ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is that only master equations for the phase-space distributions akin to Fokker-Planck equations for the evolution of classical phase-space distributions in configuration space are involved so that operators are unnecessary. The explicit solution of these equations can be expanded for an arbitrary spin Hamiltonian in a finite series of spherical harmonics like in the classical case. The expansion coefficients (statistical moments or averages of the spherical harmonics which are obviously by virtue of the Wigner-Stratonovich map the averages of the polarization operators) may be determined from differential-recurrence relations in a manner similar to the classical case. Furthermore, the phase space representation via the Weyl symbols of the relevant spin operators suggests how powerful computation techniques developed for Fokker-Planck equations (matrix continued fractions, mean first passage time, etc.) may be transparently extended to the quantum domain.
A method for direct sampling of the exponential moments of canonical phase from the data recorded in balanced homodyne detection is presented. Analytical expressions for the sampling functions are shown which are valid for arbitrary states. A numerical simulation illustrates the applicability of the method and compares it with the direct measurement of phase by means of double homodyning.
The results of experimental study of interference induced magnetoconductivity in narrow HgTe quantum wells of hole-type conductivity with a normal energy spectrum are presented. Interpretation of the data is performed with taking into account the strong spin-orbit splitting of the energy spectrum of the two-dimensional hole subband. It is shown that the phase relaxation time found from the analysis of the shape of magnetoconductivity curves for the relatively low conductivity when the Fermi level lies in the monotonic part of the energy spectrum of the valence band behaves itself analogously to that observed in narrow HgTe quantum wells of electron-type conductivity. It increases in magnitude with the increasing conductivity and decreasing temperature following the $1/T$ law. Such a behavior corresponds to the inelasticity of electron-electron interaction as the main mechanism of the phase relaxation and agrees well with the theoretical predictions. For the higher conductivity, despite the fact that the dephasing time remains inversely proportional to the temperature, it strongly decreases with the increasing conductivity. It is presumed that a nonmonotonic character of the hole energy spectrum could be the reason for such a peculiarity. An additional channel of the inelastic interaction between the carriers in the main and secondary maxima occurs when the Fermi level arrives the secondary maxima in the depth of the valence.
Perpendicularly magnetized nanowires exhibit distinct domain wall types depending on the geometry. Wide wires contain Bloch walls, narrow wires N\'eel walls. Here, the transition region is investigated by direct imaging of the wall structure using high-resolution spin-polarized scanning electron microscopy. An achiral intermediate wall type is discovered that is unpredicted by established theoretical models. With the help of micromagnetic simulations, the formation of this novel wall type is explained.
It has been shown by Shchekinov & Vasiliev2006 (SV06) that HD molecules can be an important cooling agent in high redshift z >10 haloes if they undergo mergers under specific conditions so suitable shocks are created. Here we build upon Prieto et al. (2012) who studied in detail the merger-generated shocks, and show that the conditions for HD cooling can be studied by combining these results with a suite of dark-matter only simulations. We have performed a number of dark matter only simulations from cosmological initial conditions inside boxes with sizes from 1 to 4 Mpc. We look for haloes with at least two progenitors of which at least one has mass M > M_cr (z), where M_cr (z) is the SV06 critical mass for HD over-cooling. We find that the fraction of over-cooled haloes with mass between M_cr (z) and 10^{0.2} M_cr (z), roughly below the atomic cooling limit, can be as high as ~ 0.6 at z ~ 10 depending on the merger mass ratio. This fraction decreases at higher redshift reaching a value ~0.2 at z ~ 15. For higher masses, i.e. above 10^{0.2} M_cr (z) up to 10^{0.6} M_cr (z), above the atomic cooling limit, this fraction rises to values ~ 0.8 until z ~ 12.5. As a consequence, a non negligible fraction of high redshift z > 10 mini-haloes can drop their gas temperature to the Cosmic Microwave Background temperature limit allowing the formation of low mass stars in primordial environments.
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.
Critical wetting is an elusive phenomenon for solid-fluid interfaces. Using interfacial models we show that the diverging length scales, which characterize complete wetting at an apex, precisely mimic critical wetting with the apex angle behaving as the contact angle. Transfer matrix, renormalization group (RG) and mean field analysis (MF) shows this covariance is obeyed in 2D, 3D and for long and short ranged forces. This connection should be experimentally accesible and provides a means of checking theoretical predictions for critical wetting.
We define a Mendelsohn triple system (MTS) with self-distributive quasigroup multiplication and order coprime with $3$ to be distributive, non-ramified (DNR). We classify, up to isomorphism, all DNR MTS and enumerate isomorphism classes (extending the work of Donovan, Griggs, McCourt, Opr\v{s}al, and Stanovsk\'{y}). The classification is accomplished via the representation theory of the Eisenstein integers, $\mathbb{Z}[\zeta]=\mathbb{Z}[X]/(X^2-X+1)$. Containing the class of DNR MTS is that of MTS with an entropic (linear over an abelian group) quasigroup operation. Partial results on the classification of entropic MTS with order divisible by $3$ are given, and a complete classification is conjectured. We also prove that for any entropic MTS, the qualities of being non-ramified, pure, and self-orthogonal are equivalent. We introduce the varieties $\mathbf{RE}$ and $\mathbf{LE}$ of (resp. right and left) Eisenstein quasigroups, whose respective linear representation theories correspond to the alternative presentation $\mathbb{Z}[X]/(X^2+X+1)$ of the Eisenstein integers.
We have investigated the effects of a non-thermal electron population on the ionization and recombination rates. The considered electron distribution is defined as a Maxwellian function below a break energy E_b and as a power-law function of index alpha above this energy. We have calculated the collisional (direct and excitation autoionization) ionization coefficient rates as well as the (radiative and dielectronic) recombination rates. Practical methods are given to calculate these rates in order to be easily included in a computer code. The ionization rates are very sensitive to the non-thermal electron population and can be increased by several orders of magnitude depending on the temperature and parameters of the power-law function (E_b and alpha). The non-thermal electrons have a much weaker effect on the (radiative and dielectronic) recombination rates. We have determined the mean electric charge of elements C, N, O, Ne, Mg, Si, S, Ar, Ca, Fe and Ni for different values of the break energy and power-law index. The ionization balance is affected significantly, whereas the effect is smaller in ionizing plasmas.
In this paper we describe the general theory of constructing toroidal compactifications of locally symmetric spaces and using these to compute dimension formulas for spaces of modular forms. We focus explicitly on the case of the orthogonal locally symmetric spaces arising from quadratic forms of signature $(2,n)$, giving explicit details of the constructions, structures and results in these cases. This article does not give explicit cone decompositions, compute explicit intersection pairings, or count cusps and thus does not give any complete formulas for the dimensions.   This article is still `in preparation'.
For the two-dimensional electron system in silicon MOSFET's, the scaled magnetoconductivity has been shown to exhibit critical behavior at finite density $n_0$. Analysis of these magnetotransport experiments yields a product $g^*m^*$ that diverges at this density (here $g^*$ is the interaction-enhanced Land\'e $g$-factor and $m^*$ is the effective mass). This claim has been disputed based on direct determinations of the $g^*m^*$ obtained from Shubnikov-de Haas measurements. We briefly review these experiments, and possible sources of the discrepancies.
In this paper we complete the proof began by A. Polishchuk and E. Zaslow (math.AG/9801119) of a weak version of Kontsevich's homological mirror symmetry conjecture for elliptic curves. The main difference to the work of Polishchuk and Zaslow is that we consider morphisms between any pair of objects, not only in the transversal case. This enables us to show the conjectured equivalence of categories.
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single rod introduced in [6] and on the extension of this technique to a multi-structure. We characterize the asymptotic behavior of the infimum of the total elastic energy as the minimum of a limit functional for an energy of order $\delta^\beta$ ($2<\beta\le 4$).
After a period of inflationary expansion, the Universe reheated and reached full thermal equilibrium at the reheating temperature. In this talk, based on the paper, arXiv:0710.3349, we point out that, in the context of effective low-energy supersymmetric models, LHC measurements may allow one to determine reheating temperature as a function of the mass of the dark matter particle assumed to be either an axino or a gravitino. An upper bound on their mass and on the reheating temperature may also be derived.
Environment is one of the key external drivers of the galaxies, while active galactic nucleus (AGN) is one of the key internal drivers. Both of them play fundamental roles in regulating the formation and evolution of galaxies. We explore the interrelationship between environment and AGN in SDSS. At a given stellar mass, the specific star formation rate distribution of the AGN host galaxies remains unchanged with over-density, with the peak of the distribution around the Green Valley. We show that, at a given stellar mass, the AGN fraction that has been commonly used in previous studies (defined as the number of AGNs relative to all galaxies including passive and star forming ones) does decrease with increasing over-density for satellites. This is largely due to the fact that the fraction of passive galaxies strongly depends on environment. In order to investigate the intrinsic correlation between AGN and environment, especially under the assumption that AGN feedback is responsible for star formation quenching, the AGN fraction should be defined as the number of AGNs relative to the star-forming galaxies only. With the new definition, we find little dependence of AGN fraction on over-density, central/satellite, and group halo mass. There is only marginal evidence that AGN may prefer denser regions, which is possibly due to more frequent interaction of galaxies or higher merger rate in groups. Our results support the scenario that internal secular evolution is the predominant mechanism of triggering AGN activity, while external environment related processes only play a minor role.
We investigate the relationships between the parabolic Harnack inequality, heat kernel estimates, some geometric conditions, and some analytic conditions for random walks with long range jumps. Unlike the case of diffusion processes, the parabolic Harnack inequality does not, in general, imply the corresponding heat kernel estimates.
A novel Hamiltonian description of the dynamics of a spherically symmetric, light-like, self-gravitating shell is presented. It is obtained via the systematic reduction of the phase space with respect to the Gauss-Codazzi constraints, model and rare procedure in the Canonical Gravity. The Hamiltonian of the system (numerically equal to the value of the ADM mass) is explicitly calculated in terms of the gauge-invariant "true degrees of freedom", i.e. as a function on the reduced phase space. A geometric interpretation of the momentum canonically conjugate to the shell's radius is given. Models of matter compatible with the shell dynamics are found. A transformation between the different time parameterizations of the shell is calculated. The presented model may become a new toy model of quantum gravity.
We investigate anomalies on heterotic orbifolds and their blowups. We give a simple example of an orbifold blowup which contains anomalous U(1) symmetries that are canceled by axions which couple non-universally to the different gauge groups, thus clarifying some confusion which recently arose in the literature concerning anomaly universality. We argue that non-universal axionic couplings are the general case, and that the couplings are only universal in the case of orbifolds. We comment on the consequences of this non-universality for discrete R symmetries. We furthermore investigate the origin of discrete (R and non-R) symmetries on smooth Calabi-Yau manifolds.
We address the role of large scale magnetic stress in the angular momentum transport, as well as the formation of different kinds of magnetic barrier in geometrically thick, optically thin, vertically averaged 1.5-dimensional advective accretion flows around black holes. The externally generated magnetic fields are captured by the accretion process from the environment, say, companion stars or interstellar medium. This field becomes dynamically dominant near the event horizon of a black hole due to continuous advection of the magnetic flux. In such magnetically dominated accretion flows, the accreting matter either decelerates or faces magnetic barrier in vicinity of the black hole depending on the magnetic field geometry. We find that the accumulated strong poloidal fields along with certain toroidal field geometry help in the formation of magnetic barrier which may knock the matter to infinity. When matter is trying to go back to infinity after getting knocked out by the barrier, in some cases it is prevented being escaped due to cumulative action of strong magnetic tension and gravity, and hence another magnetic barrier. We suggest, this kind of flow may be responsible for the formation of episodic jets in which magnetic field can lock the matter in between these two barriers. We also find that for the toroidally dominated disc, the accreting matter rotates very fast and decelerates towards the central black hole.
The kinetics of irreversible adsorption of spherical particles onto a flat surface is theoretically studied. Previous models, in which hydrodynamic interactions were disregarded, predicted a power-law behavior $t^{-2/3}$ for the time dependence of the coverage of the surface near saturation. Experiments, however, are in agreement with a power-law behavior of the form $t^{-1/2}$. We outline that, when hydrodynamic interactions are considered, the assymptotic behavior is found to be compatible with the experimental results in a wide region near saturation.
We will show how both elliptic and radial flow generated during the first fm/c at RHIC can be expressed in a form which is quasi-independent of the state of matter and depends only on the initial energy density profile. Descriptions based on partons or classical fields, thermalized or highly anisotropic, all lead to the same collective velocity given a few easily satisfied conditions. This significantly narrows the uncertainty for initializing hydrodynamic prescriptions.
We present a flexible and efficient ultrafast time-resolved spontaneous Raman spectroscopy setup to study collective excitation and quasi-particle dynamics in quantum matter. The setup has a broad energy tuning range extending from the visible to near infrared spectral regions for both the pump excitation and Raman probe pulses. Additionally, the balance between energy and time-resolution can be controlled. A high light collecting efficiency is realized by high numerical aperture collection optics and a high-throughput flexible spectrometer. We demonstrate the functionality of the setup with a study of the zone-center longitudinal optical phonon and hole continuum dynamics in silicon, and discuss the role of the Raman tensor in time-resolved Raman scattering. In addition, we show evidence for unequal phonon softening rates at different high symmetry points in the Brillouin zone of silicon by means of detecting pump-induced changes in the two-phonon overtone spectrum. Demagnetization dynamics in the helimagnet Cu2OSeO3 is studied by observing softening and broadening of a magnon after photo-excitation, underlining the unique power of measuring transient dynamics in the frequency domain, and the feasibility to study phase transitions in quantum matter.
Magnetoelectric properties of a molecular crystal formed by dysprosium triangular clusters are investigated. The effective spin-electric Hamiltonian is derived on the base of developed quantum mechanical model of the cluster spin structure. The magnetoelectric contribution to the free energy of the crystal is calculated. The analysis reveals several distinctive features of the magnetoelectric effect, which are not typical for conventional paramagnetic systems at low temperatures. The peculiarities are explained by the chirality of the dysprosium core of the molecules.
In the paper, we show that $\lambda(z_1) -\lambda(z_2)$, $\lambda(z_1)$ and $1-\lambda(z_1)$ are all Borcherds products in $X(2) \times X(2)$. We then use the big CM value formula of Bruinier, Kudla, and Yang to give explicit factorization formulas for the norms of $\lambda(\frac{d+\sqrt d}2)$, $1-\lambda(\frac{d+\sqrt d}2)$, and $\lambda(\frac{d_1+\sqrt{d_1}}2) -\lambda(\frac{d_2+\sqrt{d_2}}2)$, with the latter under the condition $(d_1, d_2)=1$. Finally, we use these results to show that $\lambda(\frac{d+\sqrt d}2)$ is always an algebraic integer and can be easily used to construct units in the ray class field of $\mathbb{Q}(\sqrt{d})$ of modulus $2$. In the process, we also give explicit formulas for a whole family of local Whittaker functions, which are of independent interest.
The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or "causal sets". The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity.   In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.
Maxwell's equations can be obtained in generalized coordinates by considering the electromagnetic field as an external agent. The work here presented shows how to obtain the electrodynamics for a charged particle in generalized coordinates eliminating the concept of external force. Based on Kaluza's formalism, the one here presented extends the 5x5 metric into a 6x6 space-time giving enough room to include magnetic monopoles in a very natural way.
We report the identification of the optical afterglow of GRB 980613 in R- and I-band images obtained between 16 and 48 hours after the gamma-ray burst. Early near-infrared (NIR) H and K' observations are also reported. The afterglow was optically faint (R ~ 23) at discovery but did not exhibit an unusually rapid decay (power-law decay slope alpha < 1.8 at 2 sigma). The optical/NIR spectral index (beta_RH < 1.1) was consistent with the optical-to-X-ray spectral index (beta_RX ~ 0.6), indicating a maximal reddening of the afterglow of ~0.45 mag in R. Hence the dimness of the optical afterglow was mainly due to the fairly flat spectral shape rather than internal reddening in the host galaxy. We also present late-time HST/STIS images of the field in which GRB 980613 occurred, obtained 799 days after the burst. These images show that GRB 980613 was located close to a very compact, blue V = 26.1 object inside a complex region consisting of star-forming knots and/or interacting galaxy fragments. Therefore, GRB 980613 constitutes a strong case for the association of cosmological gamma-ray bursts with star-forming regions.
Motivated by recent experiments, we study the interaction corrections to the damping of magnetooscillations in a two-dimensional electron gas (2DEG). We identify leading contributions to the interaction-induced damping which are induced by corrections to the effective mass and quantum scattering time. The damping factor is calculated for Coulomb and short-range interaction in the whole range of temperatures, from the ballistic to the diffusive regime. It is shown that the dominant effect is that of the renormalization of the effective electron mass due to the interplay of the interaction and impurity scattering. The results are relevant to the analysis of experiments on magnetooscillations (in particular, for extracting the value of the effective mass) and are expected to be useful for understanding the physics of a high-mobility 2DEG near the apparent metal-insulator transition.
From electrodeless time-resolved microwave conductivity measurements, the efficiency of charge carrier generation, their mobility, and decay kinetics on photo-excitation were studied in arrays of Si nanowires grown by the vapor-liquid-solid mechanism. A large enhancement in the magnitude of the photoconductance and charge carrier lifetime are found depending on the incorporation of impurities during the growth. They are explained by the internal electric field that builds up, due to a higher doped sidewalls, as revealed by detailed analysis of the nanowire morphology and chemical composition.