ShantanuT01/DACTYL-Pretraining huggingface dataset:
Quantum spin-1/2 antiferromagnetic Heisenberg trimerized chain with strong intradimer and weak monomer-dimer coupling constants is studied using the novel many-body perturbation expansion, which is developed from the exactly solved spin-1/2 Ising-Heisenberg diamond chain preserving correlations between all interacting spins of the trimerized chain unlike the standard perturbation scheme developed on the grounds of noninteracting spin monomers and dimers. The Heisenberg trimerized chain shows the intermediate one-third plateau, which was also observed in the magnetization curve of the polymeric compound Cu$_3$(P$_2$O$_6$OH)$_2$ affording its experimental realization. Within the modified strong-coupling method we have obtained the effective Hamiltonians for the magnetic-field range from zero to one-third plateau, and from one-third plateau to the saturation magnetization. The second-order perturbation theory shows reliable results even for the moderate ratio between weaker dimer-monomer and stronger intradimer coupling constants. We have also examined thermodynamic properties and recovered the low-temperature peak in the specific heat. The accuracy of the developed method is tested through a comparison with numerical density-matrix renormalization group and quantum Monte Carlo simulations. Using the results for the effective Hamiltonian we suggest straightforward procedure for finding the microscopic parameters of one-dimensional trimerized magnetic compounds with strong intradimer and weak monomer-dimer couplings. We found the refined values for the coupling constants of Cu$_3$(P$_2$O$_6$OH)$_2$ by matching the theoretical results with the available experimental data for the magnetization and magnetic susceptibility in a wide range of temperatures and magnetic fields.
It is argued that the Strong Free Will Theorem (Conway-Kochen) does not prove nonlocal determinism wrong. This is done by the before-before (Suarez-Scarani) experiment, which is used here to prove the following General Free Will Theorem: If humans have a certain amount of free will, there are other free beings outside space-time producing nonlocal effects in our world, which are both random and lawful.
In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between classical properties and connectedness for closure spaces. The main result is a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'
We present new observations of the cataclysmic variable V523 Lyr, a member of the open cluster NGC 6791. The Kepler Space telescope obtained photometric observations of this source and we examine the nearly 3 year long light curve. The observations show numerous small amplitude outbursts recurring on average every 33 days, intermittent quasi-periodic oscillations, and a significant fully coherent period of ~3.8 hr which we identify as the orbital period of the binary. Contemporaneous optical spectroscopy of V523 Lyr reveals a faint blue source with broad Balmer absorption lines containing narrow emission cores. H$\alpha$ is in emission above the continuum. The low amplitude of the photometric signal and no detected velocity motion suggest a low orbital inclination. We discuss the properties of V523 Lyr and show that it is a member of the growing group of anomalous Z Cam type CVs, systems which show stunted outbursts, light curve standstills, and occasional deep drops in brightness.
We analyze in detail the quantum phase transitions that arise in models based on the $u(2)$ algebraic description for bosonic systems with two types of scalar bosons. First we discuss the quantum phase transition that occurs in hamiltonians that admix the two dynamical symmetry chains $u(2)\supset u(1)$ and $u(2)\supset so(2)$ by diagonalizing the problem exactly in the $u(1)$ basis. Then we apply the coherent state formalism to determine the energy functional. Finally we show that a quantum phase transition of a different nature, but displaying similar characteristics, may arise also within a single chain just by including higher order terms in the hamiltonian.
Helioseismic inversions reveal a major discrepancy in sound speed between the Sun and the standard solar model just below the base of solar convection zone. We demonstrate that this discrepancy is caused by the inherent shortcomings of the local mixing-length theory adopted in the standard solar model. Using a self-consistent nonlocal convection theory, we construct an envelope model of the Sun for sound-speed inversion. Our solar model has a very smooth transition from the convective envelope to the radiative interior; and the convective energy flux changes sign crossing the boundaries of the convection zone. It shows evident improvement over the standard solar model, with a significant reduction in the discrepancy in sound speed between the Sun and local convection models.
We show that any covariant scattering amplitude of the $W_3$ string will contain, as part of its integrand, a factor that obeys the differential equations satisfied by an Ising model correlation function. This factor can thus be identified with such a correlation function, in agreement with a previous result of the authors. The $W_3$ string is also shown to contain an $N=2$ parafermion theory, and hence to contain in addition the non-linear infinite-dimensional $W$-algebra corresponding to this parafermion theory. The physical states form a representation of this algebra.
We discuss the holographic counterpart of a recent conjecture regarding R-symmetric RG-flows in four-dimensional supersymmetric field theories. In such theories, a quantity \tau_U can be defined at the fixed points which was conjectured in arXiv:1109.3279 to be larger in the UV than in the IR, \tau_U^{UV} > \tau_U^{IR}. We analyze this conjecture from a dual supergravity perspective: using some general properties of domain wall solutions dual to R-symmetric RG flows, we define a bulk quantity which interpolates between the correct \tau_U at the UV and IR fixed points, and study its monotonicity properties in a class of examples. We find a monotonic behavior for theories flowing to an interacting IR fixed point. For gapped theories, the monotonicity is still valid up to a finite value of the radial coordinate where the function vanishes, reflecting the gap scale of the field theory.
We develop a theory in which there are couplings amongst Dirac spinor, dilaton and non-Riemannian gravity and explore the nature of connection-induced dilaton couplings to gravity and Dirac spinor when the theory is reformulated in terms of the Levi-Civita connection. After presenting some exact solutions without spinors, we investigate the minimal spinor couplings to the model and in conclusion we can not find any nontrivial dilaton couplings to spinor.
We work out the complete descent via 4-isogeny for a family of rational elliptic curves with a rational point of order 4; such a family is of the form $y^2 + x y + a y = x^3 + a x^2$ where $\sqrt{-a} \in \mathbb Q^\times$. In the process we exhibit the 4-isogeny and the isogenous curve, explicitly present the principal homogeneous spaces, and discuss examples by computing the rank.
A correspondence between type IIB string theory with N D7-branes on R^{1,3} x C^1/Z_2 x T^2/Z_2 x T^2/Z_2 and pure N=1 SU(N) gauge theory in four dimensions is proposed and argued. First the supergravity background of unwrapped and flat D7-branes with running axion and dilaton on R^{1,7} x C^1/Z_2 is studied together with the corresponding N=1 SU(N) gauge theory in eight dimensions. The D7-branes are then wrapped over a 4-cycle on T^2/Z_2 x T^2/Z_2 which turns on all F_1, F_3, H_3, and F_5 fluxes of type IIB theory and induces torsion. The supergravity solutions are explicitly constructed with exact analytic expressions for all components of the metric and the fluxes. The background geometry of the four-dimensional gauge theory is compact and conformally Calabi-Yau. The internal space normal to the wrapped D7-branes at the infrared boundary is S^1 whose radius is set by the nonperturbative scale of the gauge theory and spacetime is R^{1,3} at the ultraviolet boundary. The gauge coupling of the four-dimensional gauge theory is related to the gauge coupling of the eight-dimensional gauge theory and the volume of the 4-cycle. The gravity theory reproduces the renormalization group flow and the pattern of chiral symmetry breaking of the gauge theory and leads to confinement. The curvature is small and nearly constant and the supergravity flow is smooth in the infrared region where the gauge theory is strongly coupled and a dual gravity description is useful. String loop corrections are small for large N. The scale of string tension in four dimensions is of the same order as the scale of Kaluza-Klein masses.
Let $\left( X,\left\Vert \cdot\right\Vert_{X}\right) $ and $\left( Y,\left\Vert \cdot\right\Vert_{Y}\right) $ be Banach spaces over $\mathbb{R},$ with $X$ uniformly convex and compactly embedded into $Y.$ The inverse iteration method is applied to solve the abstract eigenvalue problem $A(w)=\lambda\left\Vert w\right\Vert_{Y}^{p-q}B(w),$ where the maps $A:X\rightarrow X^{\star}$ and $B:Y\rightarrow Y^{\star}$ are homogeneous of degrees $p-1$ and $q-1,$ respectively.
We survey the properties of the log-correlated Gaussian field (LGF), which is a centered Gaussian random distribution (generalized function) $h$ on $\mathbb R^d$, defined up to a global additive constant. Its law is determined by the covariance formula $$\mathrm{Cov}\bigl[ (h, \phi_1), (h, \phi_2) \bigr] = \int_{\mathbb R^d \times \mathbb R^d} -\log|y-z| \phi_1(y) \phi_2(z)dydz$$ which holds for mean-zero test functions $\phi_1, \phi_2$. The LGF belongs to the larger family of fractional Gaussian fields obtained by applying fractional powers of the Laplacian to a white noise $W$ on $\mathbb R^d$. It takes the form $h = (-\Delta)^{-d/4} W$. By comparison, the Gaussian free field (GFF) takes the form $(-\Delta)^{-1/2} W$ in any dimension. The LGFs with $d \in \{2,1\}$ coincide with the 2D GFF and its restriction to a line. These objects arise in the study of conformal field theory and SLE, random surfaces, random matrices, Liouville quantum gravity, and (when $d=1$) finance. Higher dimensional LGFs appear in models of turbulence and early-universe cosmology. LGFs are closely related to cascade models and Gaussian branching random walks. We review LGF approximation schemes, restriction properties, Markov properties, conformal symmetries, and multiplicative chaos applications.
We review a manifestly supersymmetric off-shell formulation of a wide class of torsionful $(4,4)$ $2D$ sigma models and their massive deformations in the harmonic superspace with a double set of $SU(2)$ harmonic variables. Sigma models with both commuting and non-commuting left and right complex structures are treated.
We investigate the basic properties of voids from high resolution, cosmological N-body simulations of {\Lambda}-dominated cold dark matter ({\Lambda}CDM) models, in order to compare with the analytical model of Sheth and van de Weygaert (SvdW) for void statistics. For the subsample of five dark matter simulations in the {\Lambda}CDM cosmology with box sizes ranging from 1000 Mpc/h to 8 Mpc/h, we find that the standard void-in-cloud effect is too simplified to explain several properties of identified small voids in simulations. (i) The number density of voids is found to be larger than the prediction of the analytical model up to 2 orders of magnitude below 1 Mpc/h scales. The Press-Schechter model with the linear critical threshold of void {\delta}_v = -2.71, or a naive power law, is found to provide an excellent agreement with the void size function, suggesting that the void-in-cloud effect does not suppress as much voids as predicted by the SvdW model. (ii) We then measured the density and velocity profiles of small voids, and find that they are mostly partially collapsing underdensities, instead of being completely crushed in the standard void-in-cloud scenario. (iii) Finally, we measure the void distributions in four different tidal environments, and find that the void-in-void effect alone can explain the correlation between distribution and environments, whereas the void-in-cloud effect is only weakly influencing the abundance of voids, even in filaments and clusters.
2.5D time-dependent ideal magnetohydrodynamic (MHD) models in Cartesian coordinates were used in previous studies to seek MHD equilibria involving a magnetic flux rope embedded in a bipolar, partially open background field. As demonstrated by these studies, the equilibrium solutions of the system are separated into two branches: the flux rope sticks to the photosphere for solutions at the lower branch but is suspended in the corona for those at the upper branch. Moreover, a solution originally at the lower branch jumps to the upper, as the related control parameter increases and reaches a critical value, and the associated jump is here referred to as upward catastrophe. The present paper advances these studies in three aspects. First, the magnetic field is changed to be force-free. The system still experiences an upward catastrophe with an increase in each control parameter. Secondly, under the force-free approximation, there also exists a downward catastrophe, characterized by a jump of a solution from the upper branch to the lower. Both catastrophes are irreversible processes connecting the two branches of equilibrium solutions so as to form a cycle. Finally, the magnetic energy in the numerical domain is calculated. It is found that there exists a magnetic energy release for both catastrophes. The Amp\`{e}re's force, which vanishes everywhere for force-free fields, appears only during the catastrophes and does a positive work, which serves as a major mechanism for the energy release. The implications of the downward catastrophe and its relevance to solar activities are briefly discussed.
We review a bit our earlier novel string field theory\cite{self2,self8} stressing the interesting property, that it becomes expressed in terms of particle like objects called by us "objects" which in our formalism do not at all develop in time. So in this way there is in our picture, in spite of it being supposed to reproduce string theory with an arbitrary number strings present -- in this sense a string field theory -- in fact no time! This strange missing of time in the formalism gives rise to slight speculations about the philosophy of the concept of time. There is course then also no need for a Hamiltonian, but we construct or rather attempt to do so, a fake Hamiltonian or phantasy Hamiltonian,
We study the electronic structure of Bi(2)Se(3) employing high resolution photoemission spectroscopy and discover the dependence of the behavior of Dirac particles on surface terminations. The Dirac cone apex appears at different energies and exhibits contrasting shift on Bi and Se terminated surface with complex time dependence emerging from subtle adsorbed oxygen-surface atom interactions. These results uncover the surface states behavior of real systems possessing topologically ordered surface.
Atomically thin semiconducting transition-metal dichalcogenides provide novel insights into the physics of many-body effects mediated by Coulomb interactions. Here, we report on temperature-dependent ($T$ = 7-295 K) reflectance contrast and photoluminescence studies of three-particle complexes in n-doped WS$_2$ monolayers. In low-temperature reflectance contrast spectra we observe distinct resonances of the neutral exciton, negative trion and exciton bound to a donor (X, X$^-$ and X$^D$). For temperatures above 80 K, reflectance contrast signatures of the X$^D$ disappear, whereas the X$^-$ remains detectable up to 240 K, despite the fact that the X$^D$ signal is more red-shifted from the neutral exciton than that of the X$^-$. This experimental observation underlines that in WS$_2$ the dissociation energy of X$^-$ considerably exceeds (factor of 2.5) that of X$^D$. In the laser-power dependent photoluminescence experiments, performed at room temperature, we demonstrate the control of the intensity ratio and energy position of the X and X$^-$ lines, which allows us to evaluate the trion binding energy. Moreover, we demonstrate that the room-temperature PL is sensitive to the environmental gas (ambient, N$_2$, He).
The resistance due to the convergence from bulk to a constriction, for example, a nanopore, is a mainstay of transport phenomena. In classical electrical conduction, Maxwell, and later Hall for ionic conduction, predicted this access or convergence resistance to be independent of the bulk dimensions and inversely dependent on the pore radius, $a$, for a perfectly circular pore. More generally, though, this resistance is contextual, it depends on the presence of functional groups/charges and fluctuations, as well as the (effective) constriction geometry/dimensions. Addressing the context generically requires all-atom simulations, but this demands enormous resources due to the algebraically decaying nature of convergence. We develop a finite-size scaling analysis, reminiscent of the treatment of critical phenomena, that makes the convergence resistance accessible in such simulations. This analysis suggests that there is a "golden aspect ratio" for the simulation cell that yields the infinite system result with a finite system. We employ this approach to resolve the experimental and theoretical discrepancies in the radius-dependence of graphene nanopore resistance.
A physical description of the formation and propagation of the working surface inside the relativistic jet of the Blazar PKS 1510-089 are used to model its gamma-ray variability light curve using FERMI-LAT data from 2008 to 2012. The physical model is based on conservation laws of mass and momentum at the working surface as explained by Mendoza et al. (2009). The hydrodynamical description of the working surface is parametrised by the initial velocity and mass injection rate at the base of the jet. We show that periodic variations on the injected velocity profiles are able to account for the observed luminosity. With this, we are able to obtain mass ejection rates of the central engine which are injected at the base of the jet, and oscillation frequencies of the flow, amongst other physical parameters.
Let $\mathcal X_g$ be a genus $g\geq 2$ superelliptic curve, $F$ its field of moduli, and $K$ the minimal field of definition. In this short note we construct an equation of the curve $\mathcal X_g$ over its minimal field of definition $K$ when $\mathcal X_g$ has extra automorphisms. We make use of the dihedral invariants of superelliptic curves as defined by Shaska in [6] and results on the automorphism groups of superelliptic curves as in [10].
We present a new sample of purely near infra-red selected KVega<16.5 extremely red ((J-K)>2.5) quasar candidates at z~2 from 900 sq deg of data in the UKIDSS Large Area Survey (LAS). Five of these are spectroscopically confirmed to be heavily reddened Type 1 AGN with broad emission lines bringing our total sample of reddened quasars from the UKIDSS-LAS to 12 at z=1.4-2.7. At these redshifts, Ha (6563A) is in the K-band. However, the mean Ha equivalent width of the reddened quasars is only ten per cent larger than that of the optically selected population and cannot explain the extreme colours. Instead, dust extinction of Av~2-6 mags is required to reproduce the continuum colours of our sources. This is comparable to the dust extinctions seen in submillimetre galaxies at similar redshifts. We argue that the AGN are likely being observed in a relatively short-lived breakout phase when they are expelling gas and dust following a massive starburst, subsequently turning into UV-luminous quasars. Some of our quasars show direct evidence for strong outflows (v~800-1000 km/s) affecting the Ha line consistent with this scenario. We predict that a larger fraction of reddened quasar hosts are likely to be submillimetre bright compared to the UV-luminous quasar population. We use our sample to place new constraints on the fraction of obscured Type 1 AGN likely to be missed in optical surveys. Taken at face-value our findings suggest that the obscured fraction depends on quasar luminosity. The space density of obscured quasars is ~5x that inferred for UV-bright quasars from the SDSS luminosity function at Mi<-30 but seems to drop at lower luminosities even accounting for various sources of incompleteness in our sample (abridged).
A quantum scalar field in anti de Sitter space is considered in two coordinate systems: static and FRW-like ones. It is shown that quantum vacua corresponding to each of these coordinatizations are not unitary equivalent. A choice of a physical ground state between these vacua is discussed under different setups.
We give two contructions of sets of masks on cograssmannian permutations that can be used in Deodhar's formula for Kazhdan-Lusztig basis elements of the Iwahori-Hecke algebra. The constructions are respectively based on a formula of Lascoux-Schutzenberger and its geometric interpretation by Zelevinsky. The first construction relies on a basis of the Hecke algebra constructed from principal lower order ideals in Bruhat order and a translation of this basis into sets of masks. The second construction relies on an interpretation of masks as cells of the Bott-Samelson resolution. These constructions give distinct answers to a question of Deodhar.
We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped Rb87 atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence.
The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of two-photon processes that can be observed using a very faint, but quantum-correlated biphoton field. These are optical up-conversion and an external photoelectric effect. We estimate the correlation enhancement factor for the biphoton light compared to coherent light, report and discuss the preliminary experimental results.