of supersymmetry.
The Monoceros R2 region was first recognized as a chain of reflection nebulae illuminated by A- and B-type stars. These nebulae are associated with a giant molecular cloud that is one of the closest massive star forming regions to the Sun. This chapter reviews the properties of the Mon R2 region, including the namesake reflection nebulae, the large scale molecular cloud, global star formation activity, and properties of prominent star forming regions in the cloud.
We present exact expressions for the Sagnac effect of Goedel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Goedel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.
We study the symmetric nuclear matter using bare nucleon-nucleon ($NN$) interactions with finite particle-number approach within finite cubic boxes. Due to the $NN$ correlations originating from bare $NN$ interaction, two nucleons can be excited to the high-momentum region, leading to the increase of the kinetic energy in nuclear matter. We further consider the spin excitations in the nucleon pairs, where the spin of the two nucleons are changed, and this excitation is important for the tensor correlation. The unitary correlation operator method (UCOM) is used to treat the short-range correlation. The tail correction coming from the neighbouring boxes is also included. We demonstrate the contributions of various excitations of nucleon pairs as well as the tail correction to the total energy at the normal density. We also discuss the effects of UCOM and correlated nucleon pairs on the density dependence of the total energy. We calculate the equations of state of symmetric nuclear matter using two kinds of the Argonne potentials and the results agree with those from other many-body theories. The density dependences of the Hamiltonian components are also shown.
We consider an interacting particle process on a graph which, from a macroscopic point of view, looks like $\Z^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch). There are two birth rates: an inter-patch one $\lambda$ and an intra-patch one $\phi$. Once a site is occupied, there is no breeding from outside the patch and the probability $c(i)$ of success of an intra-patch breeding decreases with the size $i$ of the population in the site. We prove the existence of a critical value $\lambda_{cr}(\phi, c, N)$ and a critical value $\phi_{cr}(\lambda, c, N)$. We consider a sequence of processes generated by the families of control functions $\{c_i\}_{i \in \N}$ and degrees $\{N_i\}_{i \in \N}$; we prove, under mild assumptions, the existence of a critical value $i_{cr}$. Roughly speaking we show that, in the limit, these processes behave as the branching random walk on $\Z^d$ with external birth rate $\lambda$ and internal birth rate $\phi$. Some examples of models that can be seen as particular cases are given.
Femtosecond laser excitation of solid-state systems creates non-equilibrium hot electrons that cool down by transferring their energy to other degrees of freedom and ultimately to lattice vibrations of the solid. By combining ab initio calculations with ultrafast diffuse electron scattering we gain a detailed understanding of the complex non-equilibrium energy transfer between electrons and phonons in laser-excited Ni metal. Our experimental results show that the wavevector resolved population dynamics of phonon modes is distinctly different throughout the Brillouin zone and are in remarkable agreement with our theoretical results. We find that zone-boundary phonon modes become occupied first. As soon as the energy in these modes becomes larger than the average electron energy a backflow of energy from lattice to electronic degrees of freedom occurs. Subsequent excitation of lower-energy phonon modes drives the thermalization of the whole system on the picosecond timescale. We determine the evolving non-equilibrium phonon occupations which we find to deviate markedly from thermal occupations.
A fullerene graph is a cubic bridgeless planar graph with twelve 5-faces such that all other faces are 6-faces. We show that any fullerene graph on n vertices can be bipartized by removing O(sqrt{n}) edges. This bound is asymptotically optimal.
A theoretical description of the radial density profile for charged particles with Yukawa interaction in a harmonic trap is described. At strong Coulomb coupling shell structure is observed in both computer simulations and experiments. Correlations responsible for such shell structure are described here using a recently developed model based in density functional theory. A wide range of particle number, Coulomb coupling, and screening lengths is considered within the fluid phase. A hypernetted chain approximation shows the formation of shell structure, but fails to give quantitative agreement with Monte Carlo simulation results at strong coupling. Significantly better agreement is obtained within the hypernetted chain structure using a renormalized coupling constant, representing bridge function corrections.
The most recent parametrization D1M of the Gogny energy density functional is used to describe fission in the isotopes $^{232-280}$ Pu. We resort to the methodology introduced in our previous studies [Phys. Rev. C \textbf{88}, 054325 (2013) and Phys. Rev. C \textbf {89}, 054310 (2014)] to compute the fission paths, collective masses and zero point quantum corrections within the Hartree-Fock-Bogoliubov framework. The systematics of the spontaneous fission half-lives t$_{SF}$, masses and charges of the fragments in Plutonium isotopes is analyzed and compared with available experimental data. We also pay attention to isomeric states, the deformation properties of the fragments as well as to the competition between the spontaneous fission and $\alpha$-decay modes. The impact of pairing correlations on the predicted t$_{SF}$ values is demonstrated with the help of calculations for $^{232-280}$Pu in which the pairing strengths of the Gogny-D1M energy density functional are modified by 5 $\%$ and 10 $\%$, respectively. We further validate the use of the D1M parametrization through the discussion of the half-lives in $^{242-262}$Fm. Our calculations corroborate that, though the uncertainties in the absolute values of physical observables are large, the Gogny-D1M Hartree-Fock-Bogoliubov framework still reproduces the trends with mass and/or neutron numbers and therefore represents a reasonable starting point to describe fission in heavy nuclear systems from a microscopic point of view.
We present a model which describes the properties of odd-even nuclei with one nucleon more, or less, with respect to the magic number. In addition to the effects related to the unpaired nucleon, we consider those produced by the excitation of the closed shell core. By using a single particle basis generated with Hartree-Fock calculations, we describe the polarization of the doubly magic-core with Random Phase Approximation collective wave functions. In every step of the calculation, and for all the nuclei considered, we use the same finite-range nucleon-nucleon interaction. We apply our model to the evaluation of electric quadrupole and magnetic dipole moments of odd-even nuclei around oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase Approximation description of the polarization of the core improves the agreement with experimental data with respect to the predictions of the independent particle model. We compare our results with those obtained in first-order perturbation theory, with those produced by Hartree-Fock-Bogolioubov calculations and with those generated within the Landau-Migdal theory of finite Fermi systems. The results of our universal, self-consistent, and parameter free approach have the same quality of those obtained with phenomenological approaches where the various terms of the nucleon-nucleon interaction are adapted to reproduce some specific experimental data. A critical discussion on the validity of the model is presented.
We report the compositional dependence of the electronic band structure for a range of III-V alloys. Density functional theory with the PBE functional is insufficient to mimic the electronic gap energies at different symmetry points of the Brillouin zone. The HSE hybrid functional with screened exchange accurately reproduces the experimental band gaps and, more importantly, the alloy concentration of the direct-indirect gap crossovers for the III-V alloys studied here: AlGaAs, InAlAs, AlInP, InGaP, and GaAsP.
For $n,\,d\ge1$ let $p(n,2d)$ denote the smallest number $p$ such that every sum of squares of forms of degree $d$ in $\mathbb{R}[x_1,\dots,x_n]$ is a sum of $p$ squares. We establish lower bounds for these numbers that are considerably stronger than the bounds known so far. Combined with known upper bounds they give $p(3,2d)\in\{d+1,\,d+2\}$ in the ternary case. Assuming a conjecture of Iarrobino-Kanev on dimensions of tangent spaces to catalecticant varieties, we show that $p(n,2d)\sim const\cdot d^{(n-1)/2}$ for $d\to\infty$ and all $n\ge3$. For ternary sextics and quaternary quartics we determine the exact value of the invariant, showing $p(3,6)=4$ and $p(4,4)=5$.
Let $X$ be a complex analytic manifold, $D\subset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper we give an algebraic description in terms of $E$ of the regular holonomic D-module whose de Rham complex is the intersection complex associated with $L$. As an application, we perform some effective computations in the case of quasi-homogeneous plane curves.
We approximate the white-noise driven stochastic heat equation by replacing the fractional Laplacian by the generator of a discrete time random walk on the one dimensional lattice, and approximating white noise by a collection of i.i.d. mean zero random variables. As a consequence, we give an alternative proof of the weak convergence of the scaled partition function of directed polymers in the intermediate disorder regime, to the stochastic heat equation; an advantage of the proof is that it gives the convergence of all moments.
In the paper we consider a generalizations of the notion of Poisson process to the case when classical convolution is replaced by generalized convolution in the sense of K. Urbanik [16] following two classical definitions of Poisson process. First, for every generalized convolution $\diamond$ we define $\diamond$-generalized Poisson process type I as a Markov process with the $\diamond$-generalized Poisson distribution. Such processes have stationary independent increments in the sense of generalized convolution, but usually they do not live on $\mathbb{N}_0$. The $\diamond$-generalized Poisson process type II is defined as a renewal process based on the sequence $S_n$, which is a Markov process with the step with the lack of memory property. Such processes take values in $\mathbb{N}_0$, however they do not have to be Markov processes, do not have to have independent increments, even in generalized convolution sense. It turns out that the second construction is possible only for monotonic generalized convolutions which admit the existence of distributions with lack of memory, thus we also study these properties.
The finite-temperature phase diagram of the Hubbard model in $d=3$ is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%--40% electron or hole doping from half filling, a new $\tau $ phase in which the electron hopping strength $t$ asymptotically becomes infinite under repeated rescalings. Next to the $\tau $ phase, a first-order phase boundary with very narrow phase separation (less than 2% jump in electron density) occurs. At temperatures above the $\tau $ phase, an incommensurate spin modulation phase is indicated. In $d=2$, we find that the Hubbard model has no phase transition at finite temperature.
Let $\ell$ and $p$ be prime numbers and $K_{n,m}=\mathbb{Q}(p^{\frac{1}{\ell^n}},\zeta_{2\ell^{m}})$. We study the $\ell$-class group of $K_{n,m}$ in this paper. When $\ell=2$, we determine the structure of the $2$-class group of $K_{n,m}$ for all $(n,m)\in \mathbb{Z}_{\geq 0}^2$ in the case $p=2$ or $p\equiv 3, 5\bmod{8}$, and for $(n,m)=(n,0)$, $(n,1)$ or $(1,m)$ in the case $p\equiv 7\bmod{16}$, eneralizing the results of Parry about the $2$-divisibility of the class number of $K_{2,0}$. We also obtain results about the $\ell$-class group of $K_{n,m}$ when $\ell$ is odd and in particular $\ell=3$. The main tools we use are class field theory, including Chevalley's ambiguous class number formula and its generalization by Gras, and a stationary result about the $\ell$-class groups in the $2$-dimensional Kummer tower $\{K_{n,m}\}$.