ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\{f_t\}$ be a family of complex polynomial functions with line singularities. We show that if $\{f_t\}$ has a uniform stable radius (for the corresponding Milnor fibrations), then the L\^e numbers of the functions $f_t$ are independent of $t$ for all small $t$. In the case of isolated singularities --- a case for which the only non-zero L\^e number coincides with the Milnor number --- a similar assertion was proved by M. Oka and D. O'Shea.   By combining our result with a theorem of J. Fern\'andez de Bobadilla --- which says that families of line singularities in $\mathbb{C}^n$, $n\geq 5$, with constant L\^e numbers are topologically trivial --- it follows that a family of line singularities in $\mathbb{C}^n$, $n\geq 5$, is topologically trivial if it has a uniform stable radius.   As an important example, we show that families of weighted homogeneous line singularities have a uniform stable radius if the nearby fibres $f_t^{-1}(\eta)$, $\eta\not=0$, are "uniformly" non-singular with respect to the deformation parameter $t$.
The behavior of hadronic matter at high baryon densities is studied within Ultrarelativistic Quantum Molecular Dynamics (URQMD). Baryonic stopping is observed for Au+Au collisions from SIS up to SPS energies. The excitation function of flow shows strong sensitivities to the underlying equation of state (EOS), allowing for systematic studies of the EOS. Effects of a density dependent pole of the $\rho$-meson propagator on dilepton spectra are studied for different systems and centralities at CERN energies.
The Pitman sampling formula has been intensively studied as a distribution of random partitions. One of the objects of interest is the length $K (= K_{n,\theta,\alpha})$ of a random partition that follows the Pitman sampling formula, where $n\in\mathbb{N}$, $\alpha\in(0,\infty)$ and $\theta > -\alpha$ are parameters. This paper presents asymptotic evaluations of its $r$-th moment $\mathsf{E}[K^r]$ ($r=1,2,\ldots$) under two asymptotic regimes. In particular, the goals of this study are to provide a finer approximate evaluation of $\mathsf{E}[K^r]$ as $n\to\infty$ than has previously been developed and to provide an approximate evaluation of $\mathsf{E}[K^r]$ as the parameters $n$ and $\theta$ simultaneously tend to infinity with $\theta/n \to 0$. The results presented in this paper will provide a more accurate understanding of the asymptotic behavior of $K$.
The thermovoltage of a chaotic quantum dot is measured using a current heating technique. The fluctuations in the thermopower as a function of magnetic field and dot shape display a non-Gaussian distribution, in agreement with simulations using Random Matrix Theory. We observe no contributions from weak localization or short trajectories in the thermopower.
We construct a vertex operator which describes an emission of the ground-state tachyon of the closed string out of the noncommutative open string. Such a vertex operator is shown to exist only when the momentum of the closed-string tachyon is subject to some constraints coming from the background $B$ field. The vertex operator has a multiplicative coupling constant $g(\sigma )$ which depends on $\sigma $ as $g(\sigma)=\sin^2 \sigma $ in $0 \le \sigma \le \pi $. This behavior is the same as in the ordinary B=0 case.
We present low- and high-resolution Spitzer/IRS spectra, supplemented by IRAC and MIPS measurements, of 22 blue compact dwarf (BCD) galaxies. The BCD sample spans a wide range in oxygen abundance [12+Log(O/H) between 7.4 and 8.3], and hardness of the interstellar radiation field (ISRF). The IRS spectra provide us with a rich set of diagnostics to probe the physics of star and dust formation in very low-metallicity environments. We find that metal-poor BCDs have harder ionizing radiation than metal-rich galaxies: [OIV] emission is roughly 4 times as common as [FeII] emission. They also have a more intense ISRF, as indicated by the 71 to 160micron luminosity ratio. Two-thirds of the sample (15 BCDs) show PAH features, although the fraction of PAH emission normalized to the total infrared (IR) luminosity is considerably smaller in metal-poor BCDs (~0.5%) than in metal-rich star-forming galaxies (~10%). We find several lines of evidence for a deficit of small PAH carriers at low metallicity, and attribute this to destruction by a hard, intense ISRF, only indirectly linked to metal abundance. Our IRS spectra reveal a variety of H2 rotational lines, and more than a third of the objects in our sample (8 BCDs) have >=3sigma detections in one or more of the four lowest-order transitions. The warm gas masses in the BCDs range from 10^3 to 10^8 Msun, and can be comparable to the neutral hydrogen gas mass; relative to their total IR luminosities, some BCDs contain more H2 than SINGS galaxies.
We offer a clear physical explanation for the emergence of the quantum operator formalism, by revisiting the role of the vacuum field in quantum mechanics. The vacuum or random zero-point radiation field has been shown previously, using the tools of stochastic electrodynamics, to be central in allowing a particle subject to a conservative binding force to reach a stationary state of motion. Here we focus on the stationary states, and consider the role of the vacuum as a driving force. We observe that the particle responds resonantly to certain field modes. A proper Hamiltonian analysis of this response allows us to unequivocally trace the origin of the basic quantum commutator, by establishing a one-to-one correspondence between the response coefficients of x and p and the respective matrix elements. The (random) driving field variables disappear thus from the description, but their Hamiltonian properties become embodied in the operator formalism. The Heisenberg equations establish the dynamical relationship between the response functions.
Using an algebraic formulation, we explore two well-known degeneracies involving the mass-squared differences for three-neutrino oscillations assuming CP symmetry is conserved. For vacuum oscillation, we derive the expression for the mixing angles that permit invariance under the interchange of two mass-squared differences. This symmetry is most easily expressed in terms of an ascending mass order. This can be used to reduce the parameter space by one half in the absence of the MSW effect. For oscillations in matter, we derive within our formalism the known approximate degeneracy between the standard and inverted mass hierarchies in the limit of vanishing $\theta_{13}$. This is done with a mass ordering that permits the map $\Delta_{31} \mapsto -\Delta_{31}$. Our techniques allow us to translate mixing angles in this mass order convention into their values for the ascending order convention. Using this dictionary, we demonstrate that the vacuum symmetry and the approximate symmetry invoked for oscillations in matter are distinctly different.
We compute explicitly the Schr\"odinger picture space of states of SU(2) Chern-Simons theory on $T^2\times R$ in the presence of temporal Wilson lines. Relation with Friedan-Shenker bundle of conformal field theory and the existence of a projective flat connection on this bundle is discussed. Talk given by the first author at the XIX International Colloquium on Group Theoretical Methods in Physics, Salamanca (Spain), June 29-July 4, 1992
An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed-matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wavefunction has remained beyond experimental reach. Here, we directly image the excitonic wavefunction in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer WSe2. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction-band states of the electron.
In 1998, Bou\'e and Dupuis proved a variational representation for exponentials of bounded Wiener functionals. Since their proof involves arguments related to the weak convergence of probability measures, the boundedness of functionals seems inevitable. In this paper, we extend the representation to unbounded functionals under a mild assumption on their integrability. As an immediate application of the extension, we prove an analogue of Pr\'ekopa's theorem for Wiener functionals, which is then applied to formulate the Brascamp-Lieb inequality in the framework of Wiener spaces.
We examine the conjecture that entropy production in subsystems of a given system can be used as a dynamical criterion for quantum chaos in the latter. Numerical results are presented for finite dimensional spin systems as also for the quantum baker's map. Of especial importance is the power spectrum of the entropy production which gets progressively more and more broad-banded as the degree of correlation in the Hamiltonian matrix is made to decrease.
We study the boundary behaviour of the of (E) $-\Gd u-\myfrac{\xk }{d^2(x)}u+g(u)=0$, where $0<\xk <\frac{1}{4}$ and $g$ is a continuous nonndecreasing function in a bounded convex domain of $\BBR^N$. We first construct the Martin kernel associated to the the linear operator $\CL_{\xk }=-\Gd-\frac{\xk }{d^2(x)}$ and give a general condition for solving equation (E) with any Radon measure $\gm$ for boundary data. When $g(u)=|u|^{q-1}u$ we show the existence of a critical exponent $q_c=q_c(N,\xk )>1$: when $0<q<q_c$ any measure is eligible for solving (E) with $\gm$ for boundary data; if $q\geq q_c$, a necessary and sufficient condition is expressed in terms of the absolute continuity of $\gm$with respect to some Besov capacity. The same capacity characterizes the removable compact boundary sets. At end any positive solution (F) $-\Gd u-\frac{\xk }{d^2(x)}u+|u|^{q-1}u=0$ with $q>1$ admits a boundary trace which is a positive outer regular Borel measure. When $1<q<q_c$ we prove that to any positive outer regular Borel measure we can associate a positive solutions of ($F$) with this boundary trace.
We suggest a new spin orientation mechanism for localized electrons: $dynamic~electron~spin~polarization~provided~by~nuclear~spin~fluctuations$. The angular momentum for the electrons is gained from the nuclear spin system via the hyperfine interaction in a weak magnetic field. For this the sample is illuminated by an unpolarized light, which directly polarizes neither the electrons nor the nuclei. We predict, that for the electrons bound in localized excitons 100% spin polarization can be reached in longitudinal magnetic fields of a few millitesla. The proof of principle experiment is performed on momentum-indirect excitons in (In,Al)As/AlAs quantum dots, where in a magnetic field of 17 mT the electron spin polarization of 30% is measured.
In a previous paper we have constructed a family of processes, starting from a set of independent standard Poisson processes, that has realizations that converge almost surely to the Brownian sheet, uniformly in the unit square. Now, a rate of convergence from these processes to Brownian sheet is given.
Quantum coherent coupling between a zone-center phonon and two acoustic phonons was observed in two GaAs/AlAs superlattices (8 nm/8 nm and 5.4 nm/5.4 nm) at ambient temperature. Using degenerate coherent phonon spectroscopy, a multi-cycle oscillation feature appears in the time-resolved phonon amplitudes of both samples, as a result of the coherent energy exchange between a driving phonon mode near first Brillouin zone center and two target acoustic phonon modes. This feature resembles the photon resonant parametric down/up-conversion processes, as well as the reversible coherent energy exchange between the optical field and a mechanical oscillator, suggesting quantum coherent coupling between the driving and target phonon modes. In the 8 nm/8 nm superlattice, the coupling strength increases nonlinearly at high pump fluences, which may eventually reach an extreme state where all three phonon modes share the same coherent state, as predicted by Orbach in the 1960s.
Within the framework of hierarchical clustering we show that a simple Press-Schechter-like approximation, based on spherical dynamics, provides a good estimate of the evolution of the density field in the quasi-linear regime up to $\Sigma \sim 1$. Moreover, it allows one to recover the exact series of the cumulants of the probability distribution of the density contrast in the limit $\Sigma \to 0$ which sheds some light on the rigorous result and on ``filtering''. We also obtain similar results for the divergence of the velocity field.   Next, we extend this prescription to the highly non-linear regime, using a stable-clustering approximation. Then we recover a specific scaling of the counts-in-cells which is indeed seen in numerical simulations, over a well-defined range. To this order we also introduce an explicit treatment of the behaviour of underdensities, which takes care of the normalization and is linked to the low-density bubbles and the walls one can see in numerical simulations. We compare this to a 1-dimensional adhesion model, and we present the consequences of our prescription for the power-law tail and the cutoff of the density distribution.
Exchange coupling between magnetic grains is essential for maintaining the stability of stored information in magnetic recording media. Using an atomistic spin model, we have investigated the coupling between neighbouring magnetic grains where magnetic impurity atoms have migrated into the non-magnetic grain boundary. We find that when the impurity density is low a biquadratic term in addition to the bilinear term is required to properly describe the inter-granular exchange coupling. The temperature dependence both terms is found to follow a power law behaviour with the biquadratic exchange constant decaying faster than the bilinear. For increasing grain boundary thickness the inter-granular exchange is lower and decays faster with temperature. Further simulations of a grain at a bit boundary show an unexpected energy minimum for in-plane magnetisation which can only be reproduced using a biquadratic exchange term.
We critically review the assumption that no new physics is acting in tree-level   $B$-meson decays and study the consequences for the ultimate precision in the direct determination of the CKM angle $\gamma$. In our exploratory study we find that sizable universal new physics contributions, $\Delta C_{1,2}$, to the tree-level Wilson coefficients $C_{1,2}$ of the effective Hamiltonian describing weak decays of the $b$ quark are currently not excluded by experimental data. In particular we find that Im $\Delta C_1 $ and Im $\Delta C_2 $ can easily be of order $\pm 10%$ without violating any constraints from data. Such a size of new physics effects in $C_1$ and $C_2$ corresponds to an intrinsic uncertainty in the CKM angle $\gamma$ of the order of $|\delta \gamma| \approx 4^\circ$, which is slightly below the current experimental precision. The accuracy in the determination of $\gamma$ can be improved by putting stronger constraints on the tree-level Wilson coefficients, in particular $C_1$. To this end we suggest a more refined theoretical study as well as a more precise measurements of the observables that currently provide the strongest bounds on hypothetical new weak phases in $C_1$ and $C_2$. We note that the semi-leptonic CP asymmetries seem to have the best prospect for improving the bound on the weak phase in $C_1$.
The dynamics of M-site, N-particle Bose-Hubbard systems is described in quantum phase space constructed in terms of generalized SU(M) coherent states. These states have a special significance for these systems as they describe fully condensed states. Based on the differential algebra developed by Gilmore, we derive an explicit evolution equation for the (generalized) Husimi-(Q)- and Glauber-Sudarshan-(P)-distributions. Most remarkably, these evolution equations turn out to be second order differential equations where the second order terms scale as 1/N with the particle number. For large N the evolution reduces to a (classical) Liouvillian dynamics. The phase space approach thus provides a distinguished instrument to explore the mean-field many-particle crossover. In addition, the thermodynamic Bloch equation is analyzed using similar techniques.
The neutral kaon meson mixing plays an important role in test of the Standard Model (SM) and new physics beyond it. Scale invariant unparticle physics induces a flavor changing neutral current (FCNC) transition of $K^0-\bar K^0$ oscillation at the tree level. In this study, we investigate the scale invariant unparticle physics effects on the $K^0-\bar K^0$ mixing. Based on the current experimental data, we give constraints of $K^0-\bar K^0$ mixing on the unparticle parameters.
What is the simplest Hamiltonian which can implement quantum computation without requiring any control operations during the computation process? In a previous paper we have constructed a 10-local finite-range interaction among qubits on a 2D lattice having this property. Here we show that pair-interactions among qutrits on a 2D lattice are sufficient, too, and can also implement an ergodic computer where the result can be read out from the time average state after some post-selection with high success probability.   Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle located at a specific lattice site, the third state is its absence. Usual hopping terms together with an attractive force among adjacent particles induce a coupled quantum walk where the particle spins are subjected to spatially inhomogeneous interactions implementing holonomic quantum computing. The holonomic method ensures that the implemented circuit does not depend on the time needed for the walk.   Even though the implementation of the required type of spin-spin interactions is currently unclear, the model shows that quite simple Hamiltonians are powerful enough to allow for universal quantum computing in a closed physical system.
In this paper, we bring together the five-dimensional Saez-Ballester~(SB) scalar-tensor theory [1] and the induced-matter-theory~(IMT) setting [2], to obtain a modified SB theory (MSBT) in four dimensions. Specifically, by using an intrinsic dimensional reduction procedure into the SB field equations in five-dimensions, a MSBT is obtained onto a hypersurface orthogonal to the extra dimension. This four-dimensional MSBT is shown to bear distinctive new features in contrast to the usual corresponding SB theory as well as to IMT and the Modified Brans-Dicke Theory (MBDT)~\cite{RFM14}. It should be emphasized that the herein appealing solutions can emerge solely from the geometrical reductional process, from presence also of extra dimension(s) and not from any ad-hoc matter either in the bulk or on the hypersurface.   Subsequently, we apply the herein MSBT to cosmology and consider an extended spatially flat FLRW geometry in a five-dimensional vacuum space-time. After obtaining the exact solutions in the bulk, we proceed to construct, by means of the MSBT setting, the corresponding dynamic, on the four-dimensional hypersurface. More precisely, we obtain the (SB) components of the induced matter, including the induced scalar potential terms. We retrieve two different classes of solutions. Concerning the first class, we show that the MSBT yields a barotropic equation of state for the induced perfect fluid. We then investigate vacuum, dust, radiation, stiff fluid and false vacuum cosmologies for this scenario and contrast the results with those obtained in the standard SB theory, IMT and BD theory. Regarding the second class solutions, we show that the scale factor behaves similar to a de Sitter (DeS) model. However, in our MSBT setting, this behavior is assisted by non-vanishing induced matter instead, without any a priori cosmological constant.
We study the stability of the cnoidal, dnoidal and snoidal elliptic functions as spatially-periodic standing wave solutions of the 1D cubic nonlinear Schr{\"o}dinger equations. First, we give global variational characterizations of each of these periodic waves, which in particular provide alternate proofs of their orbital stability with respect to same-period perturbations, restricted to certain subspaces. Second, we prove the spectral stability of the cnoidal waves against same-period perturbations (in a certain parameter range), and provide an alternate proof of this (known) fact for the snoidal waves, which does not rely on complete integrability. Third, we give a rigorous version of a formal asymptotic calculation of Rowlands to establish the instability of a class of real-valued periodic waves in 1D, which includes the cnoidal waves of the 1D cubic focusing nonlinear Schr{\"o}dinger equation, against perturbations with period a large multiple of their fundamental period. Finally, we develop a numerical method to compute the minimizers of the energy with fixed mass and momentum constraints. Numerical experiments support and complete our analytical results.
Model-independent search for the Abelian Z' gauge boson in the Drell-Yan process at the LHC at s^{1/2}= 7 TeV and 8 TeV is fulfilled. Estimations of the Z' axial-vector coupling a_f^2 to the standard model fermions, the couplings of the axial-vector to lepton vector currents a_f v_l and the couplings of the axial-vector to quark vector currents a_f v_q are derived within data on the forward-backward asymmetry presented by the CMS Collaboration. The analysis takes into consideration the behaviour of the differential cross-section which exhibits itself if the derived already special relations between the couplings proper to the renormalizable theories are accounted for. In particular, they hold in all the models of Abelian Z' usually considered in the model-dependent analysis of the LHC data. The coupling values are estimated at ~ 92 % CL by means of the maximum likelihood function. They weakly depend on the Z' mass in the investigated interval 1.2 TeV < m_Z' < 5 TeV. Taking into account the dependence of Z-Z' mixing angle theta_0 on m_Z' and the LEP constraints |theta_0|~ 10^{-3}-10^{-4}, the optimistic limits on m_{Z'} are established as 3 < m_Z' < 7-8 TeV. Comparison with the results of other authors is given.
We consider a model for a polymer chain interacting with a sequence of equispaced flat interfaces through a pinning potential. The intensity $\delta \in \mathbb {R}$ of the pinning interaction is constant, while the interface spacing $T=T_N$ is allowed to vary with the size $N$ of the polymer. Our main result is the explicit determination of the scaling behavior of the model in the large $N$ limit, as a function of $(T_N)_N$ and for fixed $\delta >0$. In particular, we show that a transition occurs at $T_N=O(\log N)$. Our approach is based on renewal theory.
We prove that the coarse moduli space of curves of genus 6 is birational to an arithmetic quotient of a bounded symmetric domain of type IV by giving a period map to the moduli space of some lattice-polarized K3 surfaces.
Several first-principles calculations of positron-annihilation characteristics in solids have added gradient corrections to the local-density approximation within the theory by Arponen and Pajanne [Ann. Phys. (N.Y.) 121, 343 (1979)] since this theory systematically overestimates the annihilation rates. As a further remedy we propose to use gradient corrections for other local density approximation schemes based on perturbed hypernetted-chain and on Quantum Monte Carlo results. Our calculations for various metals and semiconductors show that the proposed schemes generally improve the positron lifetimes when they are confronted with experiment. We also compare the resulting positron affinities in solids with data from slow-positron measurements.