ShantanuT01/DACTYL-Pretraining huggingface dataset:
The Problem of Time occurs because the `time' of GR and of ordinary Quantum Theory are mutually incompatible notions. This is problematic in trying to replace these two branches of physics with a single framework in situations in which the conditions of both apply, e.g. in black holes or in the very early universe. Emphasis in this Review is on the Problem of Time being multi-faceted and on the nature of each of the eight principal facets. Namely, the Frozen Formalism Problem, Configurational Relationalism Problem (formerly Sandwich Problem), Foliation Dependence Problem, Constraint Closure Problem (formerly Functional Evolution Problem), Multiple Choice Problem, Global Problem of Time, Problem of Beables (alias Problem of Observables) and Spacetime Reconstruction/Replacement Problem. Strategizing in this Review is not just centred about the Frozen Formalism Problem facet, but rather about each of the eight facets. Particular emphasis is placed upon A) relationalism as an underpinning of the facets and as a selector of particular strategies (especially a modification of Barbour relationalism, though also with some consideration of Rovelli relationalism). B) Classifying approaches by the full ordering in which they embrace constrain, quantize, find time/history and find observables, rather than only by partial orderings such as "Dirac-quantize". C) Foliation (in)dependence and Spacetime Reconstruction for a wide range of physical theories, strategizing centred about the Problem of Beables, the Patching Approach to the Global Problem of Time, and the role of the question-types considered in physics. D) The Halliwell- and Gambini-Porto-Pullin-type combined Strategies in the context of semiclassical quantum cosmology.
A solid-on-solid growth model for dimer adsorption and desorption is introduced and studied numerically. The special property of the model is that dimers can only desorb at the edges of terraces. It is shown that the model exhibits a roughening transition from a smooth to a rough phase. In both phases the interface remains pinned to the bottom layer and does not propagate. Close to the transition certain critical properties are related to those of a unidirectionally coupled hierarchy of parity-conserving branching-annihilating random walks.
In this paper we find an upper bound for the probability that a $3$ dimensional simple random walk covers each point in a nearest neighbor path connecting 0 and the boundary of an $L_1$ ball of radius $N$. For $d\ge 4$, it has been shown in [5] that such probability decays exponentially with respect to $N$. For $d=3$, however, the same technique does not apply, and in this paper we obtain a slightly weaker upper bound: $\forall \varepsilon>0,\exists c_\varepsilon>0,$ $$P\left({\rm Trace}(\mathcal{P})\subseteq {\rm Trace}\big(\{X_n\}_{n=0}^\infty\big) \right)\le \exp\left(-c_\varepsilon N\log^{-(1+\varepsilon)}(N)\right).$$
In this work we present a review of the most popular depth-averaged models to simulate dry granular flows such as aerial avalanches. The classical Savage-Hutter model and recent ones using a $\mu(I)$-rheology law are studied. The objective is firstly to point out the advantages of each such models and secondly to understand how the hypothesis considered in the derivation process influence on the final system.
We derive a local, gauge invariant action for the SU(N) non-linear sigma-model in 2+1 dimensions. In this setting, the model is defined in terms of a self-interacting pseudo vector-field \theta_\mu, with values in the Lie algebra of the group SU(N). Thanks to a non-trivially realized gauge invariance, the model has the correct number of degrees of freedom: only one polarization of \theta_\mu, like in the case of the familiar Yang-Mills theory in 2+1 dimensions. Moreover, since \theta_\mu is a pseudo-vector, the physical content corresponds to one massless pseudo-scalar field in the Lie algebra of SU(N), as in the standard representation of the model. We show that the dynamics of the physical polarization corresponds to that of the SU(N) non-linear sigma model in the standard representation, and also construct the corresponding BRST invariant gauge-fixed action.
We study the optical conductivity in doped nickelates, and find the dramatic difference of the spectrum in the gap ($\omega$$\alt$4 eV) between one- (1D) and two-dimensional (2D) nickelates. The difference is shown to be caused by the dependence of hopping integral on dimensionality. The theoretical results explain consistently the experimental data in 1D and   2D nickelates, Y$_{2-x}$Ca$_x$BaNiO$_5$ and La$_{2-x}$Sr$_x$NiO$_4$, respectively. The relation between the spectrum in the X-ray aborption experiments and the optical conductivity in La$_{2-x}$Sr$_x$NiO$_4$ is discussed.
In 1962-63, M. Nagata showed that an abstract variety could be embedded into a complete variety. Later, P. Deligne translated Nagata's proof into the language of schemes, but did not publish his notes. This paper, which is to appear as an appendix in a forthcoming book, gives an elaboration of Deligne's notes. It also contains some complementary results on extending divisors and vector sheaves to suitable completions.
Theoretical analysis based on the Landau-Ginzburg-Devonshire (LGD) theory is used to show that the joint action of flexoelectric effect and rotostriction leads to a large spontaneous in-plane polarization (~ 1-5 muC/cm2) and pyroelectric coefficient (~10^-3 C/m2K) in the vicinity of surfaces of otherwise non-ferroelectric ferroelastics, such as SrTiO3, with static octahedral rotations. The origin of the improper polarization and pyroelectricity is an electric field we name flexo-roto field whose strength is proportional to the convolution of the flexoelectric and rotostriction tensors with octahedral tilts and their gradients. Flexo-roto field should exist at surfaces and interfaces in all structures with static octahedral rotations, and thus it can induce surface polar states and pyroelectricity in a large class of otherwise nonpolar materials.
We demonstrate, using character sum arguments, the existence of primitive polynomials of degree n over a finite field GF(q) with the coefficients for x^(n-1), x^(n-2), and x^(n-3) prescribed, so long as char(GF(q)) is at least 5 and n is at least 9. The cases n=7, 8 are also considered.
We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue prob- lem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy depen- dence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry breaking phase transition: as a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.
The algebraic approach to the construction of the reflexive polyhedra that yield Calabi-Yau spaces in three or more complex dimensions with K3 fibres reveals graphs that include and generalize the Dynkin diagrams associated with gauge symmetries. In this work we continue to study the structure of graphs obtained from $CY_3$ reflexive polyhedra. We show how some particularly defined integral matrices can be assigned to these diagrams. This family of matrices and its associated graphs may be obtained by relaxing the restrictions on the individual entries of the generalized Cartan matrices associated with the Dynkin diagrams that characterize Cartan-Lie and affine Kac-Moody algebras. These graphs keep however the affine structure, as it was in Kac-Moody Dynkin diagrams. We presented a possible root structure for some simple cases. We conjecture that these generalized graphs and associated link matrices may characterize generalizations of these algebras.
The spin-orbit (SO) interaction in condensed matter can be described in terms of a non-Abelian potential known in high-energy physics as a color field. I show that a magnetic component of this color field inevitably generates diamagnetic color currents which are just the equilibrium spin currents discussed in a condensed matter context. These dissipationless spin currents thus represent a universal property of systems with SO interaction. In semiconductors with linear SO coupling the spin currents are related to the effective non-Abelian field via Yang-Mills magnetostatics equation.
In this paper, we make a comprehensive study of the properties of a gapped Dirac semimetal model, which was originally proposed in the magnetoinfrared spectroscopy measurement of ZeTe$_5$, and includes both the linear and parabolic dispersions in all three directions. We find that, depending on the band inversion parameters, $\zeta'$ and $\zeta_z'$, the model can support three different phases: the single Dirac point (DP) phase, the double DPs phase and the Dirac ring phase. The three different phases can be distinguished by their low-energy features in the density of states (DOS) and optical conductivity. At high energy, both the DOS and optical conductivity exhibit power-law like behaviors, with the asymptotic exponents depending heavily on the signs of $\zeta'$ and $\zeta_z'$. Moreover, the thumb-of-rule formula between the DOS and optical conductivity is satisfied only when $(\zeta',\zeta_z')>0$. The implications of our results for experiments are discussed.
Micellization is the precipitation of lipids from aqueous solution into aggregates with a broad distribution of aggregation number. Three eras of micellization are characterized in a simple kinetic model of Becker-D\"oring type. The model asigns the same constant energy to the $(k-1)$ monomer-monomer bonds in a linear chain of $k$ particles. The number of monomers decreases sharply and many clusters of small size are produced during the first era. During the second era, nucleii are increasing steadily in size until their distribution becomes a self-similar solution of the diffusion equation. Lastly, when the average size of the nucleii becomes comparable to its equilibrium value, a simple mean-field Fokker-Planck equation describes the final era until the equilibrium distribution is reached.
This thesis contains three main parts, which are largely independent. In the first part we deal with the boundary bootstrap in supersymmetric factorized scattering theory. We give a description of supersymmetry in the case when the space is a half-line and present rules for the determination of the representations in which higher level boundary bound states transform, and for the determination of the supersymmetric one-particle reflection matrix factors for the higher level boundary bound states. These rules apply under the condition that the bulk particles transform in the kink or in the boson-fermion representation. Examples for the application of these rules to specific models are also given. In the second part we investigate the problem whether the TCSA spectrum can be approximated by the spectrum of the original Hamiltonian operator in which the coefficients of the terms are suitably changed. The investigation is done in the case of the critical Ising model on a strip with an external magnetic field on one of the boundaries. Another truncation method that preserves the solvability of the model is also considered. The results of perturbative and numerical calculations show that the above approximation is possible and that the qualitative behaviour of the truncated spectrum as a function of the coupling constant depends on the truncation method. In the third part we investigate the phase structure of the two- and three-frequency sine-Gordon models using the TCSA. In the case of the three-frequency model the tricritical point, several points of the critical line and a few points of the line of first order transition are found.
The Agassi model is a schematic two-level model that involves pairing and monopole-monopole interactions. It is, therefore, an extension of the well known Lipkin-Meshkov-Glick (LMG) model. In this paper we review the algebraic formulation of an extension of the Agassi model as well as its bosonic realization through the Schwinger representation. Moreover, a mean-field approximation for the model is presented and its phase diagram discussed. Finally, a $1/j$ analysis, with $j$ proportional to the degeneracy of each level, is worked out to obtain the thermodynamic limit of the ground state energy and some order parameters from the exact Hamiltonian diagonalization for finite$-j$.
Macroscopic polarization, both of intrinsic and piezoelectric nature, is unusually strong in III-V nitrides, and the built in electric fields in the layers of nitride-based nanostructures, stemming from polarization changes at heterointerfaces, have a major impact on the properties of single and multiple quantum wells, high mobility transistors, and thin films. The concepts involved in the theory and applications of polarization in nitrides have encountered some resistance in the field. Here we discuss critically ten ``propositions'' aimed at clarifying the main controversial issues.
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding probabilistic weights (probability density or respectively the wave function). Such a model ensures theoretical estimations for predicted errors specific to the mean values as well as to the fluctuations of both types of observables. The model stands out of ourdays prevalent opinion that measurement theories must be depicted in entirely different manners in the classical respectively quantum cases.
Neutron stars are believed to contain (neutron and proton) superfluids. I will give a summary of a macroscopic description of the interior of neutron stars, in a formulation which is general relativistic. I will also present recent results on the oscillations of neutron stars, with superfluidity explicitly taken into account, which leads in particular to the existence of a new class of modes.
Massive stars exhibit a variety of instabilities, many of which are poorly understood. We explore instabilities induced by centrifugal forces and angular momentum transport in massive rotating stars. First, we derive and numerically solve linearized oscillation equations for adiabatic radial modes in polytropic stellar models. In the presence of differential rotation, we show that centrifugal and Coriolis forces combined with viscous angular momentum transport can excite stellar pulsation modes, under both low- or high-viscosity conditions. In the low-viscosity limit, which is common in real stars, we demonstrate how to compute mode growth/damping rates via a work integral. Finally, we build realistic rotating $30\,M_\odot$ star models and show that overstable (growing) radial modes are predicted to exist for most of the star's life, in the absence of non-adiabatic effects. Peak growth rates are predicted to occur while the star is crossing the Hertzsprung-Russell gap, though non-adiabatic damping may dominate over viscous driving, depending on the effective viscosity produced by convective and/or magnetic torques. Viscous instability could be a new mechanism to drive massive star pulsations and is possibly related to instabilities of luminous blue variable stars.
Since the concepts for the implementation of data storage and logic gates used in conventional electronics cannot be simply downscaled to the level of single molecule devices, new architectural paradigms are needed, where quantum interference (QI) effects are likely to provide an useful starting point. In order to be able to use QI for design purposes in single molecule electronics, the relation between their occurrence and molecular structure has to be understood at such a level that simple guidelines for electrical engineering can be established. We made a big step towards this aim by developing a graphical scheme that allows for the prediction of the occurrence or absence of QI induced minima in the transmission function and the derivation of this method will form the center piece of this review article. In addition the possible usefulness of QI effects for thermoelectric devices is addressed, where the peak shape around a transmission minimum is of crucial importance and different rules for selecting suitable molecules have to be found.
The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk with two offsprings. It is shown that two-dimensional simulations confirm the field theoretical results with logarithmic corrections. In one dimension, however, if particles exhibit hard core interaction I confirm the very recent predictions of Kwon et al. [PRL {\bf 85}, 1682 (2000)] that there are two different universality classes depending on the spatial symmetry of the offspring production characterized by $\beta_S=0.5$ and $\beta_A=2$. Elaborate analysis of simulation data shows that the order parameter exponent $\beta$ does not depend on initial conditions or on diffusion rates of species but strong correction to scaling is observed. By systematic numerical simulations the critical point properties have been explored and initial condition dependence of the dynamical exponents $Z$ and $\alpha$ is shown. In the case of a random initial state the particle-density decay at the critical point follows the $t^{-1/4}$ law with logarithmic corrections.
We have built an effective Walecka-type hadronic Lagrangian in which the hadron masses and the density dependence of the coupling constants are deduced from the quark dynamics using a Nambu-Jona-Lasinio model. The parameters of this Nambu-Jona-Lasinio model have been determined using the meson properties in the vacuum but also in the medium through the omega meson mass in nuclei measured by the TAPS collaboration. Realistic properties of nuclear matter have been obtained.
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
The interplay of magnetism and topology opens up the possibility for exotic linear response effects, such as the anomalous Hall effect and the anomalous Nernst effect, which can be strongly enhanced by designing a strong Berry curvature in the electronic structure. It is even possible to utilize this to create a quantum anomalous Hall state at high temperatures by reducing the dimensionality. Magnetic Heusler compounds are a promising class of materials for this purpose because they grow in thin films, have a high Curie temperature, and their electronic structure hosts strong topological features. Here, we provide a comprehensive study of the intrinsic anomalous transport for magnetic cubic full Heusler compounds and we illustrate that several Heusler compounds outperform the best so far reported materials. The results reveal the importance of symmetries, especially mirror planes, in combination with magnetism for giant anomalous Hall and Nernst effects, which should be valid in general for linear responses (spin Hall effect, spin orbital torque, etc.) dominated by intrinsic contributions.
The combined use of chiral $SU(3)$ and heavy quark symmetries allows one to relate the hadronic form factors for the decay $\bar B\to \bar K\e^+\e^-$ to those for $\bar B\to\pi\e^-\bar\nu$. We investigate departures from the symmetry limit which arise from chiral symmetry breaking. The analysis uses chiral perturbation theory and the heavy quark limit to compute the relevant hadronic matrix elements. We estimate the size of $SU(3)$ corrections by computing, at one loop order, the leading nonanalytic dependence on the light quark masses. The calculation is trustworthy only in the portion of the Dalitz plot in which the momentum of the kaon or pion is small. We find the corrections to be~$\sim40\%$.
We consider the physical conditions of the neutral medium within, and in the environments of, galaxies. The basic physical and morphological properties of the neutral medium within galaxy disks are now quite well-constrained. Systematic variations in temperature and phase-balance (of cool versus warm neutral gas) are indicated as a function of both radius and z-height. Interestingly, the cool medium line-widths are observed to be dominated by turbulent energy injection within cells of 10 pc to 1 kpc size. Deep new observations reveal that 5-10% of the neutral medium is associated within an extended halo which rotates more slowly and experiences radial inflow. Much of this component is likely to be associated with a ``galactic fountain'' type of phenomenon. However, compelling evidence is also accumulating for the importance of tidal disruption of satellites as well as continuous accretion (of both diffuse and discrete components) in fueling galaxy halos and disks. Continued fueling is even observed on scales of 100's of kpc in galaxy environments, where the neutral component is likely to be merely a trace constituent of a highly ionized plasma.
It is proved in Chon{\'e} and Le Meur (2001) that the problem of minimizing a Dirichlet-like functional of the function $u\_h$ discretized with $P\_1$ Finite Elements, under the constraint that $u\_h$ be convex, cannot converge. Here, we first improve this result by proving that non-convergence is due to the mesh refinment lack of richness, remains local and is true even for any mesh. Then, we investigate the consistency of various natural discretizations ($P\_1$ and $P\_2$) of second order constraints (subharmonicity and convexity) without discussing the convergence. We also numerically illustrate convergence of a method proposed in the literature that is simpler than existing methods.
In a search for new white dwarfs in DR12 of the Sloan Digital Sky Survey, Kepler et al. (2016) found atmospheric parameters for thousands of objects with effective temperatures below 20,000 K and surface gravities between 5.5 < log(g) < 6.5. They classified these objects as cool subdwarfs -- sdA -- and speculated that many may be extremely low-mass (ELM) white dwarfs (helium-core white dwarfs with masses below 0.3 Msun). We present evidence -- using radial velocities, photometric colors, and reduced proper motions -- that the vast majority (>99%) of these objects are unlikely to be ELM white dwarfs. Their true identity remains an interesting question.
We report study of recovery dynamics, followed by in-situ resistivity measurement after 100 MeV oxygen ion irradiation, in cold rolled Fe at 300K. Scaling behavior with microstructural density and temperature of sample have been used to establish stress induced defects formed during irradiation as a new type of sink. The dynamics after irradiation has been shown to be due to migration of defects to two types of sinks i.e. stress induced defect as variable sinks and internal surfaces as fixed sinks. Experimental data obtained under various experimental conditions have been fitted to theoretical curves. Parameters thus obtained from fitting are employed to establish effect of electronic energy loss and temperature on recovery dynamics and stress associated with variable sinks.
We compare the momentum-space decimation procedure used to construct the low momentum nucleon-nucleon interaction V(low-k) with the configuration-space separation method of Moszkowski and Scott. Each procedure defines a separation of scales in the nuclear many-body problem, and the extent to which these two scales coincide is studied. By studying the effects of the separation method on the relative S-state Kallio-Kolltveit potential, it is found that close agreement with V(low-k) is obtained as the configuration-space cutoff is lowered to ~ 1.0 fm.