ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study the Cauchy problem for an inhomogeneous Gross-Pitaevskii equation. We first derive a sharp threshold for global existence and blow up of the solution. Then we construct and classify finite time blow up solutions at the minimal mass threshold. Additionally, using variational techniques, we study the existence, the orbital stability and instability of standing waves.
We study weak solutions of the two-dimensional (2D) filtered Euler equations whose vorticity is a finite Radon measure and velocity has locally finite kinetic energy, which is called the vortex sheet solution. The filtered Euler equations are a regularized model based on a spatial filtering to the Euler equations. The 2D filtered Euler equations have a unique global weak solution for measure valued initial vorticity, while the 2D Euler equations require initial vorticity to be in the vortex sheet class with a distinguished sign for the existence of global solutions. In this paper, we prove that vortex sheet solutions of the 2D filtered Euler equations converge to those of the 2D Euler equations in the limit of the filtering parameter provided that initial vortex sheet has a distinguished sign. We also show that a simple application of our proof yields the convergence of the vortex blob method for vortex sheet solutions. Moreover, we make it clear what kind of condition should be imposed on the spatial filter to show the convergence results and, according to the condition, these results are applicable to well-known regularized models like the Euler-$\alpha$ model and the vortex blob model.
We construct supergravity duals of D6-branes wrapping Kahler four-cycles inside a Calabi-Yau threefold, CY_3. We obtain the purely gravitational M-theory description, which turns out to be a Calabi-Yau fourfold, CY_4. We also analyze the dynamics of a probe D6 in this background.
We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fite, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.
We report on the ultrafast dynamics of charge order and structural response during the photoinduced suppression of charge and orbital order in a mixed-valence manganite. Employing femtosecond time-resolved resonant x-ray diffraction below and at the Mn K absorption edge, we present a method to disentangle the transient charge order and structural dynamics in thin films of Pr0.5Ca0.5MnO3. Based on the static resonant scattering spectra, we extract the dispersion correction of charge ordered Mn3+ and Mn4+ ions, allowing us to separate the transient contributions of purely charge order from structural contributions to the scattering amplitude after optical excitation. Our finding of a coherent structural mode at around 2.3 THz, which primarily modulates the lattice, but does not strongly affect the charge order, confirms the picture of the charge order being the driving force of the combined charge, orbital and structural transition.
We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the alpha effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations.
This paper studies a single-suit version of the card game War on a finite deck of cards. There are varying methods of how players put the cards that they win back into their hands, but we primarily consider randomly putting the cards back and deterministically always putting the winning card before the losing card. The concept of a \emph{passthrough} is defined, which refers to a player playing through all cards in their hand from a particular point in the game. We consider games in which the second player wins during their first passthrough. We introduce several combinatorial objects related to the game: game graphs, win-loss sequences, win-loss binary trees, and game posets. We show how these objects relate to each other. We enumerate states depending on the number of rounds and the number of passthroughs.
Observables of neutrino oscillations in matter have, in general, contributions from the effective matter potential. It contaminates the CP violation asymmetry adding a fake effect that has been recently disentangled from the genuine one by their different behavior under T and CPT. Is the genuine T-odd CPT-invariant component of the CP asymmetry coincident with the T asymmetry? Contrary to CP, matter effects in uniform matter cannot induce by themselves a non-vanishing T asymmetry; however, the question of the title remained open. We demonstrate that, in the presence of genuine CP violation, there is a new non-vanishing CP-even, and so CPT-odd, component in the T asymmetry in matter, which is of odd-parity in both the phase $\delta$ of the flavor mixing and the matter parameter $a$. The two disentangled components, genuine $A^\mathrm{T;CP}_{\alpha\beta}$ and fake $A^\mathrm{T;CPT}_{\alpha\beta}$, could be experimentally separated by the measurement of the two T asymmetries in matter ($\nu_\alpha \leftrightarrow \nu_\beta$) and ($\bar\nu_\alpha \leftrightarrow \bar\nu_\beta$). For the ($\nu_\mu \leftrightarrow \nu_e$) transitions, the energy dependence of the new $A^\mathrm{T;CPT}_{\mu e}$ component is like the matter-induced term $A^\mathrm{CP;CPT}_{\mu e}$ of the CP asymmetry which is odd under a change of the neutrino mass hierarchy. We have thus completed the physics involved in all observable asymmetries in matter by means of their disentanglement into the three independent components, genuine $A^\mathrm{CP;T}_{\alpha\beta}$ and fake $A^\mathrm{CP;CPT}_{\alpha\beta}$ and $A^\mathrm{T;CPT}_{\alpha\beta}$.
Spectral properties for the two-dimensional quantum S=1 XY model were investigated with the exact diagonalization method. In the symmetry-broken phase, there appear the massive Higgs and massless Goldstone excitations, which correspond to the longitudinal and transverse modes of the spontaneous magnetic moment, respectively. The former excitation branch is embedded in the continuum of the latter, and little attention has been paid to the details, particularly, in proximity to the critical point. The finite-size-scaling behavior is improved by extending the interaction parameters. An analysis of the critical amplitude ratio for these mass gaps is made.
Using the world-line method we resum the scalar one-loop effective action. This is based on an exact expression for the one-loop action obtained for a background potential and a Taylor expansion of the potential up to quadratic order in x-space. We thus reproduce results of Masso and Rota very economically. An alternative resummation scheme is suggested using ``center of mass'' based loops which is equivalent under the assumption of vanishing third and higher derivatives in the Taylor expansion but leads to simplified expressions. In an appendix some general issues concerning the relation between world-line integrals with fixed end points versus integrals with fixed center are clarified. We finally note that this method is also very valuable for gauge field effective actions where it is based on the Euler--Heisenberg type resummation.
In this work, we establish pathwise functional It\^o formulas for non-smooth functionals of real-valued continuous semimartingales. Under finite $(p,q)$-variation regularity assumptions in the sense of two-dimensional Young integration theory, we establish a pathwise local-time decomposition   $$F_t(X_t) = F_0(X_0)+ \int_0^t\nabla^hF_s(X_s)ds + \int_0^t\nabla^wF_s(X_s)dX(s) - \frac{1}{2}\int_{-\infty}^{+\infty}\int_0^t(\nabla^w_xF_s)(^{x}X_s)d_{(s,x)}\ell^x(s).$$ Here, $X_t= \{X(s); 0\le s\le t\}$ is the continuous semimartingale path up to time $t\in [0,T]$, $\nabla^h$ is the horizontal derivative, $(\nabla^w_x F_s)(^{x}X_s)$ is a weak derivative of $F$ with respect to the terminal value $x$ of the modified path $^{x}X_s$ and $\nabla^w F_s(X_s) = (\nabla^w_x F_s)(^{x} X_s)|_{x=X(s)}$. The double integral is interpreted as a space-time 2D-Young integral with differential $d_{(s,x)}\ell^x(s)$, where $\ell$ is the local-time of $X$. Under less restrictive joint variation assumptions on $(\nabla^w_x F_t)(^{x} X_t)$, functional It\^o formulas are established when $X$ is a stable symmetric process. Singular cases when $x\mapsto (\nabla^w_x F_t)(^{x}X_t)$ is smooth off random bounded variation curves are also discussed. The results of this paper extend previous change of variable formulas in Cont and Fourni\'e and also Peskir, Feng and Zhao and Elworhty, Truman and Zhao in the context of path-dependent functionals. In particular, we provide a pathwise path-dependent version of the classical F\"{o}llmer-Protter-Shiryaev formula for continuous semimartingales.
Dropping separatedness in the definition of a toric variety, one obtains the more general notion of a toric prevariety. Toric prevarieties occur as ambient spaces in algebraic geometry and moreover they appear naturally as intermediate steps in quotient constructions. We first provide a complete description of the category of toric prevarieties in terms of convex-geometrical data, so-called systems of fans. In a second part, we consider actions of subtori H of the big torus of a toric prevariety X and investigate quotients for such actions. Using our language of systems of fans, we characterize existence of good prequotients for the action of H on X. Moreover, we show by means of an algorithmic construction that there always exists a toric prequotient for the action of H on X, that means an H-invariant toric morphism p from X to a toric prevariety Y such that every H-invariant toric morphism from X to a toric prevariety factors through p. Finally, generalizing a result of D. Cox, we prove that every toric prevariety occurs as the image of a categorical prequotient of an open toric subvariety of some complex affine space.
We study new effective curve classes on the moduli space of stable pointed rational curves given by the fixed loci of subgroups of the permutation group action. We compute their numerical classes and provide a strategy for writing them as effective linear combinations of F-curves, using Losev-Manin spaces and toric degeneration of curve classes.
We continue our study of string theory in a background that interpolates between $AdS_3$ in the infrared and a linear dilaton spacetime $R^{1,1}\times R_\phi$ in the UV. This background corresponds via holography to a $CFT_2$ deformed by an operator of dimension $(2,2)$. We discuss the structure of spatial entanglement in this model, and compare it to the closely related $T\bar T$ deformed $CFT_2$.
We present the redshift-space generalization of the equal-time angular-averaged consistency relations between $(\ell+n)$- and $n$-point polyspectra of the cosmological matter density field. Focusing on the case of $\ell=1$ large-scale mode and $n$ small-scale modes, we use an approximate symmetry of the gravitational dynamics to derive explicit expressions that hold beyond the perturbative regime, including both the large-scale Kaiser effect and the small-scale fingers-of-god effects. We explicitly check these relations, both perturbatively, for the lowest-order version that applies to the bispectrum, and nonperturbatively, for all orders but for the one-dimensional dynamics. Using a large ensemble of $N$-body simulations, we find that our squeezed bispectrum relation is valid to better than $20\%$ up to $1h$Mpc$^{-1}$, for both the monopole and quadrupole at $z=0.35$, in a $\Lambda$CDM cosmology. Additional simulations done for the Einstein-de Sitter background suggest that these discrepancies mainly come from the breakdown of the approximate symmetry of the gravitational dynamics. For practical applications, we introduce a simple ansatz to estimate the new derivative terms in the relation using only observables. Although the relation holds worse after using this ansatz, we can still recover it within $20\%$ up to $1h$Mpc$^{-1}$, at $z=0.35$ for the monopole. On larger scales, $k = 0.2 h\mathrm{Mpc}^{-1}$, it still holds within the statistical accuracy of idealized simulations of volume $\sim8h^{-3}\mathrm{Gpc}^3$ without shot-noise error.
The Reissner-Nordstrom black hole in four dimensions can be made unstable without violating the dominant energy condition by introducing a real massive scalar with non-renormalizable interactions with the gauge field. New stable black hole solutions then exist with greater entropy for fixed mass and charge than the Reissner-Nordstrom solution. In these new solutions, the scalar condenses to a non-zero value near the horizon. Various generalizations of these hairy black holes are discussed, and an attempt is made to characterize when black hole hair can occur.
We analyze the gauge symmetry of a topological mass generating action in four dimensions which contains both a vector and a second rank antisymmetric tensor fields. In the Abelian case, this system induces an effective mass for the vector gauge field via a topological coupling $B \wedge F$ in the presence of a kinetic term for the antisymmetric tensor field $B$, while maintaining a gauge symmetry. On the other hand, for the non-Abelian case the $B$ field does not have a gauge symmetry unless an auxiliary vector field is introduced to the system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and show how the auxiliary vector field enhances the symmetry. At the same time this enhanced gauge symmetry becomes reducible. We also show this phenomenon in this analysis.
The geodesic approximation is a powerful method for studying the dynamics of BPS solitons. However, there are systems, such as BPS monopoles in three-dimensional hyperbolic space, where this approach is not applicable because the moduli space metric defined by the kinetic energy is not finite. In the case of hyperbolic monopoles, an alternative metric has been defined using the abelian connection on the sphere at infinity, but its relation to the dynamics of hyperbolic monopoles is unclear. Here this metric is placed in a more general context of boundary metrics on soliton moduli spaces. Examples are studied in systems in one and two space dimensions, where it is much easier to compare the results with simulations of the full nonlinear field theory dynamics. It is found that geodesics of the boundary metric provide a reasonable description of soliton dynamics.
To describe structural peculiarities in inhomogeneous media caused by the tendency to the close packing of atoms a formalism based on the using of the Riemann geometry methods (which were successfully applied lately to the description of structures of quasicrystals and glasses) is developed. Basing on this formalism we find in particular the criterion of stability of precipitates of the Frank-Kasper phases in metallic systems. The nature of the ''rhenium effect'' in W-Re alloys is discussed.
An inequality of Hardy type is established for quadratic forms involving Dirac operator and a weight $r^{-b}$ for functions in $\R^n$. The exact Hardy constant $c_b=c_b(n)$ is found and generalized minimizers are given. The constant $c_b$ vanishes on a countable set of $b$, which extends the known case $n=2$, $b=0$ which corresponds to the trivial Hardy inequality in $\R^2$. Analogous inequalities are proved in the case $c_b=0$ under constraints and, with error terms, for a bounded domain.
I give a simple argument that demonstrates that the state |0>|1>+|1>|0>, with |0> denoting a state with 0 particles and |1> a 1-particle state, is entangled in spite of recent claims to the contrary. I also discuss new viewpoints on the old controversy about whether the above state can be said to display single-particle or single-photon nonlocality.
We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes non-negative (hence becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.
Several fixed-target experiments reported J/$\psi$ and $\Upsilon$ polarization measurements, as functions of Feynman $x$ ($x_{\rm F}$) and transverse momentum ($p_{\rm T}$), in three different polarization frames, using different combinations of beam particles, target nuclei and collision energies. The data form such a diverse and heterogeneous picture that, at first sight, no clear trends can be observed. A more detailed look, however, allows us to discern qualitative physical patterns that inspire and support a simple interpretation: the directly-produced quarkonia result from either gluon-gluon fusion or from quark-antiquark annihilation, with the former mesons being fully longitudinally polarized and the latter being fully transversely polarized. This hypothesis provides a reasonable quantitative description of the J/$\psi$ and $\Upsilon$(1S) polarizations measured in the $x_{\rm F} \lesssim 0.5$ kinematical domain. We provide predictions that can be experimentally tested, using proton and/or pion beams, and show that improved J/$\psi$ and $\psi$(2S) polarization measurements in pion-nucleus collisions can provide significant constraints on the poorly known parton distribution functions of the pion.
We investigate ergodic properties of generalized Ornstein--Uhlenbeck processes. In particular, we provide sufficient conditions for ergodicity, and for subexponential and exponential convergence to the invariant probability measure. We use the Foster--Lyapunov method. The drift conditions are obtained using the explicit form of the generator of the continuous process. In some special cases the optimality of our results can be shown.
We present a simple, pedagogical introduction to the statistics of extreme values. Motivated by a string of record high temperatures in December 1998, we consider the distribution, averages and lifetimes for a simplified model of such ``records.'' Our ``data'' are sequences of independent random numbers all of which are generated from the same probability distribution. A remarkable universality emerges: a number of results, including the lifetime histogram, are universal, that is, independent of the underlying distribution.
We study the following elliptic system concerning the fractional Laplacian operator $$(- \Delta)^ {s_i} u_i = H_i ( u_1,\cdots,u_m) \ \ \text{in}\ \ \mathbb{R}^n,$$ when $0<s_i<1$, $u_i: \mathbb R^n\to R$ and $H_i$ belongs to $C^{1,\gamma}(\mathbb{R}^m)$ for $\gamma > \max(0,1-2\min \left \{s_i \right \})$ for $1\le i \le m$. The above system is called symmetric when the matrix $\mathcal H=(\partial_j H_i(u_1,\cdots,u_m))_{i,j=1}^m$ is symmetric. The notion of symmetric systems seems crucial to study this system with a general nonlinearity $H=(H_i)_{i=1}^m$. We establish De Giorgi type results for stable and $H$-monotone solutions of symmetric systems in lower dimensions that is either $n=2$ and $0<s_i<1$ or $n=3$ and $1/2 \le \min\{s_i\}<1$. The case that $n=3$ and at least one of parameters $s_i$ belongs to $(0,1/2)$ remains open as well as the case $n \ge 4$. Applying a geometric Poincar\'{e} inequality, we conclude that gradients of components of solutions are parallel in lower dimensions when the system is coupled. More precisely, we show that the angle between vectors $\nabla u_i$ and $\nabla u_j$ is exactly $\arccos\left({|\partial_j H_i(u)|}/{\partial_j H_i(u)}\right)$. In addition, we provide Hamiltonian identities, monotonicity formulae and Liouville theorems. Lastly, we apply some of our main results to a two-component nonlinear Schr\"{o}dinger system, that is a particular case of the above system, and we prove Liouville theorems and monotonicity formulae.
In here the matrix model approach, by Dijkgraaf and Vafa, is used in order to obtain the effective superpotential for a certain deformation of N=4 SYM discovered by Leigh and Strassler. An exact solution to the matrix model Lagrangian is found and is expressed in terms of elliptic functions.
A lattice of interacting Majorana modes can occur in a superconducting film on a topological insulator in a magnetic field. The phase diagram as a function of interaction strength for the square lattice was analyzed recently using a combination of mean field theory and renormalization group methods, and was found to include second order phase transitions. One of these corresponds to spontaneous breaking of an emergent U(1) symmetry, for attractive interactions. Despite the fact that the U(1) symmetry is not exact, this transition was claimed to be in a supersymmetric universality class when time reversal symmetry is present and in the conventional XY universality class otherwise. Another second order transition was predicted for repulsive interactions with time reversal symmetry to be in the same universality class as the transition occurring in the Gross-Neveu model, despite the fact that the U(1) symmetry is not exact in the Majorana model. We analyze these phase transitions using a modified $\epsilon$-expansion, confirming the previous conclusions.
We analyze the spectrum of an unusually-low mass white dwarf, SDSSJ123410.37-022802.9 (0335-264-52000), found in our recent, white dwarf catalog from the SDSS DR1 data release. Two independent, model atmosphere fits result in an accurate determination of atmospheric and stellar parameters. The more hands-on analysis yields $T_{\rm eff}$ =17,470$\pm$750 K and $\log g$ = 6.38$\pm$0.05. We argue that the object cannot be a main sequence A star, a horizontal branch or subdwarf B star. Instead, it is interpreted as a very low mass white dwarf with a core composed of helium, with mass ($\sim$0.18-0.19$M_\odot$), similar to that published previously for the unusual companion to the millisecond pulsar J1012+5307. The star probably remains in a binary, perhaps even with an undiscovered or dead pulsar companion. However, the companion might be a more-ordinary star, provided Roche lobe mass transfer began shortly after the now-visible component left the main sequence. A second SDSS low mass white dwarf candidate is also analyzed, but the spectrum for this fainter object is of poorer quality. The sample appears to include additional, similar candidates, worthy of more accurate observation. Correct identification of any additional white dwarfs of extremely low mass requires careful observation and interpretation.