Nonlocal Stochastic Model for the Free Scalar Field Theory
NASA Astrophysics Data System (ADS)
Namsrai, Kh.
1981-05-01
The free scalar field is investigated within the framework of the Davidson stochastic model and of the hypothesis on space-time stochasticity. It is shown that the resulting Markov field obtained by averaging in this space-time is equivalent to a nonlocal Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter ν. Our result generalizes Guerra and Ruggiero's procedure of stochastic quantization of scalar fields. On the basis of the assumption about unobservability of ν in quantum field theory, the Efimov nonlocal theory is obtained from Euclidean Markov field with form factors of the class of entire analytical functions.
Contour-ordered Green's functions in stochastic field theory
NASA Astrophysics Data System (ADS)
Honkonen, J.
2013-06-01
We briefly review the functional formulation of the perturbation theory for various Green's functions in quantum field theory. In particular, we discuss the contour-ordered representation of Green's functions at a finite temperature. We show that the perturbation expansion of time-dependent Green's functions at a finite temperature can be constructed using the standard Wick rules in the functional form without introducing complex time and evolution backward in time. We discuss the factorization problem for the corresponding functional integral. We construct the Green's functions of the solution of stochastic differential equations in the Schwinger-Keldysh form with a functional-integral representation with explicitly intertwined physical and auxiliary fields.
Theory of weak scattering of stochastic electromagnetic fields from deterministic and random media
Tong Zhisong; Korotkova, Olga
2010-09-15
The theory of scattering of scalar stochastic fields from deterministic and random media is generalized to the electromagnetic domain under the first-order Born approximation. The analysis allows for determining the changes in spectrum, coherence, and polarization of electromagnetic fields produced on their propagation from the source to the scattering volume, interaction with the scatterer, and propagation from the scatterer to the far field. An example of scattering of a field produced by a {delta}-correlated partially polarized source and scattered from a {delta}-correlated medium is provided.
Exact Mapping of the Stochastic Field Theory for Manna Sandpiles to Interfaces in Random Media
NASA Astrophysics Data System (ADS)
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-01
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior.
Exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media.
Le Doussal, Pierre; Wiese, Kay Jörg
2015-03-20
We show that the stochastic field theory for directed percolation in the presence of an additional conservation law [the conserved directed-percolation (C-DP) class] can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched disorder. Along one line of the parameters commonly studied, this mapping leads to the simplest overdamped dynamics. Away from this line, an additional memory term arises in the interface dynamics; we argue that this does not change the universality class. Since C-DP is believed to describe the Manna class of self-organized criticality, this shows that Manna stochastic sandpiles and disordered elastic interfaces (i.e., the quenched Edwards-Wilkinson model) share the same universal large-scale behavior. PMID:25839253
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Using a stochastic field theory to understand group behavior in microswimmer suspensions
NASA Astrophysics Data System (ADS)
Underhill, Patrick; Qian, Yuzhou; Kramer, Peter
2015-11-01
Active suspensions of microswimmers appear both in natural biological systems (e.g. bacteria or algae) and in synthetic systems. Even without external forcing they are out of equilibrium, which gives rise to interesting properties in both small and large concentrations of the particles. These properties have been observed in experiments as well as simulation/modeling approaches. It is important to understand how hydrodynamic interactions between active swimmers cause and/or alter the suspension properties including enhanced transport and mixing. One of the most successful approaches has been a mean field theory. However, in some situations the mean field theory makes predictions that differ significantly from experiments and direct (agent or particle based) simulations. There are also some quantities that cannot be calculated by the mean field theory. In this talk, we will describe our new approach which uses a stochastic field to overcome the limitations of the mean field assumption. It allows us to calculate how interactions between organisms alter the correlations and mixing in conditions where the mean field theory cannot.
Stochastic geometry of critical curves, Schramm Loewner evolutions and conformal field theory
NASA Astrophysics Data System (ADS)
Gruzberg, Ilya A.
2006-10-01
Conformally invariant curves that appear at critical points in two-dimensional statistical mechanics systems and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm (2000 Israel J. Math. 118 221 (Preprint math.PR/9904022)) has invented a new rigorous as well as practical calculational approach to critical curves, based on a beautiful unification of conformal maps and stochastic processes, and by now known as Schramm-Loewner evolution (SLE). On the other hand, Duplantier (2000 Phys. Rev. Lett. 84 1363; Fractal Geometry and Applications: A Jubilee of Benot Mandelbrot: Part 2 (Proc. Symp. Pure Math. vol 72) (Providence, RI: American Mathematical Society) p 365 (Preprint math-ph/0303034)) has applied boundary quantum gravity methods to calculate exact multifractal exponents associated with critical curves. In the first part of this paper, I provide a pedagogical introduction to SLE. I present mathematical facts from the theory of conformal maps and stochastic processes related to SLE. Then I review basic properties of SLE and provide practical derivation of various interesting quantities related to critical curves, including fractal dimensions and crossing probabilities. The second part of the paper is devoted to a way of describing critical curves using boundary conformal field theory (CFT) in the so-called Coulomb gas formalism. This description provides an alternative (to quantum gravity) way of obtaining the multifractal spectrum of critical curves using only traditional methods of CFT based on free bosonic fields.
Stochastic Growth Theory of Spatially-Averaged Distributions of Langmuir Fields in Earth's Foreshock
NASA Technical Reports Server (NTRS)
Boshuizen, Christopher R.; Cairns, Iver H.; Robinson, P. A.
2001-01-01
Langmuir-like waves in the foreshock of Earth are characteristically bursty and irregular, and are the subject of a number of recent studies. Averaged over the foreshock, it is observed that the probability distribution is power-law P(bar)(log E) in the wave field E with the bar denoting this averaging over position, In this paper it is shown that stochastic growth theory (SGT) can explain a power-law spatially-averaged distributions P(bar)(log E), when the observed power-law variations of the mean and standard deviation of log E with position are combined with the log normal statistics predicted by SGT at each location.
Stochastic models: theory and simulation.
Field, Richard V., Jr.
2008-03-01
Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.
Effective field theory during inflation. II. Stochastic dynamics and power spectrum suppression
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2016-02-01
We obtain the nonequilibrium effective action of an inflatonlike scalar field—the system—by tracing over sub-Hubble degrees of freedom of "environmental" light scalar fields. The effective action is stochastic leading to effective Langevin equations of motion for the fluctuations of the inflatonlike field, with self-energy corrections and stochastic noise correlators that obey a de Sitter space-time analog of a fluctuation dissipation relation. We solve the Langevin equation implementing a dynamical renormalization group resummation of the leading secular terms and obtain the corrections to the power spectrum of super-Hubble fluctuations of the inflaton field, P (k ;η )=P0(k )e-γ (k ;η ) where P0(k ) is the nearly scale invariant power spectrum in absence of coupling. γ (k ;η )>0 describes the suppression of the power spectrum; it features Sudakov-type double logarithms and entails violations of scale invariance. We also obtain the effective action for the case of a heavy scalar field of mass M ≫H ; this case yields a local "Fermi" limit with a very weak self-interaction of the inflatonlike field and dissipative terms that are suppressed by powers of H /M . We conjecture on the possibility that the large scale anomalies in the cosmic microwave background may originate in dissipative processes from inflaton coupling to sub-Hubble degrees of freedom.
Stochastic field-line wandering in magnetic turbulence with shear. I. Quasi-linear theory
NASA Astrophysics Data System (ADS)
Shalchi, A.; Negrea, M.; Petrisor, I.
2016-07-01
We investigate the random walk of magnetic field lines in magnetic turbulence with shear. In the first part of the series, we develop a quasi-linear theory in order to compute the diffusion coefficient of magnetic field lines. We derive general formulas for the diffusion coefficients in the different directions of space. We like to emphasize that we expect that quasi-linear theory is only valid if the so-called Kubo number is small. We consider two turbulence models as examples, namely, a noisy slab model as well as a Gaussian decorrelation model. For both models we compute the field line diffusion coefficients and we show how they depend on the aforementioned Kubo number as well as a shear parameter. It is demonstrated that the shear effect reduces all field line diffusion coefficients.
Theory, technology, and technique of stochastic cooling
Marriner, J.
1993-10-01
The theory and technological implementation of stochastic cooling is described. Theoretical and technological limitations are discussed. Data from existing stochastic cooling systems are shown to illustrate some useful techniques.
Some remarks on Nelson's stochastic field
NASA Astrophysics Data System (ADS)
Lim, S. C.
1980-09-01
An attempt to extend Nelson's stochastic quantization procedure to tensor fields indicates that the results of Guerra et al. on the connection between a euclidean Markov scalar field and a stochastic scalar field fails to hold for tensor fields.
Wu, Wei; Wang, Jin
2014-09-14
We have established a general non-equilibrium thermodynamic formalism consistently applicable to both spatially homogeneous and, more importantly, spatially inhomogeneous systems, governed by the Langevin and Fokker-Planck stochastic dynamics with multiple state transition mechanisms, using the potential-flux landscape framework as a bridge connecting stochastic dynamics with non-equilibrium thermodynamics. A set of non-equilibrium thermodynamic equations, quantifying the relations of the non-equilibrium entropy, entropy flow, entropy production, and other thermodynamic quantities, together with their specific expressions, is constructed from a set of dynamical decomposition equations associated with the potential-flux landscape framework. The flux velocity plays a pivotal role on both the dynamic and thermodynamic levels. On the dynamic level, it represents a dynamic force breaking detailed balance, entailing the dynamical decomposition equations. On the thermodynamic level, it represents a thermodynamic force generating entropy production, manifested in the non-equilibrium thermodynamic equations. The Ornstein-Uhlenbeck process and more specific examples, the spatial stochastic neuronal model, in particular, are studied to test and illustrate the general theory. This theoretical framework is particularly suitable to study the non-equilibrium (thermo)dynamics of spatially inhomogeneous systems abundant in nature. This paper is the second of a series.
Stochastic kinetic mean field model
NASA Astrophysics Data System (ADS)
Erdélyi, Zoltán; Pasichnyy, Mykola; Bezpalchuk, Volodymyr; Tomán, János J.; Gajdics, Bence; Gusak, Andriy M.
2016-07-01
This paper introduces a new model for calculating the change in time of three-dimensional atomic configurations. The model is based on the kinetic mean field (KMF) approach, however we have transformed that model into a stochastic approach by introducing dynamic Langevin noise. The result is a stochastic kinetic mean field model (SKMF) which produces results similar to the lattice kinetic Monte Carlo (KMC). SKMF is, however, far more cost-effective and easier to implement the algorithm (open source program code is provided on
Stochastic-field cavitation model
Dumond, J.; Magagnato, F.; Class, A.
2013-07-15
Nonlinear phenomena can often be well described using probability density functions (pdf) and pdf transport models. Traditionally, the simulation of pdf transport requires Monte-Carlo codes based on Lagrangian “particles” or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on Eulerian fields has been proposed which eliminates the necessity to mix Eulerian and Lagrangian techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and, in particular, to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. First, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.
Multiple fields in stochastic inflation
NASA Astrophysics Data System (ADS)
Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Vennin, Vincent; Wands, David
2016-06-01
Stochastic effects in multi-field inflationary scenarios are investigated. A hierarchy of diffusion equations is derived, the solutions of which yield moments of the numbers of inflationary e-folds. Solving the resulting partial differential equations in multi-dimensional field space is more challenging than the single-field case. A few tractable examples are discussed, which show that the number of fields is, in general, a critical parameter. When more than two fields are present for instance, the probability to explore arbitrarily large-field regions of the potential, otherwise inaccessible to single-field dynamics, becomes non-zero. In some configurations, this gives rise to an infinite mean number of e-folds, regardless of the initial conditions. Another difference with respect to single-field scenarios is that multi-field stochastic effects can be large even at sub-Planckian energy. This opens interesting new possibilities for probing quantum effects in inflationary dynamics, since the moments of the numbers of e-folds can be used to calculate the distribution of primordial density perturbations in the stochastic-δ N formalism.
The theory of hybrid stochastic algorithms
Kennedy, A.D. . Supercomputer Computations Research Inst.)
1989-11-21
These lectures introduce the family of Hybrid Stochastic Algorithms for performing Monte Carlo calculations in Quantum Field Theory. After explaining the basic concepts of Monte Carlo integration we discuss the properties of Markov processes and one particularly useful example of them: the Metropolis algorithm. Building upon this framework we consider the Hybrid and Langevin algorithms from the viewpoint that they are approximate versions of the Hybrid Monte Carlo method; and thus we are led to consider Molecular Dynamics using the Leapfrog algorithm. The lectures conclude by reviewing recent progress in these areas, explaining higher-order integration schemes, the asymptotic large-volume behaviour of the various algorithms, and some simple exact results obtained by applying them to free field theory. It is attempted throughout to give simple yet correct proofs of the various results encountered. 38 refs.
Stochastic processes, estimation theory and image enhancement
NASA Technical Reports Server (NTRS)
Assefi, T.
1978-01-01
An introductory account of stochastic processes, estimation theory, and image enhancement is presented. The book is primarily intended for first-year graduate students and practicing engineers and scientists whose work requires an acquaintance with the theory. Fundamental concepts of probability were reviewed that are required to support the main topics. The appendices discuss the remaining mathematical background.
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Topological charge conservation in stochastic optical fields
NASA Astrophysics Data System (ADS)
Roux, Filippus S.
2016-05-01
The fact that phase singularities in scalar stochastic optical fields are topologically conserved implies the existence of an associated conserved current, which can be expressed in terms of local correlation functions of the optical field and its transverse derivatives. Here, we derive the topological charge current for scalar stochastic optical fields and show that it obeys a conservation equation. We use the expression for the topological charge current to investigate the topological charge flow in inhomogeneous stochastic optical fields with a one-dimensional topological charge density.
Unstable infinite nuclear matter in stochastic mean field approach
Colonna, M.; Chomaz, P. Laboratorio Nazionale del Sud, Viale Andrea Doria, Catania )
1994-04-01
In this article, we consider a semiclassical stochastic mean-field approach. In the case of unstable infinite nuclear matter, we calculate the characteristic time of the exponential growing of fluctuations and the diffusion coefficients associated to the unstable modes, in the framework of the Boltzmann-Langevin theory. These two quantities are essential to describe the dynamics of fluctuations and instabilities since, in the unstable regions, the evolution of the system will be dominated by the amplification of fluctuations. In order to make realistic 3D calculations feasible, we suggest to replace the complicated Boltzmann-Langevin theory by a simpler stochastic mean-field approach corresponding to a standard Boltzmann evolution, complemented by a simple noise chosen to reproduce the dynamics of the most unstable modes. Finally we explain how to approximately implement this method by simply tuning the noise associated to the use of a finite number of test particles in Boltzman-like calculations.
Stochastic Vorticity and Associated Filtering Theory
Amirdjanova, A.; Kallianpur, G.
2002-12-19
The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod-Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is considered and a corresponding Fujisaki-Kallianpur-Kunita stochastic differential equation for the optimal filter is derived.
Why Earthquakes Stop: Growth and Arrest in Stochastic Fields
Rundle, J.; Preston, E.; McGinnis, S.; Klein, W.
1998-06-01
Classical theory predicts that earthquakes growing in a homogeneous stress field should not arrest until the fault boundaries are encountered. However, earthquakes on natural faults, where stresses are heterogeneous, are observed over a wide range of sizes. Here we suggest that heterogeneity should be characterized by the Hausdorff dimension {ital H} of the walk associated with a stochastic stress difference field. The critical value for arrest, H=0.5 , corresonds to a Brownian walk through the stress difference field. {copyright} {ital 1998} {ital The American Physical Society}
The Stochastic Theory of Cell Proliferation
Bronk, Burt V.; Dienes, G. J.; Paskin, Arthur
1968-01-01
A stochastic theory of cell kinetics has been developed based on a realistic model of cell proliferation. A characteristic transit time, t̄i, has been assigned to each of the four states (G1, S, G2, M) of the cell cycle. The actual transit time, ti, for any cell is represented by a distribution around t̄i with a variance σi2. Analytic and computer formulations have been used to describe the time development of such characteristics as age distribution, labeling experiments, and response to perturbations of the system by, for example, irradiation and temperature. The decay of synchrony is analyzed in detail and is shown to proceed as a damped wave. From the first few peaks of the synchrony decay one can obtain the distribution function for the cell cycle time. The later peaks decay exponentially with a characteristic decay constant, λ, which depends only on the average cell-cycle time, T̄, and the associated variance. It is shown that the system, upon any sudden disturbance, approaches new “equilibrium” proliferation characteristics via damped periodic transients, the damping being characterized by λ. Thus, the response time of the system, T̄/λ, is as basic a parameter of the system as the cell-cycle time. PMID:5696217
Kheirandish, F.; Amooshahi, M.
2008-11-18
Quantum field theory of a damped vibrating string as the simplest dissipative scalar field theory is investigated by introducing a minimal coupling method. The rate of energy flowing between the system and its environment is obtained.
Majorana approach to the stochastic theory of line shapes
NASA Astrophysics Data System (ADS)
Komijani, Yashar; Coleman, Piers
2016-08-01
Motivated by recent Mössbauer experiments on strongly correlated mixed-valence systems, we revisit the Kubo-Anderson stochastic theory of spectral line shapes. Using a Majorana representation for the nuclear spin we demonstrate how to recast the classic line-shape theory in a field-theoretic and diagrammatic language. We show that the leading contribution to the self-energy can reproduce most of the observed line-shape features including splitting and line-shape narrowing, while the vertex and the self-consistency corrections can be systematically included in the calculation. This approach permits us to predict the line shape produced by an arbitrary bulk charge fluctuation spectrum providing a model-independent way to extract the local charge fluctuation spectrum of the surrounding medium. We also derive an inverse formula to extract the charge fluctuation from the measured line shape.
Theory of correlations in stochastic neural networks
NASA Astrophysics Data System (ADS)
Ginzburg, Iris; Sompolinsky, Haim
1994-10-01
One of the main experimental tools in probing the interactions between neurons has been the measurement of the correlations in their activity. In general, however, the interpretation of the observed correlations is difficult since the correlation between a pair of neurons is influenced not only by the direct interaction between them but also by the dynamic state of the entire network to which they belong. Thus a comparison between the observed correlations and the predictions from specific model networks is needed. In this paper we develop a theory of neuronal correlation functions in large networks comprising several highly connected subpopulations and obeying stochastic dynamic rules. When the networks are in asynchronous states, the cross correlations are relatively weak, i.e., their amplitude relative to that of the autocorrelations is of order of 1/N, N being the size of the interacting populations. Using the weakness of the cross correlations, general equations that express the matrix of cross correlations in terms of the mean neuronal activities and the effective interaction matrix are presented. The effective interactions are the synaptic efficacies multiplied by the gain of the postsynaptic neurons. The time-delayed cross-correlation matrix can be expressed as a sum of exponentially decaying modes that correspond to the (nonorthogonal) eigenvectors of the effective interaction matrix. The theory is extended to networks with random connectivity, such as randomly dilute networks. This allows for a comparison between the contribution from the internal common input and that from the direct interactions to the correlations of monosynaptically coupled pairs. A closely related quantity is the linear response of the neurons to external time-dependent perturbations. We derive the form of the dynamic linear response function of neurons in the above architecture in terms of the eigenmodes of the effective interaction matrix. The behavior of the correlations and the
A stochastic model for palaeomagnetic field variations
NASA Astrophysics Data System (ADS)
Buffett, Bruce A.; Ziegler, Leah; Constable, Cathy G.
2013-10-01
Regeneration of the Earth's magnetic field by convection in the liquid core produces a broad spectrum of time variation. Relative palaeointensity measurements in marine sediments provide a detailed record over the past 2 Myr, but an explicit reconstruction of the underlying dynamics is not feasible. A more practical alternative is to construct a stochastic model from estimates of the virtual axial dipole moment. The deterministic part of the model (drift term) describes time-averaged behaviour, whereas the random part (diffusion term) characterizes complex interactions over convective timescales. We recover estimates of the drift and diffusion terms from the SINT2000 model of Valet et al. and the PADM2M model of Ziegler et al. The results are used in numerical solutions of the Fokker-Planck equation to predict statistical properties of the palaeomagnetic field, including the average rates of magnetic reversals and excursions. A physical interpretation of the stochastic model suggests that the timescale for adjustments in the axial dipole moment is set by the dipole decay time τd. We obtain τd = 29 kyr from the stochastic models, which falls within the expected range for the Earth's core. We also predict the amplitude of convective fluctuations in the core, and establish a physical connection to the rates of magnetic reversals and excursions. Chrons lasting longer than 10 Myr are unlikely under present-day conditions. However, long chrons become more likely if the diffusion term is reduced by a factor of 2. Such a change is accomplished by reducing the velocity fluctuations in the core by a factor of √2, which could be attributed to a shift in the spatial pattern of heat flux from the core or a reduction in the total core heat flow.
Existence Theory for Stochastic Power Law Fluids
NASA Astrophysics Data System (ADS)
Breit, Dominic
2015-06-01
We consider the equations of motion for an incompressible non-Newtonian fluid in a bounded Lipschitz domain during the time interval (0, T) together with a stochastic perturbation driven by a Brownian motion W. The balance of momentum reads as where v is the velocity, the pressure and f an external volume force. We assume the common power law model and show the existence of martingale weak solution provided . Our approach is based on the -truncation and a harmonic pressure decomposition which are adapted to the stochastic setting.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Stochastic mean-field polycrystal plasticity methods
NASA Astrophysics Data System (ADS)
Tonks, Michael R.
To accommodate multiple length scales, mean-field polycrystal plasticity models treat each material point as an aggregate of N crystals. The crystal velocity gradients Lc are approximated and then used to evaluate the crystal stresses T c. The Tc are averaged to determine the material point stress T. Commonly, the Lc are approximated with the fully constrained model (FCM) based on the Taylor hypothesis which equates Lc to the macro-scale velocity gradient L. Herein, we present two stochastic models that relax the FCM constraint. Through various applications we show that these computationally efficient stochastic models provide realistic response predictions. We first investigate the texture evolution in a planar polycrystal with our stochastic Taylor model (STM), in which we define L c as a realization of a normal distribution with mean equal to L. Our STM predictions agree with crystal plasticity finite element method (CPFEM) predictions, demonstrating the development of a steady-state texture that is not predicted by the FCM. The computational cost of the STM is comparable to the FCM, i.e. substantially less than the CPFEM. We develop the STM for 3-D polycrystals based on CPFEM analysis results which show that Lc follows a normal distribution. In addition to the STM, we develop the stochastic no-constraints model (SNCM), which differs from the STM in the manner with which the Lc distribution means are determined. Calibration and validation of the models are performed using tantalum compression experiment data. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is slightly more computationally expensive than the FCM, while the SNCM is three times more expensive. Finally, we incorporate the STM in a finite element simulation of the Taylor impact of two tantalum specimens. Our simulation predictions mimic the texture and deformation data measured from a powder metallurgy
Stochastic Phase Resetting: a Theory for Deep Brain Stimulation
NASA Astrophysics Data System (ADS)
Tass, Peter A.
2000-03-01
A stochastic approach to phase resetting in clusters of interacting oscillators is presented. This theory explains how a stimulus, especially a single pulse, induces synchronization and desynchronization processes. The theory is used to design a new technique for deep brain stimulation in patients suffering from Parkinson's disease or essential tremor that do no longer respond to drug therapy. This stimulation mode is a feedback controlled single pulse stimulation. The feedback signal is registered with the deep brain electrode, and the desynchronizing pulses are administered via the same electrode. The stochastic phase resetting theory is used as a starting point of a model based design of intelligent and gentle deep brain stimulation techniques.
Records in stochastic processes—theory and applications
NASA Astrophysics Data System (ADS)
Wergen, Gregor
2013-06-01
In recent years there has been a surge of interest in the statistics of record-breaking events in stochastic processes. Along with that, many new and interesting applications of the theory of records were discovered and explored. The record statistics of uncorrelated random variables sampled from time-dependent distributions was studied extensively. The findings were applied in various areas to model and explain record-breaking events in observational data. Particularly interesting and fruitful was the study of record-breaking temperatures and their connection with global warming, but also records in sports, biology and some areas in physics were considered in the last years. Similarly, researchers have recently started to understand the record statistics of correlated processes such as random walks, which can be helpful to model record events in financial time series. This review is an attempt to summarize and evaluate the progress that has been made in the field of record statistics throughout recent years.
Towards a theory of stochastic vorticity-augmentation. [tornado model
NASA Technical Reports Server (NTRS)
Liu, V. C.
1977-01-01
A new hypothesis to account for the formation of tornadoes is presented. An elementary one-dimensional theory is formulated for vorticity transfer between an ambient sheared wind and a transverse penetrating jet. The theory points out the relevant quantities to be determined in describing the present stochastic mode of vorticity augmentation.
Jerks in Stochastic Synthetic Magnetic Fields
NASA Astrophysics Data System (ADS)
Brown, W. J.; Mound, J. E.; Livermore, P. W.
2014-12-01
The geomagnetic field is generated by the constant motion of the fluid outer core and varies on timescales from months to millions of years. Geomagnetic jerks are rapid changes in the secular variation of Earth's magnetic field, attributed primarily to changing flows near the surface of the outer core. Various generation mechanisms have been suggested for these rapid changes but none have conclusively explained the phenomena. Jerks can be seen in magnetic observatory records over the last 170~years and in satellite data of the last 15~years. This data coverage, spatially limited and/or temporally restricted, makes it difficult to interpret the true character of jerks at the surface or their origins in the core. This leads us to investigate what further insight we can gain from synthetic magnetic fields such as those which are described by modelling stochastic processes. Such fields are not restricted by the temporal smoothing of most magnetic field models and can better represent rapid variations such as jerks. We compare the characteristics of the synthetic fields with those of observatory and satellite data and hence, finding great similarity, study the presence of jerks in stochastic synthetic fields. Synthetic jerks are seen which resemble observed jerks, occurring frequently with regional periodic variations in amplitudes. These synthetic jerks occur without related features in the large scale secular acceleration power at the CMB. The flexible spatial and temporal sampling of the models creates a means of validating the robustness of observed features in the real field, which suffer from limited sampling. Initial results suggest that the distribution of magnetic observatories is sufficient to accurately recover the large scale features of jerks. As such comparisons between jerks seen in observatory and satellite data may be drawn. We further investigate the spectral properties of jerks in the synthetic fields using spherical harmonic analysis with a view to
Plasma Equilibrium in a Magnetic Field with Stochastic Regions
J.A. Krommes and Allan H. Reiman
2009-04-23
The nature of plasma equilibrium in a magnetic field with stochastic regions is examined. It is shown that the magnetic differential equation that determines the equilibrium Pfirsch-Schluter currents can be cast in a form similar to various nonlinear equations for a turbulent plasma, allowing application of the mathematical methods of statistical turbulence theory. An analytically tractable model, previously studied in the context of resonance-broadening theory, is applied with particular attention paid to the periodicity constraints required in toroidal configurations. It is shown that even a very weak radial diffusion of the magnetic field lines can have a significant effect on the equilibrium in the neighborhood of the rational surfaces, strongly modifying the near-resonant Pfirsch-Schluter currents. Implications for the numerical calculation of 3D equilibria are discussed
Evaluation of Uncertainty in Runoff Analysis Incorporating Theory of Stochastic Process
NASA Astrophysics Data System (ADS)
Yoshimi, Kazuhiro; Wang, Chao-Wen; Yamada, Tadashi
2015-04-01
The aim of this paper is to provide a theoretical framework of uncertainty estimate on rainfall-runoff analysis based on theory of stochastic process. SDE (stochastic differential equation) based on this theory has been widely used in the field of mathematical finance due to predict stock price movement. Meanwhile, some researchers in the field of civil engineering have investigated by using this knowledge about SDE (stochastic differential equation) (e.g. Kurino et.al, 1999; Higashino and Kanda, 2001). However, there have been no studies about evaluation of uncertainty in runoff phenomenon based on comparisons between SDE (stochastic differential equation) and Fokker-Planck equation. The Fokker-Planck equation is a partial differential equation that describes the temporal variation of PDF (probability density function), and there is evidence to suggest that SDEs and Fokker-Planck equations are equivalent mathematically. In this paper, therefore, the uncertainty of discharge on the uncertainty of rainfall is explained theoretically and mathematically by introduction of theory of stochastic process. The lumped rainfall-runoff model is represented by SDE (stochastic differential equation) due to describe it as difference formula, because the temporal variation of rainfall is expressed by its average plus deviation, which is approximated by Gaussian distribution. This is attributed to the observed rainfall by rain-gauge station and radar rain-gauge system. As a result, this paper has shown that it is possible to evaluate the uncertainty of discharge by using the relationship between SDE (stochastic differential equation) and Fokker-Planck equation. Moreover, the results of this study show that the uncertainty of discharge increases as rainfall intensity rises and non-linearity about resistance grows strong. These results are clarified by PDFs (probability density function) that satisfy Fokker-Planck equation about discharge. It means the reasonable discharge can be
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric A.; Hohm, Olaf; Penas, Victor A.; Riccioni, Fabio
2016-06-01
We present the dual formulation of double field theory at the linearized level. This is a classically equivalent theory describing the duals of the dilaton, the Kalb-Ramond field and the graviton in a T-duality or O( D, D) covariant way. In agreement with previous proposals, the resulting theory encodes fields in mixed Young-tableau representations, combining them into an antisymmetric 4-tensor under O( D, D). In contrast to previous proposals, the theory also requires an antisymmetric 2-tensor and a singlet, which are not all pure gauge. The need for these additional fields is analogous to a similar phenomenon for "exotic" dualizations, and we clarify this by comparing with the dualizations of the component fields. We close with some speculative remarks on the significance of these observations for the full non-linear theory yet to be constructed.
NASA Astrophysics Data System (ADS)
DeBock, M. F. M.; Classen, I. G. J.; Busch, C.; Jaspers, R. J. E.; Koslowski, H. R.; Unterberg, B.; TEXTOR Team
2008-01-01
For fusion reactors, based on the principle of magnetic confinement, it is important to avoid so-called magnetic islands or tearing modes. They reduce confinement and can be the cause of major disruptions. One class of magnetic islands is that of the perturbation field driven modes. This perturbation field can, for example, be the intrinsic error field. Theoretical work predicts a strong relationship between plasma rotation and the excitation of perturbation field modes. Experimentally, the theory on mode excitation and plasma rotation has been confirmed on several tokamaks. In those experiments, however, the control over the plasma rotation velocity and direction, and over the externally applied perturbation field was limited. In this paper experiments are presented that were carried out at the TEXTOR tokamak. Two tangential neutral beam injectors and a set of helical perturbation coils, called the dynamic ergodic divertor (DED), provide control over both the plasma rotation and the external perturbation field in TEXTOR. This made it possible to set up a series of experiments to test the theory on mode excitation and plasma rotation in detail. The perturbation field induced by the DED not only excites magnetic islands, it also sets up a layer near the plasma boundary where the magnetic field is stochastic. It will be shown that this stochastic field alters both the rotational response of the plasma on the perturbation field and the threshold for mode excitation. It therefore has to be included in an extended theory on mode excitation.
A stochastic filtering technique for fluid flow velocity fields tracking.
Cuzol, Anne; Mémin, Etienne
2009-07-01
In this paper, we present a method for the temporal tracking of fluid flow velocity fields. The technique we propose is formalized within a sequential Bayesian filtering framework. The filtering model combines an Itô diffusion process coming from a stochastic formulation of the vorticity-velocity form of the Navier-Stokes equation and discrete measurements extracted from the image sequence. In order to handle a state space of reasonable dimension, the motion field is represented as a combination of adapted basis functions, derived from a discretization of the vorticity map of the fluid flow velocity field. The resulting nonlinear filtering problem is solved with the particle filter algorithm in continuous time. An adaptive dimensional reduction method is applied to the filtering technique, relying on dynamical systems theory. The efficiency of the tracking method is demonstrated on synthetic and real-world sequences. PMID:19443925
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
NASA Astrophysics Data System (ADS)
Nemenman, Ilya
2008-03-01
A variety of stochastic systems, from enzyme kinetics to epidemiology, exhibit pump-like behaviors, where adiabatic changes of parameters result in a nonzero directed current through the system. Using the stochastic path integral technique from mesoscopic physics, we have been able to relate these and similar phenomena to geometric effects in mesoscopic stochastic kinetics and construct their unifying theory. In the talk, this methodology will be demonstrated on three examples: (1) an adiabatic pump effect in the evolution of a Michaelis-Menten enzyme, treated as a classical two-state stochastic system; (2) a reversible ratchet; and (3) a related novel phenomenon in a previously unexplored domain, namely the SIS epidemiological model. In all of these examples, pump-like currents follow from very similar geometric phase contributions to the effective action in the stochastic path integral representation of the moment generating functional, and our construction provides the universal technique for identification, prediction, and calculation of these currents in an arbitrary mesoscopic stochastic framework.
Stochastic modeling of the archeomagnetic field
NASA Astrophysics Data System (ADS)
Hellio, Gabrielle; Bouligand, Claire; Gillet, Nicolas; Jault, Dominique
2014-05-01
Modeling of the archeomagnetic field relies on indirect estimations of the ancient field recorded both in archeological artifacts and lake sediments. The sparse repartition of archeomagnetic data in space and time and their associated large measurement and dating uncertainties limit our ability to recover the spatio-temporal variations of the geomagnetic field over the past few millennia. The time regularization generally used to overcome the problem of non-uniqueness leads to models that are generally too smooth compared to geomagnetic time-series. The aim of this study is to perform a stochastic inversion of archeomagnetic data in order to build an ensemble of regional models covering the past few millennia. The inverse problem is solved using a priori information on the Gauss coefficients. We rely on a time correlation function, which is compatible with present knowledge of the geomagnetic spectra and also with the rapid fluctuations observed in the geomagnetic time series. The method we developed allows us to account for dating errors in a probabilistic framework, at the expense of an inflated dataspace. We argue also the importance of covariance existing between inclination and intensity which provides additional information when few data are available. The resulting ensemble of models not only provides reliable information for processes occurring in the core but is also useful in a purpose of archeomagnetic dating. We present synthetic results to test the validity of our method and to illustrate the effect of dating errors. Furthermore, we take advantage of the large amount of data and the relatively dense temporal coverage in Western Europe to construct intensity master curves for Syria and directional and intensity curves for France. The last curves allow us to discuss the importance of covariance between inclination and intensity.
Fluid Physics Under a Stochastic Acceleration Field
NASA Technical Reports Server (NTRS)
Vinals, Jorge
2001-01-01
The research summarized in this report has involved a combined theoretical and computational study of fluid flow that results from the random acceleration environment present onboard space orbiters, also known as g-jitter. We have focused on a statistical description of the observed g-jitter, on the flows that such an acceleration field can induce in a number of experimental configurations of interest, and on extending previously developed methodology to boundary layer flows. Narrow band noise has been shown to describe many of the features of acceleration data collected during space missions. The scale of baroclinically induced flows when the driving acceleration is random is not given by the Rayleigh number. Spatially uniform g-jitter induces additional hydrodynamic forces among suspended particles in incompressible fluids. Stochastic modulation of the control parameter shifts the location of the onset of an oscillatory instability. Random vibration of solid boundaries leads to separation of boundary layers. Steady streaming ahead of a modulated solid-melt interface enhances solute transport, and modifies the stability boundaries of a planar front.
Stochastic quantum Zeno by large deviation theory
NASA Astrophysics Data System (ADS)
Gherardini, Stefano; Gupta, Shamik; Saverio Cataliotti, Francesco; Smerzi, Augusto; Caruso, Filippo; Ruffo, Stefano
2016-01-01
Quantum measurements are crucial for observing the properties of a quantum system, which, however, unavoidably perturb its state and dynamics in an irreversible way. Here we study the dynamics of a quantum system being subjected to a sequence of projective measurements applied at random times. In the case of independent and identically distributed intervals of time between consecutive measurements, we analytically demonstrate that the survival probability of the system to remain in the projected state assumes a large deviation (exponentially decaying) form in the limit of an infinite number of measurements. This allows us to estimate the typical value of the survival probability, which can therefore be tuned by controlling the probability distribution of the random time intervals. Our analytical results are numerically tested for Zeno-protected entangled states, which also demonstrate that the presence of disorder in the measurement sequence further enhances the survival probability when the Zeno limit is not reached (as it happens in experiments). Our studies provide a new tool for protecting and controlling the amount of quantum coherence in open complex quantum systems by means of tunable stochastic measurements.
NASA Astrophysics Data System (ADS)
Magnen, Jacques; Unterberger, Jérémie
2012-03-01
{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \\cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\\'evy area.
Pluralistic and stochastic gene regulation: examples, models and consistent theory
Salas, Elisa N.; Shu, Jiang; Cserhati, Matyas F.; Weeks, Donald P.; Ladunga, Istvan
2016-01-01
We present a theory of pluralistic and stochastic gene regulation. To bridge the gap between empirical studies and mathematical models, we integrate pre-existing observations with our meta-analyses of the ENCODE ChIP-Seq experiments. Earlier evidence includes fluctuations in levels, location, activity, and binding of transcription factors, variable DNA motifs, and bursts in gene expression. Stochastic regulation is also indicated by frequently subdued effects of knockout mutants of regulators, their evolutionary losses/gains and massive rewiring of regulatory sites. We report wide-spread pluralistic regulation in ≈800 000 tightly co-expressed pairs of diverse human genes. Typically, half of ≈50 observed regulators bind to both genes reproducibly, twice more than in independently expressed gene pairs. We also examine the largest set of co-expressed genes, which code for cytoplasmic ribosomal proteins. Numerous regulatory complexes are highly significant enriched in ribosomal genes compared to highly expressed non-ribosomal genes. We could not find any DNA-associated, strict sense master regulator. Despite major fluctuations in transcription factor binding, our machine learning model accurately predicted transcript levels using binding sites of 20+ regulators. Our pluralistic and stochastic theory is consistent with partially random binding patterns, redundancy, stochastic regulator binding, burst-like expression, degeneracy of binding motifs and massive regulatory rewiring during evolution. PMID:26823500
Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.
Neuhauser, Daniel; Rabani, Eran; Cytter, Yael; Baer, Roi
2016-05-19
We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe-Salpeter approach. PMID:26651840
Pluralistic and stochastic gene regulation: examples, models and consistent theory.
Salas, Elisa N; Shu, Jiang; Cserhati, Matyas F; Weeks, Donald P; Ladunga, Istvan
2016-06-01
We present a theory of pluralistic and stochastic gene regulation. To bridge the gap between empirical studies and mathematical models, we integrate pre-existing observations with our meta-analyses of the ENCODE ChIP-Seq experiments. Earlier evidence includes fluctuations in levels, location, activity, and binding of transcription factors, variable DNA motifs, and bursts in gene expression. Stochastic regulation is also indicated by frequently subdued effects of knockout mutants of regulators, their evolutionary losses/gains and massive rewiring of regulatory sites. We report wide-spread pluralistic regulation in ≈800 000 tightly co-expressed pairs of diverse human genes. Typically, half of ≈50 observed regulators bind to both genes reproducibly, twice more than in independently expressed gene pairs. We also examine the largest set of co-expressed genes, which code for cytoplasmic ribosomal proteins. Numerous regulatory complexes are highly significant enriched in ribosomal genes compared to highly expressed non-ribosomal genes. We could not find any DNA-associated, strict sense master regulator. Despite major fluctuations in transcription factor binding, our machine learning model accurately predicted transcript levels using binding sites of 20+ regulators. Our pluralistic and stochastic theory is consistent with partially random binding patterns, redundancy, stochastic regulator binding, burst-like expression, degeneracy of binding motifs and massive regulatory rewiring during evolution. PMID:26823500
NASA Astrophysics Data System (ADS)
Detournay, Stéphane; Hartman, Thomas; Hofman, Diego M.
2012-12-01
We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the two-dimensional conformal group but in some respects is equally powerful in constraining the theory. In particular, the symmetries on a torus lead to modular covariance of the partition function, which is used to derive a universal formula for the asymptotic density of states. For an application we turn to the holographic description of black holes in quantum gravity, motivated by the fact that the symmetries in the near-horizon geometry of any extremal black hole are identical to those of a two-dimensional field theory with chiral scaling. We consider two examples: black holes in warped AdS3 in topologically massive gravity and in string theory. In both cases, the density of states in the two-dimensional field theory reproduces the Bekenstein-Hawking entropy of black holes in the gravity theory.
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type
Hosking, John Joseph Absalom
2012-12-15
We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.
NASA Astrophysics Data System (ADS)
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Continuum regularization of quantum field theory
Bern, Z.
1986-04-01
Possible nonperturbative continuum regularization schemes for quantum field theory are discussed which are based upon the Langevin equation of Parisi and Wu. Breit, Gupta and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the ''fifth-time'' of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, two difficulties arise which, in general, ruins the scheme. One problem is that the superficial quadratic divergences force a bottomless action for the noise. Another difficulty is that stochastic regularization by fifth-time smearing is incompatible with Zwanziger's gauge fixing, which is the only known nonperturbaive covariant gauge fixing for nonabelian gauge theories. Finally, a successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest. Hopefully, the scheme will lend itself to nonperturbative analysis. 44 refs., 16 figs.
Multifractal vector fields and stochastic Clifford algebra
Schertzer, Daniel Tchiguirinskaia, Ioulia
2015-12-15
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra
NASA Astrophysics Data System (ADS)
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.
Multifractal vector fields and stochastic Clifford algebra.
Schertzer, Daniel; Tchiguirinskaia, Ioulia
2015-12-01
In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166
Extended conformal field theories
NASA Astrophysics Data System (ADS)
Taormina, Anne
1990-08-01
Some extended conformal field theories are briefly reviewed. They illustrate how non minimal models of the Virasoro algebra (c≥1) can become minimal with respect to a larger algebra. The accent is put on N-extended superconformal algebras, which are relevant in superstring compactification.
Stochastic resonance-a nonlinear control theory interpretation
NASA Astrophysics Data System (ADS)
Repperger, D. W.; Farris, K. A.
2010-07-01
Stochastic resonance (SR) is an effect that has been known (Benzi, R., Sutera, A., and Vulpiani, A. (1981), 'The Mechanism of Stochastic Resonance', Journal of Physics, A14, L453-L457) for almost three decades and has been extensively studied in biology, statistics, signal processing and in numerous other eclectic areas (Wiesenfeld, K., and Moss, F. (1995), 'Stochastic Resonance and the Benefits of Noise: From Ice Ages to Crayfish and Squids', Nature, 373, 33-36). Herein, a nonlinear control theory analysis is conducted on how to better understand the class of systems that may exhibit the SR effect. Using nonlinear control theory methods, equilibrium points are manipulated to create the SR response (similar to shaping dynamical response in a phase plane). From this approach, a means of synthesising and designing the appropriate class of nonlinear systems is introduced. New types of nonlinear dynamics that demonstrate the SR effects are discovered, which may have utility in control theory as well as in many diverse applications. A numerical simulation illustrates some powerful attributes of these systems.
Stochastic Phase Resetting: A Theory for Deep Brain Stimulation
NASA Astrophysics Data System (ADS)
Tass, P. A.
The basic principles of a stochastic approach to phase resetting in populations of interacting phase oscillators are presented in this article. This theory explains how synchronization and desynchronization processes are caused by a pulsatile stimulus. It is a central goal of this approach to establish a theoretical basis for the design of efficient and intelligent new deep brain stimulation techniques. Accordingly, the theory is used to design a new deep brain stimulation technique with feedback control in patients suffering from Parkinson's disease or essential tremor.
Holographic effective field theories
NASA Astrophysics Data System (ADS)
Martucci, Luca; Zaffaroni, Alberto
2016-06-01
We derive the four-dimensional low-energy effective field theory governing the moduli space of strongly coupled superconformal quiver gauge theories associated with D3-branes at Calabi-Yau conical singularities in the holographic regime of validity. We use the dual supergravity description provided by warped resolved conical geometries with mobile D3-branes. Information on the baryonic directions of the moduli space is also obtained by using wrapped Euclidean D3-branes. We illustrate our general results by discussing in detail their application to the Klebanov-Witten model.
Applications of queueing theory to stochastic models of gene expression
NASA Astrophysics Data System (ADS)
Kulkarni, Rahul
2012-02-01
The intrinsic stochasticity of cellular processes implies that analysis of fluctuations (`noise') is often essential for quantitative modeling of gene expression. Recent single-cell experiments have carried out such analysis to characterize moments and entire probability distributions for quantities of interest, e.g. mRNA and protein levels across a population of cells. Correspondingly, there is a need to develop general analytical tools for modeling and interpretation of data obtained from such single-cell experiments. One such approach involves the mapping between models of stochastic gene expression and systems analyzed in queueing theory. The talk will provide an overview of this approach and discuss how theorems from queueing theory (e.g. Little's Law) can be used to derive exact results for general stochastic models of gene expression. In the limit that gene expression occurs in bursts, analytical results can be obtained which provide insight into the effects of different regulatory mechanisms on the noise in protein steady-state distributions. In particular, the approach can be used to analyze the effect of post-transcriptional regulation by non-coding RNAs leading to new insights and experimentally testable predictions.
Kinetic theory of age-structured stochastic birth-death processes
NASA Astrophysics Data System (ADS)
Greenman, Chris D.; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution.
Kinetic theory of age-structured stochastic birth-death processes.
Greenman, Chris D; Chou, Tom
2016-01-01
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but are unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Stochastic theories that treat semi-Markov age-dependent processes using, e.g., the Bellman-Harris equation do not resolve a population's age structure and are unable to quantify population-size dependencies. Conversely, current theories that include size-dependent population dynamics (e.g., mathematical models that include carrying capacity such as the logistic equation) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new, fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a Bogoliubov--Born--Green--Kirkwood--Yvon-like hierarchy. Explicit solutions are derived in three limits: no birth, no death, and steady state. These are then compared with their corresponding mean-field results. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. PMID:26871029
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then we consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Explore Stochastic Instabilities of Periodic Points by Transition Path Theory
NASA Astrophysics Data System (ADS)
Cao, Yu; Lin, Ling; Zhou, Xiang
2016-06-01
We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.
Beyond mean field theory: statistical field theory for neural networks
Buice, Michael A; Chow, Carson C
2014-01-01
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze. However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects. Here, we consider various possible approaches for going beyond mean field theory and incorporating correlation effects. Statistical field theory methods, in particular the Doi–Peliti–Janssen formalism, are particularly useful in this regard. PMID:25243014
Electron heat transport from stochastic fields in gyrokinetic simulationsa)
NASA Astrophysics Data System (ADS)
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-01
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as βe is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of βe. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, dm [A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Electron heat transport from stochastic fields in gyrokinetic simulations
Wang, E.; Nevins, W. M.; Candy, J.; Hatch, D.; Terry, P.; Guttenfelder, W.
2011-05-15
GYRO is used to examine the perturbed magnetic field structure generated by electromagnetic gyrokinetic simulations of the CYCLONE base case as {beta}{sub e} is varied from 0.1% to 0.7%, as investigated by J. Candy [Phys. Plasmas 12, 072307 (2005)]. Poincare surface of section plots obtained from integrating the self-consistent magnetic field demonstrates widespread stochasticity for all nonzero values of {beta}{sub e}. Despite widespread stochasticity of the perturbed magnetic fields, no significant increase in electron transport is observed. The magnetic diffusion, d{sub m}[A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett 40, 38 (1978)], is used to quantify the degree of stochasticity and related to the electron heat transport for hundreds of time slices in each simulation.
Stochastical modeling for Viral Disease: Statistical Mechanics and Network Theory
NASA Astrophysics Data System (ADS)
Zhou, Hao; Deem, Michael
2007-04-01
Theoretical methods of statistical mechanics are developed and applied to study the immunological response against viral disease, such as dengue. We use this theory to show how the immune response to four different dengue serotypes may be sculpted. It is the ability of avian influenza, to change and to mix, that has given rise to the fear of a new human flu pandemic. Here we propose to utilize a scale free network based stochastic model to investigate the mitigation strategies and analyze the risk.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
NASA Astrophysics Data System (ADS)
Choy, Ting-Pong
One of the leading problems in condensed matter physics is what state of matter obtain when there is a strong Coulomb repulsion between the electrons. One of the exotic examples is the high temperature superconductivity which was discovered in copper-oxide ceramics (cuprates) over twenty years ago. Thus far, a satisfactory theory is absent. In particular, the nature of the electron state outside the superconducting phase remains controversial. In analogy with the BCS theory of a conventional superconductor, in which the metal is well known to be a Fermi liquid, a complete understanding of the normal state of cuprate is necessary prior to the study of the superconducting mechanism in the high temperature superconductors. In this thesis, we will provide a theory for these exotic normal state properties by studying the minimal microscopic model which captures the physics of strong electron correlation. Even in such a simple microscopic model, striking properties including charge localization and presence of a Luttinger surface resemble the normal state properties of cuprate. An exact low energy theory of a doped Mott insulator will be constructed by explicitly integrating (rather than projecting) out the degrees of freedom far away from the chemical potential. The exact low energy theory contains degrees of freedom that cannot be obtained from projective schemes. In particular, a charge 2e bosonic field which is not made out of elemental excitations emerges at low energies. Such a field accounts for dynamical spectral weight transfer across the Mott gap. At half-filling, we show that two such excitations emerge which play a crucial role in preserving the Luttinger surface along which the single-particle Green function vanishes. We also apply this method to the Anderson-U impurity and show that in addition to the Kondo interaction, bosonic degrees of freedom appear as well. We show that many of the normal state properties of the cuprates can result from this new charge
Equilibrium thermodynamics and stochastic nonlinear acoustic fields. [in crystalline lattices
NASA Technical Reports Server (NTRS)
Cantrell, J. H.
1985-01-01
A crystalline solid is considered to consist of a large number of incoherent nonlinear acoustic radiation sources identified with the vibrating particles of the crystalline lattice. Randomization of the field, together with the assumption of a stochastically independent, fluctuating, radiation field at the absolue zero of temperature, leads to an expression of the temperature-dependent radiation field in terms of the zero-point field. The equation is identified with the Planck distribution formula of quantum mechanics in the linear field limit. The thermodynamic state functions are also obtained in terms of the nonlinear acoustic modal energies per unit mass and reduce to the results of the Debye-Einstein stochastic quantum oscillator model in the linear field limit.
Simulation of magnetic field line stochasticity at the magnetopause
NASA Technical Reports Server (NTRS)
Wang, Zhi; Ashour-Abdalla, Maha
1994-01-01
We have conducted a three-dimensional particle simulation to study the magnetic field line stochasticity at the magnetopause current layer. Our results show that the magnetic field lines become stochastic due to the overlap of the destabilized multiple tearing mode islands, which agrees with the percolation model suggested by Galeev et al. (1986). After the field lines become stochastic, these tearing modes grow even 2-3 times faster than in the linear stage and saturate at an amplitude level 3-4 times bigger than the single tearing mode without mode-mode coupling. The field line stochasticity also causes a strong particle diffusion across the current layer. The diffusion coefficient reaches to 10(exp 9) sq m/s for typical magnetopause parameters. Associated with the particle diffusion, the current layer becomes broader in width. As a result, the magnetic energy is dissipated into particle energy by heating parallel to the local magnetic field. The particle energy increases by 60%, while the magnetic helicity, which has always been regarded as a good invariant, changes by 20%.
Logarithmic conformal field theory
NASA Astrophysics Data System (ADS)
Gainutdinov, Azat; Ridout, David; Runkel, Ingo
2013-12-01
Conformal field theory (CFT) has proven to be one of the richest and deepest subjects of modern theoretical and mathematical physics research, especially as regards statistical mechanics and string theory. It has also stimulated an enormous amount of activity in mathematics, shaping and building bridges between seemingly disparate fields through the study of vertex operator algebras, a (partial) axiomatisation of a chiral CFT. One can add to this that the successes of CFT, particularly when applied to statistical lattice models, have also served as an inspiration for mathematicians to develop entirely new fields: the Schramm-Loewner evolution and Smirnov's discrete complex analysis being notable examples. When the energy operator fails to be diagonalisable on the quantum state space, the CFT is said to be logarithmic. Consequently, a logarithmic CFT is one whose quantum space of states is constructed from a collection of representations which includes reducible but indecomposable ones. This qualifier arises because of the consequence that certain correlation functions will possess logarithmic singularities, something that contrasts with the familiar case of power law singularities. While such logarithmic singularities and reducible representations were noted by Rozansky and Saleur in their study of the U (1|1) Wess-Zumino-Witten model in 1992, the link between the non-diagonalisability of the energy operator and logarithmic singularities in correlators is usually ascribed to Gurarie's 1993 article (his paper also contains the first usage of the term 'logarithmic conformal field theory'). The class of CFTs that were under control at this time was quite small. In particular, an enormous amount of work from the statistical mechanics and string theory communities had produced a fairly detailed understanding of the (so-called) rational CFTs. However, physicists from both camps were well aware that applications from many diverse fields required significantly more
Polymer parametrized field theory
Laddha, Alok; Varadarajan, Madhavan
2008-08-15
Free scalar field theory on 2-dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using loop quantum gravity (LQG) type 'polymer' representations for the matter field and the inertial variables. The quantum constraints are solved via group averaging techniques and, analogous to the case of spatial geometry in LQG, the smooth (flat) spacetime geometry is replaced by a discrete quantum structure. An overcomplete set of Dirac observables, consisting of (a) (exponentials of) the standard free scalar field creation-annihilation modes and (b) canonical transformations corresponding to conformal isometries, are represented as operators on the physical Hilbert space. None of these constructions suffer from any of the 'triangulation'-dependent choices which arise in treatments of LQG. In contrast to the standard Fock quantization, the non-Fock nature of the representation ensures that the group of conformal isometries as well as that of the gauge transformations generated by the constraints are represented in an anomaly free manner. Semiclassical states can be analyzed at the gauge invariant level. It is shown that 'physical weaves' necessarily underlie such states and that such states display semiclassicality with respect to, at most, a countable subset of the (uncountably large) set of observables of type (a). The model thus offers a fertile testing ground for proposed definitions of quantum dynamics as well as semiclassical states in LQG.
A stochastic perturbation theory for non-autonomous systems
Moon, W.; Wettlaufer, J. S.
2013-12-15
We develop a perturbation theory for a class of first order nonlinear non-autonomous stochastic ordinary differential equations that arise in climate physics. The perturbative procedure produces moments in terms of integral delay equations, whose order by order decay is characterized in a Floquet-like sense. Both additive and multiplicative sources of noise are discussed and the question of how the nature of the noise influences the results is addressed theoretically and numerically. By invoking the Martingale property, we rationalize the transformation of the underlying Stratonovich form of the model to an Ito form, independent of whether the noise is additive or multiplicative. The generality of the analysis is demonstrated by developing it both for a Brownian particle moving in a periodically forced quartic potential, which acts as a simple model of stochastic resonance, as well as for our more complex climate physics model. The validity of the approach is shown by comparison with numerical solutions. The particular climate dynamics problem upon which we focus involves a low-order model for the evolution of Arctic sea ice under the influence of increasing greenhouse gas forcing ΔF{sub 0}. The deterministic model, developed by Eisenman and Wettlaufer [“Nonlinear threshold behavior during the loss of Arctic sea ice,” Proc. Natl. Acad. Sci. U.S.A. 106(1), 28–32 (2009)] exhibits several transitions as ΔF{sub 0} increases and the stochastic analysis is used to understand the manner in which noise influences these transitions and the stability of the system.
Stochastic queueing-theory approach to human dynamics
NASA Astrophysics Data System (ADS)
Walraevens, Joris; Demoor, Thomas; Maertens, Tom; Bruneel, Herwig
2012-02-01
Recently, numerous studies have shown that human dynamics cannot be described accurately by exponential laws. For instance, Barabási [Nature (London)NATUAS0028-083610.1038/nature03459 435, 207 (2005)] demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws. He presumes that these power laws are caused by a priority selection mechanism among the tasks. Priority models are well-developed in queueing theory (e.g., for telecommunication applications), and this paper demonstrates the (quasi-)immediate applicability of such a stochastic priority model to human dynamics. By calculating generating functions and by studying them in their dominant singularity, we prove that nonexponential tails result naturally. Contrary to popular belief, however, these are not necessarily triggered by the priority selection mechanism.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Hermes, Matthew R.; Hirata, So
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
NASA Astrophysics Data System (ADS)
Hermes, Matthew R.; Hirata, So
2014-08-01
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm-1 and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Matrix models and stochastic growth in Donaldson-Thomas theory
Szabo, Richard J.; Tierz, Miguel
2012-10-15
We show that the partition functions which enumerate Donaldson-Thomas invariants of local toric Calabi-Yau threefolds without compact divisors can be expressed in terms of specializations of the Schur measure. We also discuss the relevance of the Hall-Littlewood and Jack measures in the context of BPS state counting and study the partition functions at arbitrary points of the Kaehler moduli space. This rewriting in terms of symmetric functions leads to a unitary one-matrix model representation for Donaldson-Thomas theory. We describe explicitly how this result is related to the unitary matrix model description of Chern-Simons gauge theory. This representation is used to show that the generating functions for Donaldson-Thomas invariants are related to tau-functions of the integrable Toda and Toeplitz lattice hierarchies. The matrix model also leads to an interpretation of Donaldson-Thomas theory in terms of non-intersecting paths in the lock-step model of vicious walkers. We further show that these generating functions can be interpreted as normalization constants of a corner growth/last-passage stochastic model.
Unification Theory of Optimal Life Histories and Linear Demographic Models in Internal Stochasticity
Oizumi, Ryo
2014-01-01
Life history of organisms is exposed to uncertainty generated by internal and external stochasticities. Internal stochasticity is generated by the randomness in each individual life history, such as randomness in food intake, genetic character and size growth rate, whereas external stochasticity is due to the environment. For instance, it is known that the external stochasticity tends to affect population growth rate negatively. It has been shown in a recent theoretical study using path-integral formulation in structured linear demographic models that internal stochasticity can affect population growth rate positively or negatively. However, internal stochasticity has not been the main subject of researches. Taking account of effect of internal stochasticity on the population growth rate, the fittest organism has the optimal control of life history affected by the stochasticity in the habitat. The study of this control is known as the optimal life schedule problems. In order to analyze the optimal control under internal stochasticity, we need to make use of “Stochastic Control Theory” in the optimal life schedule problem. There is, however, no such kind of theory unifying optimal life history and internal stochasticity. This study focuses on an extension of optimal life schedule problems to unify control theory of internal stochasticity into linear demographic models. First, we show the relationship between the general age-states linear demographic models and the stochastic control theory via several mathematical formulations, such as path–integral, integral equation, and transition matrix. Secondly, we apply our theory to a two-resource utilization model for two different breeding systems: semelparity and iteroparity. Finally, we show that the diversity of resources is important for species in a case. Our study shows that this unification theory can address risk hedges of life history in general age-states linear demographic models. PMID:24945258
NASA Technical Reports Server (NTRS)
Huang, Dong; Knyazikhin, Yuri; Wang, Weile; Deering, Donald W,; Stenberg, Pauline; Shabanov, Nikolay; Tan, Bin; Myneni, Ranga B.
2008-01-01
Radiation reflected from vegetation canopies exhibits high spatial variation. Satellite-borne sensors measure the mean intensities emanating from heterogeneous vegetated pixels. The theory of radiative transfer in stochastic media provides the most logical linkage between satellite observations and the three-dimensional canopy structure through a closed system of simple equations which contains the mean intensity and higher statistical moments directly as its unknowns. Although this theory has been a highly active research field in recent years, its potential for satellite remote sensing of vegetated surfaces has not been fully realized because of the lack of models of a canopy pair-correlation function that the stochastic radiative transfer equations require. The pair correlation function is defined as the probability of finding simultaneously phytoelements at two points. This paper presents analytical and Monte Carlo generated pair correlation functions. Theoretical and numerical analyses show that the spatial correlation between phytoelements is primarily responsible for the effects of the three-dimensional canopy structure on canopy reflective and absorptive properties. The pair correlation function, therefore, is the most natural and physically meaningful measure of the canopy structure over a wide range of scales. The stochastic radiative transfer equations naturally admit this measure and thus provide a powerful means to investigate the three-dimensional canopy structure from space. Canopy reflectances predicted by the stochastic equations are assessed by comparisons with the PARABOLA measurements from coniferous and broadleaf forest stands in the BOREAS Southern Study Areas. The pair correlation functions are derived from data on tree structural parameters collected during field campaigns conducted at these sites. The simulated canopy reflectances compare well with the PARABOLA data.
Full particle orbit effects in regular and stochastic magnetic fields
NASA Astrophysics Data System (ADS)
Ogawa, Shun; Cambon, Benjamin; Leoncini, Xavier; Vittot, Michel; del Castillo-Negrete, Diego; Dif-Pradalier, Guilhem; Garbet, Xavier
2016-07-01
We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the
Vector field theories in cosmology
Tartaglia, A.; Radicella, N.
2007-10-15
Recently proposed theories based on the cosmic presence of a vectorial field are compared and contrasted. In particular the so-called Einstein aether theory is discussed in parallel with a recent proposal of a strained space-time theory (cosmic defect theory). We show that the latter fits reasonably well the cosmic observed data with only one, or at most two, adjustable parameters, while other vector theories use much more. The Newtonian limits are also compared. Finally we show that the cosmic defect theory may be considered as a special case of the aether theories, corresponding to a more compact and consistent paradigm.
Optomechanically induced stochastic resonance and chaos transfer between optical fields
NASA Astrophysics Data System (ADS)
Monifi, Faraz; Zhang, Jing; Özdemir, Şahin Kaya; Peng, Bo; Liu, Yu-Xi; Bo, Fang; Nori, Franco; Yang, Lan
2016-06-01
Chaotic dynamics has been reported in many physical systems and has affected almost every field of science. Chaos involves hypersensitivity to the initial conditions of a system and introduces unpredictability into its output. Thus, it is often unwanted. Interestingly, the very same features make chaos a powerful tool to suppress decoherence, achieve secure communication and replace background noise in stochastic resonance—a counterintuitive concept that a system's ability to transfer information can be coherently amplified by adding noise. Here, we report the first demonstration of chaos-induced stochastic resonance in an optomechanical system, as well as the optomechanically mediated chaos transfer between two optical fields such that they follow the same route to chaos. These results will contribute to the understanding of nonlinear phenomena and chaos in optomechanical systems, and may find applications in the chaotic transfer of information and for improving the detection of otherwise undetectable signals in optomechanical systems.
Stochastic Landau-Lifshitz-Gilbert Equation with Delayed Feedback Field
NASA Astrophysics Data System (ADS)
Tutu, H.; Horita, T.
2008-08-01
A time-delayed feedback control to stabilize a swinging motion of magnetic moment in a single-domain magnetic system under AC field is studied. The system has a uniaxial anisotropy, and the AC field is parallel to this. Without control, it prefers the Ising state that is (anti)parallel to the anisotropy axis. The control stabilizes the oscillation across the equatorial plane perpendicular to the anisotropy axis (swinging motion). Employing a stochastic Landau-Lifshitz-Gilbert (LLG) equation, we study the effects of thermal fluctuation on the controlled state. Linear fluctuation, in which variance linearly depends on noise intensity, around the controlled state is analyzed in terms of correlation function and spectral density, and a criterion for the existence of such a linear relationship is obtained. Several technical improvements in the treatment of the stochastic LLG equation and the corresponding Fokker-Planck equation with stereographic coordinate system are also show n.
Flow damping due to stochastization of the magnetic field
Ida, K.; Yoshinuma, M.; Tsuchiya, H.; Kobayashi, T.; Suzuki, C.; Yokoyama, M.; Shimizu, A.; Nagaoka, K.; Inagaki, S.; Itoh, K.; Akiyama, T.; Emoto, M.; Evans, T.; Dinklage, A.; Du, X.; Fujii, K.; Goto, M.; Goto, T.; Hasuo, M.; Hidalgo, C.; Ichiguchi, K.; Ishizawa, A.; Jakubowski, M.; Kamiya, K.; Kasahara, H.; Kawamura, G.; Kato, D.; Kobayashi, M.; Morita, S.; Mukai, K.; Murakami, I.; Murakami, S.; Narushima, Y.; Nunami, M.; Ohdach, S.; Ohno, N.; Osakabe, M.; Pablant, N.; Sakakibara, S.; Seki, T.; Shimozuma, T.; Shoji, M.; Sudo, S.; Tanaka, K.; Tokuzawa, T.; Todo, Y.; Wang, H.; Yamada, H.; Takeiri, Y.; Mutoh, T.; Imagawa, S.; Mito, T.; Nagayama, Y.; Watanabe, K. Y.; Ashikawa, N.; Chikaraishi, H.; Ejiri, A.; Furukawa, M.; Fujita, T.; Hamaguchi, S.; Igami, H.; Isobe, M.; Masuzaki, S.; Morisaki, T.; Motojima, G.; Nagasaki, K.; Nakano, H.; Oya, Y.; Suzuki, Y.; Sakamoto, R.; Sakamoto, M.; Sanpei, A.; Takahashi, H.; Tokitani, M.; Ueda, Y.; Yoshimura, Y.; Yamamoto, S.; Nishimura, K.; Sugama, H.; Yamamoto, T.; Idei, H.; Isayama, A.; Kitajima, S.; Masamune, S.; Shinohara, K.; Bawankar, P. S.; Bernard, E.; von Berkel, M.; Funaba, H.; Huang, X. L.; Ii, T.; Ido, T.; Ikeda, K.; Kamio, S.; Kumazawa, R.; Moon, C.; Muto, S.; Miyazawa, J.; Ming, T.; Nakamura, Y.; Nishimura, S.; Ogawa, K.; Ozaki, T.; Oishi, T.; Ohno, M.; Pandya, S.; Seki, R.; Sano, R.; Saito, K.; Sakaue, H.; Takemura, Y.; Tsumori, K.; Tamura, N.; Tanaka, H.; Toi, K.; Wieland, B.; Yamada, I.; Yasuhara, R.; Zhang, H.; Kaneko, O.; Komori, A.
2015-01-01
The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport. PMID:25569268
Stochastic Definitions of Planck and Boltzmann Constants and Quantum Theory of Gravitation
NASA Astrophysics Data System (ADS)
Sohrab, S. H.
2001-04-01
Physical space is identified as a tachyonic fluid that is Dirac's "stochastic ether" or de Broglie's "hidden thermostat", and is described in terms of stochastic definitions of Planck h=m_k<λ_k>c and Boltzmann k=m_k<ν_k>c constants leading to photon gravitational mass m_k=(hk/c^3)^1/2 and Avogadro number N^o = 1/(hkc)^1/2. The finite pressure of vacuum is P_kV=N^okT_k=1 where T_k=<λ_k>= 0.11935 K, and pressures of matter Pm and anti-matter Pa fields lie in the range from black-hole P=∞ to white-hole P=0 singularities 0
Sheared Plasma Rotation in Partially Stochastic Magnetic Fields
Wingen, A.; Spatschek, K. H.
2009-05-08
It is shown that resonant magnetic perturbations generate sheared flow velocities in magnetized plasmas. Stochastic magnetic fields in incomplete chaos influence the drift motion of electrons and ions differently. Using a fast mapping technique, it is demonstrated that a radial electric field is generated due to the different behavior of passing particles (electrons and ions) in tokamak geometry; magnetic trapping of ions is neglected. Radial profiles of the polodial velocity resulting from the force balance in the presence of a strong toroidal magnetic field are obtained. Scaling laws for plasma losses and the forms of sheared plasma rotation profiles are discussed.
Stochastic Mean-Field Dynamics For Nuclear Collisions
Ayik, Sakir
2008-11-11
We discuss a stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. For small amplitude fluctuations, this approach gives a result for the dispersion of a one-body observable that is identical to the result obtained previously through a variational approach. Furthermore, it incorporates one-body dissipation and fluctuation mechanisms in accordance with quantal fluctuation-dissipation relation.
Nonlocal heat transport in a stochastic magnetic field
Rax, J.M.; White, R.B.
1991-12-01
Heat transport in a stochastic magnetic field configuration is shown to be nonlocal. Collisional transport processes, in such a disordered media, cannot always be reduced to a standard diffusion process, and the concept of a diffusion coefficient is meaningless for a wide range of typical tokamak parameters. In the nonlocal regime the relaxation of a gradient is described by an integral equation, involving a nonlocal propagator. This propagator is calculated, and the relation to previous results is elucidated. 15 refs.
Stochastic cooling of bunched beams from fluctuation and kinetic theory
Chattopadhyay, S.
1982-09-01
A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlation of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented.
Field theory and particle physics
Eboli, O.J.P.; Gomes, M.; Santoro, A.
1990-01-01
This book contains the proceedings of the topics covered during the fifth Jorge Andre Swieca Summer School. The first part of the book collects the material devoted to quantum field theory. There were four courses on methods in Field Theory; H. O. Girotti lectured on constrained dynamics, R. Jackiw on the Schrodinger representation in Field Theory, S.-Y. Pi on the application of this representation to quantum fields in a Robertson-Walker spacetime, and L. Vinet on Berry Connections. There were three courses on Conformal Field Theory: I. Todorov focused on the problem of construction and classification of conformal field theories. Lattice models, two-dimensional S matrices and conformal field theory were looked from the unifying perspective of the Yang-Baxter algebras in the lectures given by M. Karowski. Parasupersymmetric quantum mechanics was discussed in the lectures by L. Vinet. Besides those courses, there was an introduction to string field theory given by G. Horowitz. There were also three seminars: F. Schaposnik reported on recent applications of topological methods in field theory, P. Gerbert gave a seminar on three dimensional gravity and V. Kurak talked on two dimensional parafermionic models. The second part of this proceedings is devoted to phenomenology. There were three courses on Particle Physics: Dan Green lectured on collider physics, E. Predrazzi on strong interactions and G. Cohen-Tanoudji on the use of strings in strong interactions.
Invariants from classical field theory
Diaz, Rafael; Leal, Lorenzo
2008-06-15
We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. By applying our methods to several field theories such as Abelian BF, Chern-Simons, and two-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss' and the second Milnor's invariant for links in S{sup 3}, and invariants under area-preserving diffeomorphisms for configurations of immersed planar curves.
Incorporation of generalized uncertainty principle into Lifshitz field theories
Faizal, Mir; Majumder, Barun
2015-06-15
In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.
A field test of a simple stochastic radiative transfer model
Byrne, N.
1995-09-01
The problem of determining the effect of clouds on the radiative energy balance of the globe is of well-recognized importance. One can in principle solve the problem for any given configuration of clouds using numerical techniques. This knowledge is not useful however, because of the amount of input data and computer resources required. Besides, we need only the average of the resulting solution over the grid scale of a general circulation model (GCM). Therefore, we are interested in estimating the average of the solutions of such fine-grained problems using only coarse grained data, a science or art called stochastic radiation transfer. Results of the described field test indicate that the stochastic description is a somewhat better fit to the data than is a fractional cloud cover model, but more data are needed. 1 ref., 3 figs.
Two stochastic mean-field polycrystal plasticity methods
Tonks, Michael
2008-01-01
In this work, we develop two mean-field polycrystal plasticity models in which the L{sup c} are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L{sup c} tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the STM and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates D{sup c} are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the FCM, and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.
The generalized Fényes-Nelson model for free scalar field theory
NASA Astrophysics Data System (ADS)
Davidson, Mark
1980-03-01
The generalized Fényes-Nelson model of quantum mechanics is applied to the free scalar field. The resulting Markov field is equivalent to the Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. This result is consistent with Guerra's earlier work on stochastic quantization of scalar fields. It suggests a deep connection between Euclidean field theory and the stochastic interpretation of quantum mechanics. The question of Lorentz covariance is also discussed.
Resolving Witten's superstring field theory
NASA Astrophysics Data System (ADS)
Erler, Theodore; Konopka, Sebastian; Sachs, Ivo
2014-04-01
We regulate Witten's open superstring field theory by replacing the picturechanging insertion at the midpoint with a contour integral of picture changing insertions over the half-string overlaps of the cubic vertex. The resulting product between string fields is non-associative, but we provide a solution to the A ∞ relations defining all higher vertices. The result is an explicit covariant superstring field theory which by construction satisfies the classical BV master equation.
The Nonlinear Field Space Theory
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2016-08-01
In recent years the idea that not only the configuration space of particles, i.e. spacetime, but also the corresponding momentum space may have nontrivial geometry has attracted significant attention, especially in the context of quantum gravity. The aim of this letter is to extend this concept to the domain of field theories, by introducing field spaces (i.e. phase spaces of field values) that are not affine spaces. After discussing the motivation and general aspects of our approach we present a detailed analysis of the prototype (quantum) Nonlinear Field Space Theory of a scalar field on the Minkowski background. We show that the nonlinear structure of a field space leads to numerous interesting predictions, including: non-locality, generalization of the uncertainty relations, algebra deformations, constraining of the maximal occupation number, shifting of the vacuum energy and renormalization of the charge and speed of propagation of field excitations. Furthermore, a compact field space is a natural way to implement the "Principle of finiteness" of physical theories, which once motivated the Born-Infeld theory. Thus the presented framework has a variety of potential applications in the theories of fundamental interactions (e.g. quantum gravity), as well as in condensed matter physics (e.g. continuous spin chains), and can shed new light on the issue of divergences in quantum field theories.
On collisional diffusion in a stochastic magnetic field
Abdullaev, S. S.
2013-08-15
The effect of particle collisions on the transport in a stochastic magnetic field in tokamaks is investigated. The model of resonant magnetic perturbations generated by external coils at the plasma edge is used for the stochastic magnetic field. The particle collisions are simulated by a random walk process along the magnetic field lines and the jumps across the field lines at the collision instants. The dependencies of the local diffusion coefficients on the mean free path λ{sub mfp}, the diffusion coefficients of field lines D{sub FL}, and the collisional diffusion coefficients, χ{sub ⊥} are studied. Based on these numerical data and the heuristic arguments, the empirical formula, D{sub r}=χ{sub ⊥}+v{sub ||}D{sub FL}/(1+L{sub c}/λ{sub mfp}), for the local diffusion coefficient is proposed, where L{sub c} is the characteristic length of order of the connection length l{sub c}=πqR{sub 0}, q is the safety factor, R{sub 0} is the major radius. The formula quite well describes the results of numerical simulations. In the limiting cases, the formula describes the Rechester-Rosenbluth and Laval scalings.
On collisional diffusion in a stochastic magnetic field
NASA Astrophysics Data System (ADS)
Abdullaev, S. S.
2013-08-01
The effect of particle collisions on the transport in a stochastic magnetic field in tokamaks is investigated. The model of resonant magnetic perturbations generated by external coils at the plasma edge is used for the stochastic magnetic field. The particle collisions are simulated by a random walk process along the magnetic field lines and the jumps across the field lines at the collision instants. The dependencies of the local diffusion coefficients on the mean free path λmfp, the diffusion coefficients of field lines DFL, and the collisional diffusion coefficients, χ⊥ are studied. Based on these numerical data and the heuristic arguments, the empirical formula, Dr=χ⊥+v||DFL/(1+Lc/λmfp), for the local diffusion coefficient is proposed, where Lc is the characteristic length of order of the connection length lc=πqR0, q is the safety factor, R0 is the major radius. The formula quite well describes the results of numerical simulations. In the limiting cases, the formula describes the Rechester-Rosenbluth and Laval scalings.
String field theory and tachyon field
NASA Astrophysics Data System (ADS)
Yang, Yi
In this thesis, we study Sen's conjecture on tachyon condensation by using string field theories, i.e. boundary string field theory (BSFT) and cubic string field theory (CSFT). In the BSFT side, the first explicit calculation of effective tachyon action for the bosonic string was given by Witten ten years ago and by many other authors in the last two years. It was extended to the superstring case shortly after. In our work, we give an explicit calculation of Green functions for the fermionic fields and compute the effective tachyon action for the superstring. The results we obtain agree with earlier results. We then generalize the BSFT method to one loop level. The tachyon condensation at one loop level is systematically studied, and many interesting results are obtained which verify Sen's conjecture. We also apply this method to the non-orientable theory at one loop level, where the expected divergence cancellation is reproduced and the similar effective tachyon action is obtained. By using the boundary state formalism, we verify the duality between open and closed strings. In the CSFT side, since there is no known solution to this theory, tachyon condensation can only be studied by numerical methods, i.e. level truncation. However, at the tachyon vacuum, CSFT is simplified to vacuum string field theory (VSFT) which has a solution - sliver state. By adding a tachyon vertex to the boundary of the sliver state, we have calculated the effective action.
Introduction to Statistical Field Theory
NASA Astrophysics Data System (ADS)
Brézin, Edouard
2010-07-01
1. A few well-known basic results; 2. Introduction: order parameters, broken symmetries; 3. Examples of physical situations modelled by the Ising model; 4. A few results about the Ising model; 5. High temperature and low temperature expansions; 6. Some geometric problems related to phase transitions; 7. Phenomenological description of the critical behaviour; 8. Mean field theory; 9. Beyond mean field theory; 10. Introduction to the renormalization group; 11. Renormalization group for the φ4 theory; 12. Renormalized theory; 13. Goldstone modes; 14. Large n; Index.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
The Theory of Conceptual Fields
ERIC Educational Resources Information Center
Vergnaud, Gerard
2009-01-01
The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…
Cosmology with many light scalar fields: Stochastic inflation and loop corrections
NASA Astrophysics Data System (ADS)
Adshead, Peter; Easther, Richard; Lim, Eugene A.
2009-03-01
We explore the consequences of the existence of a very large number of light scalar degrees of freedom in the early universe. We distinguish between participator and spectator fields. The former have a small mass, and can contribute to the inflationary dynamics; the latter are either strictly massless or have a negligible VEV. In N-flation and generic assisted inflation scenarios, inflation is a cooperative phenomenon driven by N participator fields, none of which could drive inflation on its own. We review upper bounds on N, as a function of the inflationary Hubble scale H. We then consider stochastic and eternal inflation in models with N participator fields showing that individual fields may evolve stochastically while the whole ensemble behaves deterministically, and that a wide range of eternal inflationary scenarios are possible in this regime. We then compute one-loop quantum corrections to the inflationary power spectrum. These are largest with N spectator fields and a single participator field, and the resulting bound on N is always weaker than those obtained in other ways. We find that loop corrections to the N-flation power spectrum do not scale with N, and thus place no upper bound on the number of participator fields. This result also implies that, at least to leading order, the theory behaves like a composite single scalar field. In order to perform this calculation, we address a number of issues associated with loop calculations in the Schwinger-Keldysh “in-in” formalism.
Double field theory inspired cosmology
Wu, Houwen; Yang, Haitang E-mail: hyanga@scu.edu.cn
2014-07-01
Double field theory proposes a generalized spacetime action possessing manifest T-duality on the level of component fields. We calculate the cosmological solutions of double field theory with vanishing Kalb-Ramond field. It turns out that double field theory provides a more consistent way to construct cosmological solutions than the standard string cosmology. We construct solutions for vanishing and non-vanishing symmetry preserving dilaton potentials. The solutions assemble the pre- and post-big bang evolutions in one single line element. Our results show a smooth evolution from an anisotropic early stage to an isotropic phase without any special initial conditions in contrast to previous models. In addition, we demonstrate that the contraction of the dual space automatically leads to both an inflation phase and a decelerated expansion of the ordinary space during different evolution stages.
Stochastic inflation in a simple two-field model
Mollerach, S. ); Matarrese, S. ); Ortolan, A. ); Lucchin, F. )
1991-09-15
The dynamics of a nondominating scalar field during inflation is considered in the framework of the stochastic approach where its motion and that of the inflaton are described by two coupled Langevin equations. Curvature perturbations induced by the inflaton make the problem that of a Brownian motion in a random medium. The associated Fokker-Planck equation is solved for a free massless field in a power-law inflation driven by an inflaton with an exponential potential: this simple model could describe the dynamics of the axion, or any other pseudoGoldstone boson, during inflation. In spite of being free, the field shows a highly non-Gaussian behavior on scales much larger than the present horizon; on observable scales it gives rise to isocurvature perturbations which are both essentially Gaussian and scale-free.
Status of dual control theory. [stochastic decision making
NASA Technical Reports Server (NTRS)
Tse, E.
1975-01-01
Theoretical studies of decision making and stochastic processes are discussed. Several approaches are described for an improved performing control method. It is shown that control performance is highly dependent on the knowledge of the unknown parameters in the system.
Nonlocal and quasilocal field theories
NASA Astrophysics Data System (ADS)
Tomboulis, E. T.
2015-12-01
We investigate nonlocal field theories, a subject that has attracted some renewed interest in connection with nonlocal gravity models. We study, in particular, scalar theories of interacting delocalized fields, the delocalization being specified by nonlocal integral kernels. We distinguish between strictly nonlocal and quasilocal (compact support) kernels and impose conditions on them to insure UV finiteness and unitarity of amplitudes. We study the classical initial value problem for the partial integro-differential equations of motion in detail. We give rigorous proofs of the existence but accompanying loss of uniqueness of solutions due to the presence of future, as well as past, "delays," a manifestation of acausality. In the quantum theory we derive a generalization of the Bogoliubov causality condition equation for amplitudes, which explicitly exhibits the corrections due to nonlocality. One finds that, remarkably, for quasilocal kernels all acausal effects are confined within the compact support regions. We briefly discuss the extension to other types of fields and prospects of such theories.
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Oizumi, Ryo; Kuniya, Toshikazu; Enatsu, Yoichi
2016-01-01
Despite the fact that density effects and individual differences in life history are considered to be important for evolution, these factors lead to several difficulties in understanding the evolution of life history, especially when population sizes reach the carrying capacity. r/K selection theory explains what types of life strategies evolve in the presence of density effects and individual differences. However, the relationship between the life schedules of individuals and population size is still unclear, even if the theory can classify life strategies appropriately. To address this issue, we propose a few equations on adaptive life strategies in r/K selection where density effects are absent or present. The equations detail not only the adaptive life history but also the population dynamics. Furthermore, the equations can incorporate temporal individual differences, which are referred to as internal stochasticity. Our framework reveals that maximizing density effects is an evolutionarily stable strategy related to the carrying capacity. A significant consequence of our analysis is that adaptive strategies in both selections maximize an identical function, providing both population growth rate and carrying capacity. We apply our method to an optimal foraging problem in a semelparous species model and demonstrate that the adaptive strategy yields a lower intrinsic growth rate as well as a lower basic reproductive number than those obtained with other strategies. This study proposes that the diversity of life strategies arises due to the effects of density and internal stochasticity. PMID:27336169
Field-theory methods in coagulation theory
Lushnikov, A. A.
2011-08-15
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W(Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = (n{sub 1}, n{sub 2}, ..., n{sub g}, ...), where n{sub g} is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional {Psi} for the probability W(Q, t). The time evolution of {Psi} is described by an equation that is similar to the Schroedinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Field-theory methods in coagulation theory
NASA Astrophysics Data System (ADS)
Lushnikov, A. A.
2011-08-01
Coagulating systems are systems of chaotically moving particles that collide and coalesce, producing daughter particles of mass equal to the sum of the masses involved in the respective collision event. The present article puts forth basic ideas underlying the application of methods of quantum-field theory to the theory of coagulating systems. Instead of the generally accepted treatment based on the use of a standard kinetic equation that describes the time evolution of concentrations of particles consisting of a preset number of identical objects (monomers in the following), one introduces the probability W( Q, t) to find the system in some state Q at an instant t for a specific rate of transitions between various states. Each state Q is characterized by a set of occupation numbers Q = { n 1, n 2, ..., n g , ...}, where n g is the total number of particles containing precisely g monomers. Thereupon, one introduces the generating functional Ψ for the probability W( Q, t). The time evolution of Ψ is described by an equation that is similar to the Schrödinger equation for a one-dimensional Bose field. This equation is solved exactly for transition rates proportional to the product of the masses of colliding particles. It is shown that, within a finite time interval, which is independent of the total mass of the entire system, a giant particle of mass about the mass of the entire system may appear in this system. The particle in question is unobservable in the thermodynamic limit, and this explains the well-known paradox of mass-concentration nonconservation in classical kinetic theory. The theory described in the present article is successfully applied in studying the time evolution of random graphs.
Exceptional field theory: SL(5)
NASA Astrophysics Data System (ADS)
Musaev, Edvard T.
2016-02-01
In this work the exceptional field theory formulation of supergravity with SL (5) gauge group is considered. This group appears as a U-duality group of D = 7 maximal supergravity. In the formalism presented the hidden global duality group is promoted into a gauge group of a theory in dimensions 7+number of extended directions. This work is a continuation of the series of works for E 8,7,6 , SO (5 , 5) and SL (3) × SL (2) duality groups.
Fluid Stochastic Petri Nets: Theory, Applications, and Solution
NASA Technical Reports Server (NTRS)
Horton, Graham; Kulkarni, Vidyadhar G.; Nicol, David M.; Trivedi, Kishor S.
1996-01-01
In this paper we introduce a new class of stochastic Petri nets in which one or more places can hold fluid rather than discrete tokens. We define a class of fluid stochastic Petri nets in such a way that the discrete and continuous portions may affect each other. Following this definition we provide equations for their transient and steady-state behavior. We present several examples showing the utility of the construct in communication network modeling and reliability analysis, and discuss important special cases. We then discuss numerical methods for computing the transient behavior of such nets. Finally, some numerical examples are presented.
Testing Stochastic Models for Climate Field Reconstructions using Instrumental Data
NASA Astrophysics Data System (ADS)
Werner, J.; Toreti, A.; Luterbacher, J.
2012-12-01
Over the last decades, several different methods have been used to reconstruct past climatic change. These methods consist of an - often statistical - model and a related inference step. While recently a lot of the discussion has been focused on the latter (Smerdon et al. 2011, Christiansen et al. 2011), we here turn to the modelling part. A series of recent pseudoproxy experiments (PPE) focused on climate field reconstructions (Tingley+Huybers 2010a,b; Werner et al. 2012) has used Bayesian inference together with a localized stochastic description of the spatio-temporal evolution of climate field variables: Rather than using large patterns over the full spatial domain to describe the climate field variables, local temporal evolution and spatial coherence were modelled directly. While the stochastic model, a multivariate AR(1) process, was based on few simple assumptions it could nevertheless reconstruct most of the climate variability in the used dataset. Here we show how such a simple localized model could be derived from available observational data or at least be validated using the Kramers-Moyal-Expansion (KME). While KME often can require large amounts of data, we show that at least some results are stable in the context of PPEs with respect to data availability. Finally we apply this method to real world climate data from the CRU and the Global Historical Climate Network (GHCN) to arrive at a suitable model for European gridded mean summer temperature reconstructions. Smerdon J.E. et al. JClim 24, 1284-1309 (2011) Tingley M.P. and Huybers P. JClim 10, 2759-2781, 2782-2800 (2010a,b) Christiansen, B. and Ljundqvist, F.C. JClim 24, 6013-6034 (2011) Werner J.P. et al. JClim accepted (2012)
NASA Astrophysics Data System (ADS)
Sato, Masanori; Matsubara, Takahiko
2013-06-01
It is crucial to understand and model a behavior of galaxy biasing for future ambitious galaxy redshift surveys. Using 40 large cosmological N-body simulations for a standard ΛCDM cosmology, we study the cross-correlation coefficient between matter and the halo density field, which is an indicator of the stochasticity of bias, over a wide redshift range 0≤z≤3. The cross-correlation coefficient is important to extract information on the matter density field, e.g., by combining galaxy clustering and galaxy-galaxy lensing measurements. We compare the simulation results with integrated perturbation theory (iPT) proposed by one of the present authors and standard perturbation theory combined with a phenomenological model of local bias. The cross-correlation coefficient derived from the iPT agrees with N-body simulation results down to r˜15(10)h-1Mpc within 0.5 (1.0)% for all redshifts and halo masses we consider. The standard perturbation theory with local bias does not explain complicated behaviors on quasilinear scales at low redshifts, while roughly reproduces the general behavior of the cross-correlation coefficient on fully nonlinear scales. The iPT is powerful to predict the cross-correlation coefficient down to quasilinear regimes with a high precision.
The adhesion model as a field theory for cosmological clustering
Rigopoulos, Gerasimos
2015-01-01
The adhesion model has been proposed in the past as an improvement of the Zel'dovich approximation, providing a good description of the formation of the cosmic web. We recast the model as a field theory for cosmological large scale structure, adding a stochastic force to account for power generated from very short, highly non-linear scales that is uncorrelated with the initial power spectrum. The dynamics of this Stochastic Adhesion Model (SAM) is reminiscent of the well known Kardar-Parisi-Zhang equation with the difference that the viscosity and the noise spectrum are time dependent. Choosing the viscosity proportional to the growth factor D restricts the form of noise spectrum through a 1-loop renormalization argument. For this choice, the SAM field theory is renormalizable to one loop. We comment on the suitability of this model for describing the non-linear regime of the CDM power spectrum and its utility as a relatively simple approach to cosmological clustering.
An introduction to stochastic control theory, path integrals and reinforcement learning
NASA Astrophysics Data System (ADS)
Kappen, Hilbert J.
2007-02-01
Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory and I give an overview of the possible application of control theory to the modeling of animal behavior and learning. I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral or by MC sampling. In this control formalism the central concept of cost-to-go becomes a free energy and methods and concepts from statistical physics can be readily applied.
Stochastic Soil Moisture Estimation and Forecasting for Irrigated Fields
NASA Astrophysics Data System (ADS)
Aboitiz, Martin; Labadie, John W.; Heermann, Dale F.
1986-02-01
A methodology is developed for estimating and forecasting soil water depletion and crop evapotranspiration, with explicit consideration of modeling errors and stochastic inputs. The water balance of an irrigated field and a time series model for reference crop evapotranspiration are formulated in state-space form, with soil moisture depletion and reference evapotranspiration as state variables. The Kalman filter is used to generate estimates and forecasts of the state variables, together with statistical information on their associated errors. Model calibration and validity tests are performed with two independent data sets from locations in Colorado. Each set includes several years of reference crop evapotranspiration data calculated from climatological observations, one season of soil moisture measurements, and concurrent irrigation applications. The estimates, forecasts, and error covariance information provided by the model can allow irrigation decisions to be made with explicit consideration of the inherent risks of crop damage or failure under limitations in water, energy, labor, and capital.
Field theory for string fluids
NASA Astrophysics Data System (ADS)
Schubring, Daniel; Vanchurin, Vitaly
2015-08-01
We develop a field theory description of nondissipative string fluids and construct an explicit mapping between field theory degrees of freedom and hydrodynamic variables. The theory generalizes both a perfect particle fluid and pressureless string fluid to what we call a perfect string fluid. Ideal magnetohydrodynamics is shown to be an example of the perfect string fluid whose equations of motion can be obtained from a particular choice of the Lagrangian. The Lagrangian framework suggests a straightforward extension of the perfect string fluid to more general anisotropic fluids describing higher dimensional branes such as domain walls. Other modifications of the Lagrangian are discussed which may be useful in describing relativistic superfluids and fluids containing additional currents.
Introduction to string theory and conformal field theory
Belavin, A. A. Tarnopolsky, G. M.
2010-05-15
A concise survey of noncritical string theory and two-dimensional conformal field theory is presented. A detailed derivation of a conformal anomaly and the definition and general properties of conformal field theory are given. Minimal string theory, which is a special version of the theory, is considered. Expressions for the string susceptibility and gravitational dimensions are derived.
Libor at crossroads: Stochastic switching detection using information theory quantifiers
NASA Astrophysics Data System (ADS)
Bariviera, Aurelio F.; Guercio, M. Belén; Martinez, Lisana B.; Rosso, Osvaldo A.
2016-07-01
This paper studies the 28 time series of Libor rates, classified in seven maturities and four currencies), during the last 14 years. The analysis was performed using a novel technique in financial economics: the Complexity-Entropy Causality Plane. This planar representation allows the discrimination of different stochastic and chaotic regimes. Using a temporal analysis based on moving windows, this paper unveals an abnormal movement of Libor time series arround the period of the 2007 financial crisis. This alteration in the stochastic dynamics of Libor is contemporary of what press called "Libor scandal", i.e. the manipulation of interest rates carried out by several prime banks. We argue that our methodology is suitable as a market watch mechanism, as it makes visible the temporal redution in informational efficiency of the market.
Robust synthetic biology design: stochastic game theory approach
Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching
2009-01-01
Motivation: Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. Results: A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi–Sugeno (T–S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. Availability: http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf Contact: bschen@ee.nthu.edu.tw Supplementary information: Supplementary data are available at Bioinformatics online. PMID:19435742
Modelling baryon acoustic oscillations with perturbation theory and stochastic halo biasing
NASA Astrophysics Data System (ADS)
Kitaura, Francisco-Shu; Yepes, Gustavo; Prada, Francisco
2014-03-01
In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel PATCHY code. In particular, we use Augmented Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution - including an additional parameter - to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ˜ 1 h Mpc-1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ˜ 0.4 h Mpc-1. These results indicate the need to account for an accurate
Nonlinear analysis of the cooperation of strategic alliances through stochastic catastrophe theory
NASA Astrophysics Data System (ADS)
Xu, Yan; Hu, Bin; Wu, Jiang; Zhang, Jianhua
2014-04-01
The excitation intervention of strategic alliance may change with the changes in the parameters of circumstance (e.g., external alliance tasks). As a result, the stable cooperation between members may suffer a complete unplanned betrayal at last. However, current perspectives on strategic alliances cannot adequately explain this transition mechanism. This study is a first attempt to analyze this nonlinear phenomenon through stochastic catastrophe theory (SCT). A stochastic dynamics model is constructed based on the cooperation of strategic alliance from the perspective of evolutionary game theory. SCT explains the discontinuous changes caused by the changes in environmental parameters. Theoretically, we identify conditions where catastrophe can occur in the cooperation of alliance members.
Variational methods for field theories
Ben-Menahem, S.
1986-09-01
Four field theory models are studied: Periodic Quantum Electrodynamics (PQED) in (2 + 1) dimensions, free scalar field theory in (1 + 1) dimensions, the Quantum XY model in (1 + 1) dimensions, and the (1 + 1) dimensional Ising model in a transverse magnetic field. The last three parts deal exclusively with variational methods; the PQED part involves mainly the path-integral approach. The PQED calculation results in a better understanding of the connection between electric confinement through monopole screening, and confinement through tunneling between degenerate vacua. This includes a better quantitative agreement for the string tensions in the two approaches. Free field theory is used as a laboratory for a new variational blocking-truncation approximation, in which the high-frequency modes in a block are truncated to wave functions that depend on the slower background modes (Boron-Oppenheimer approximation). This ''adiabatic truncation'' method gives very accurate results for ground-state energy density and correlation functions. Various adiabatic schemes, with one variable kept per site and then two variables per site, are used. For the XY model, several trial wave functions for the ground state are explored, with an emphasis on the periodic Gaussian. A connection is established with the vortex Coulomb gas of the Euclidean path integral approach. The approximations used are taken from the realms of statistical mechanics (mean field approximation, transfer-matrix methods) and of quantum mechanics (iterative blocking schemes). In developing blocking schemes based on continuous variables, problems due to the periodicity of the model were solved. Our results exhibit an order-disorder phase transition. The transfer-matrix method is used to find a good (non-blocking) trial ground state for the Ising model in a transverse magnetic field in (1 + 1) dimensions.
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.« less
A Lagrangian effective field theory
Vlah, Zvonimir; White, Martin; Aviles, Alejandro
2015-09-02
We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher z the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. Furthermore, all the perturbative models fare better than linear theory.
Renormalized field theory of collapsing directed randomly branched polymers.
Janssen, Hans-Karl; Wevelsiep, Frank; Stenull, Olaf
2009-10-01
We present a dynamical field theory for directed randomly branched polymers and in particular their collapse transition. We develop a phenomenological model in the form of a stochastic response functional that allows us to address several interesting problems such as the scaling behavior of the swollen phase and the collapse transition. For the swollen phase, we find that by choosing model parameters appropriately, our stochastic functional reduces to the one describing the relaxation dynamics near the Yang-Lee singularity edge. This corroborates that the scaling behavior of swollen branched polymers is governed by the Yang-Lee universality class as has been known for a long time. The main focus of our paper lies on the collapse transition of directed branched polymers. We show to arbitrary order in renormalized perturbation theory with epsilon expansion that this transition belongs to the same universality class as directed percolation. PMID:19905335
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Stochastic systems with delay: Perturbation theory for second order statistics
NASA Astrophysics Data System (ADS)
Frank, T. D.
2016-03-01
Within the framework of delay Fokker-Planck equations, a perturbation theoretical method is developed to determine second-order statistical quantities such as autocorrelation functions for stochastic systems with delay. Two variants of the perturbation theoretical approach are presented. The first variant is based on a non-local Fokker-Planck operator. The second variant requires to solve a Fokker-Planck equation with source term. It is shown that the two variants yield consistent results. The perturbation theoretical approaches are applied to study negative autocorrelations that are induced by feedback delays and mediated by the strength of the fluctuating forces that act on the feedback systems.
Topological field theory of dynamical systems
Ovchinnikov, Igor V.
2012-09-15
Here, it is shown that the path-integral representation of any stochastic or deterministic continuous-time dynamical model is a cohomological or Witten-type topological field theory, i.e., a model with global topological supersymmetry (Q-symmetry). As many other supersymmetries, Q-symmetry must be perturbatively stable due to what is generically known as non-renormalization theorems. As a result, all (equilibrium) dynamical models are divided into three major categories: Markovian models with unbroken Q-symmetry, chaotic models with Q-symmetry spontaneously broken on the mean-field level by, e.g., fractal invariant sets (e.g., strange attractors), and intermittent or self-organized critical (SOC) models with Q-symmetry dynamically broken by the condensation of instanton-antiinstanton configurations (earthquakes, avalanches, etc.) SOC is a full-dimensional phase separating chaos and Markovian dynamics. In the deterministic limit, however, antiinstantons disappear and SOC collapses into the 'edge of chaos.' Goldstone theorem stands behind spatio-temporal self-similarity of Q-broken phases known under such names as algebraic statistics of avalanches, 1/f noise, sensitivity to initial conditions, etc. Other fundamental differences of Q-broken phases is that they can be effectively viewed as quantum dynamics and that they must also have time-reversal symmetry spontaneously broken. Q-symmetry breaking in non-equilibrium situations (quenches, Barkhausen effect, etc.) is also briefly discussed.
Stochastic analysis of a field-scale unsaturated transport experiment
NASA Astrophysics Data System (ADS)
Severino, G.; Comegna, A.; Coppola, A.; Sommella, A.; Santini, A.
2010-10-01
Modelling of field-scale transport of chemicals is of deep interest to public as well as private sectors, and it represents an area of active theoretical research in many environmentally-based disciplines. However, the experimental data needed to validate field-scale transport models are very limited due to the numerous logistic difficulties that one faces out. In the present paper, the migration of a tracer (Cl -) was monitored during its movement in the unsaturated zone beneath the surface of 8 m × 50 m sandy soil. Under flux-controlled, steady-state water flow ( Jw = 10 mm/day) was achieved by bidaily sprinkler irrigation. A pulse of 105 g/m 2 KCl was applied uniformly to the surface, and subsequently leached downward by the same (chloride-free) flux Jw over the successive two months. Chloride concentration monitoring was carried out in seven measurement campaigns (each one corresponding to a given time) along seven (parallel) transects. The mass recovery was near 100%, therefore underlining the very good-quality of the concentration data-set. The chloride concentrations are used to test two field-scale models of unsaturated transport: (i) the Advection-Dispersion Equation (ADE), which models transport far from the zone of solute entry, and (ii) the Stochastic- Convective Log- normal (CLT) transfer function model, which instead accounts for transport near the release zone. Both the models provided an excellent representation of the solute spreading at z > 0.45 m (being z = 0.45 m the calibration depth). As a consequence, by the depth z ≈ 50 cm one can regard transport as Fickian. The ADE model dramatically underestimates solute spreading at shallow depths. This is due to the boundary effects which are not captured by the ADE. The CLT model appears to be a more robust tool to mimic transport at every depth.
Rearranging Pionless Effective Field Theory
Martin Savage; Silas Beane
2001-11-19
We point out a redundancy in the operator structure of the pionless effective field theory which dramatically simplifies computations. This redundancy is best exploited by using dibaryon fields as fundamental degrees of freedom. In turn, this suggests a new power counting scheme which sums range corrections to all orders. We explore this method with a few simple observables: the deuteron charge form factor, n p -> d gamma, and Compton scattering from the deuteron. Higher dimension operators involving electroweak gauge fields are not renormalized by the s-wave strong interactions, and therefore do not scale with inverse powers of the renormalization scale. Thus, naive dimensional analysis of these operators is sufficient to estimate their contribution to a given process.
Modern Quantum Field Theory II - Proceeeings of the International Colloquium
NASA Astrophysics Data System (ADS)
Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.
1995-08-01
The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory
Stochastic Models of Tropical Rain-Rate Fields
NASA Technical Reports Server (NTRS)
Bell, Thomas L.
2003-01-01
Because of the extreme variability of rain rate in space and time and the difficulties with remote sensing methods of measuring rain rates, accurate determination of rainfall over large areas and time periods has long been a problem for hydrologists, meteorogists, and climatologists. A number of statistical models of rain have been developed in order to investigate the impact of rain variability on satellite remote sensing methods, validation of satellite rain products, and generation of rain maps with accompanying error estimates. These models may be useful in examining 'sub-grid scale' issues in representing precipitation in numerical mdoels. A stochastic model will first be described which can generate time-dependent high-resolution spatial rain fields with space and time correlations similar to those seen in rain data, as well as representing the presence of areas with zero rain rate and log-normally distributed rain rates where there is rain. A simpler model derived from this, formulated in the spectral domain, seems to imply fractal-like rain statistics at small scales when fit to rain data.
Theory Learning as Stochastic Search in the Language of Thought
ERIC Educational Resources Information Center
Ullman, Tomer D.; Goodman, Noah D.; Tenenbaum, Joshua B.
2012-01-01
We present an algorithmic model for the development of children's intuitive theories within a hierarchical Bayesian framework, where theories are described as sets of logical laws generated by a probabilistic context-free grammar. We contrast our approach with connectionist and other emergentist approaches to modeling cognitive development. While…
Rapid change of field line connectivity and reconnection in stochastic magnetic fields
Huang, Yi-Min; Bhattacharjee, A.; Boozer, Allen H.
2014-10-01
Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, and hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideally stable force-free equilibrium, the system is allowed to undergo resistive relaxation. Two distinct phases are found in the process of resistive relaxation. During the quasi-static phase, rapid change of field line connectivity and strong induced flow are found in regions of high field line exponentiation. However, although the field line connectivity of individual field lines can change rapidly, the overall pattern of field line mapping appears to deform gradually. From this perspective, field line exponentiation appears to cause enhanced diffusion rather than reconnection. In some cases, resistive quasi-static evolution can cause the ideally stable initial equilibrium to cross a stability threshold, leading to formation of intense current filaments and rapid change of field line mapping into a qualitatively different pattern. It is in this onset phase that the change of field line connectivity is more appropriately designated as magnetic reconnection. Our results show that rapid change of field line connectivity appears to be a necessary, but not a sufficient condition for fast reconnection.
A kinetic theory for age-structured stochastic birth-death processes
NASA Astrophysics Data System (ADS)
Chou, Tom; Greenman, Chris
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates. Conversely, current theories that include size-dependent population dynamics (e.g., carrying capacity) cannot be easily extended to take into account age-dependent birth and death rates. In this paper, we present a systematic derivation of a new fully stochastic kinetic theory for interacting age-structured populations. By defining multiparticle probability density functions, we derive a hierarchy of kinetic equations for the stochastic evolution of an aging population undergoing birth and death. We show that the fully stochastic age-dependent birth-death process precludes factorization of the corresponding probability densities, which then must be solved by using a BBGKY-like hierarchy. Our results generalize both deterministic models and existing master equation approaches by providing an intuitive and efficient way to simultaneously model age- and population-dependent stochastic dynamics applicable to the study of demography, stem cell dynamics, and disease evolution. NSF.
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Stochastic mean-field dynamics for fermions in the weak-coupling limit
Lacroix, Denis
2006-04-15
Assuming that the effect of the residual interaction beyond the mean field is weak and has a short memory time, two approximate treatments of correlation in fermionic systems by means of the Markovian quantum jump are presented. A simplified scenario for the introduction of fluctuations beyond the mean field is presented first. In this theory, part of the quantum correlations between the residual interaction and the one-body density matrix are neglected and jumps occur between many-body densities formed of pairs of states D={phi}{sub a}><{phi}{sub b}/<{phi}{sub b}{phi}{sub a}>, where {phi}{sub a}> and {phi}{sub b}> are antisymmetrized products of single-particle states. The underlying stochastic mean-field theory is discussed and is applied to the monopole vibration of a spherical {sup 40}Ca nucleus under the influence of a statistical ensemble of two-body contact interactions. This framework is however too simplistic to account for both fluctuation and dissipation. In the second part of this work, an alternative quantum jump method is obtained without making the approximation on quantum correlations. By restricting to two-particle-two-hole residual interactions, the evolution of the one-body density matrix of a correlated system is transformed into a Lindblad equation. The associated dissipative dynamics can be simulated by quantum jumps between densities written as D=|{phi}><{phi}|, where |{phi}> is a normalized Slater determinant. The associated stochastic Schroedinger equation for single-particle wave functions is given.
Topics in low-dimensional field theory
Crescimanno, M.J.
1991-04-30
Conformal field theory is a natural tool for understanding two- dimensional critical systems. This work presents results in the lagrangian approach to conformal field theory. The first sections are chiefly about a particular class of field theories called coset constructions and the last part is an exposition of the connection between two-dimensional conformal theory and a three-dimensional gauge theory whose lagrangian is the Chern-Simons density.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Effective field theory in nuclear physics
Martin J. Savage
2000-12-12
I review recent developments in the application of effective field theory to nuclear physics. Emphasis is placed on precision two-body calculations and efforts to formulate the nuclear shell model in terms of an effective field theory.
Effective field theory, past and future
NASA Astrophysics Data System (ADS)
Weinberg, Steven
2016-02-01
I reminisce about the early development of effective field theories of the strong interactions, comment briefly on some other applications of effective field theories, and then take up the idea that the Standard Model and General Relativity are the leading terms in an effective field theory. Finally, I cite recent calculations that suggest that the effective field theory of gravitation and matter is asymptotically safe.
Vertex operator algebras and conformal field theory
Huang, Y.Z. )
1992-04-20
This paper discusses conformal field theory, an important physical theory, describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. The study of conformal field theory will deepen the understanding of these theories and will help to understand string theory conceptually. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and Lie groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera and elliptic cohomology, Calabi-Yau manifolds, tensor categories, and knot theory, are revealed in the study of conformal field theory. It is therefore believed that the study of the mathematics involved in conformal field theory will ultimately lead to new mathematical structures which would be important to both mathematics and physics.
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
NASA Astrophysics Data System (ADS)
Koide, T.; Kodama, T.
2015-09-01
The stochastic variational method (SVM) is the generalization of the variational approach to systems described by stochastic variables. In this paper, we investigate the applicability of SVM as an alternative field-quantization scheme, by considering the complex Klein-Gordon equation. There, the Euler-Lagrangian equation for the stochastic field variables leads to the functional Schrödinger equation, which can be interpreted as the Euler (ideal fluid) equation in the functional space. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, e.g., in the definition of Noether charges.
Kalyuzhny, Michael; Kadmon, Ronen; Shnerb, Nadav M
2015-06-01
Understanding the forces shaping ecological communities is crucial to basic science and conservation. Neutral theory has made considerable progress in explaining static properties of communities, like species abundance distributions (SADs), with a simple and generic model, but was criticised for making unrealistic predictions of fundamental dynamic patterns and for being sensitive to interspecific differences in fitness. Here, we show that a generalised neutral theory incorporating environmental stochasticity may resolve these limitations. We apply the theory to real data (the tropical forest of Barro Colorado Island) and demonstrate that it much better explains the properties of short-term population fluctuations and the decay of compositional similarity with time, while retaining the ability to explain SADs. Furthermore, the predictions are considerably more robust to interspecific fitness differences. Our results suggest that this integration of niches and stochasticity may serve as a minimalistic framework explaining fundamental static and dynamic characteristics of ecological communities. PMID:25903067
Thermodynamic and stochastic theory of hydrodynamic and power-producing processes
Ross, J.
1992-09-16
Thermodynamics of the transport processes of diffusion, thermal conduction, and viscous flow at a macroscopic level are developed for the simplest cases of one-dimensional transport in fluids for individual linear and nonlinear processes approaching a stationary non-equilibrium state. Formulation has started of thermodynamic and stochastic theory of combinations of transport processes. Global thermodynamic and stochastic theory of open chemical systems frar from equilibrium is continued with analysis of a broad class of isothermal, multicomponent reaction mechanisms with multiple steady states with assumed local equilibrium. Stationary solutions are obtained of the master equation for single and multi-intermediate autocatalytic chemical systems. A kinetic potential is identified that governs the deterministic time evolution of coupled tank reactors. A second-order response theory was developed to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor.
On a theory of stability for nonlinear stochastic chemical reaction networks
NASA Astrophysics Data System (ADS)
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-05-01
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.
On a theory of stability for nonlinear stochastic chemical reaction networks
Smadbeck, Patrick; Kaznessis, Yiannis N.
2015-05-14
We present elements of a stability theory for small, stochastic, nonlinear chemical reaction networks. Steady state probability distributions are computed with zero-information (ZI) closure, a closure algorithm that solves chemical master equations of small arbitrary nonlinear reactions. Stochastic models can be linearized around the steady state with ZI-closure, and the eigenvalues of the Jacobian matrix can be readily computed. Eigenvalues govern the relaxation of fluctuation autocorrelation functions at steady state. Autocorrelation functions reveal the time scales of phenomena underlying the dynamics of nonlinear reaction networks. In accord with the fluctuation-dissipation theorem, these functions are found to be congruent to response functions to small perturbations. Significant differences are observed in the stability of nonlinear reacting systems between deterministic and stochastic modeling formalisms.
Nonlocal stochastic mixing-length theory and the velocity profile in the turbulent boundary layer
NASA Astrophysics Data System (ADS)
Dekker, H.; de Leeuw, G.; Maassen van den Brink, A.
1995-02-01
Turbulence mixing by finite size eddies will be treated by means of a novel formulation of nonlocal K-theory, involving sample paths and a stochastic closure hypothesis, which implies a well defined recipe for the calculation of sampling and transition rates. The connection with the general theory of stochastic processes will be established. The relation with other nonlocal turbulence models (e.g. transilience and spectral diffusivity theory) is also discussed. Using an analytical sampling rate model (satisfying exchange) the theory is applied to the boundary layer (using a scaling hypothesis), which maps boundary layer turbulence mixing of scalar densities onto a nondiffusive (Kubo-Anderson or kangaroo) type stochastic process. The resulting transpport equation for longitudinal momentum P x ≡ ϱ U is solved for a unified description of both the inertial and the viscous sublayer including the crossover. With a scaling exponent ε ≈ 0.58 (while local turbulence would amount to ε → ∞) the velocity profile U+ = ƒ(y +) is found to be in excellent agreement with the experimental data. Inter alia (i) the significance of ε as a turbulence Cantor set dimension, (ii) the value of the integration constant in the logarithmic region (i.e. if y+ → ∞), (iii) linear timescaling, and (iv) finite Reynolds number effects will be investigated. The (analytical) predictions of the theory for near-wall behaviour (i.e. if y+ → 0) of fluctuating quantities also perfectly agree with recent direct numerical simulations.
Linear kinetic theory and particle transport in stochastic mixtures
Pomraning, G.C.
1995-12-31
We consider the formulation of linear transport and kinetic theory describing energy and particle flow in a random mixture of two or more immiscible materials. Following an introduction, we summarize early and fundamental work in this area, and we conclude with a brief discussion of recent results.
Instantons in Lifshitz field theories
NASA Astrophysics Data System (ADS)
Fujimori, Toshiaki; Nitta, Muneto
2015-10-01
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, we study anisotropic BPS baby Skyrmion 1+1 dimensions and BPS Skyrmion in 2+1 dimensions, for which we take Kähler 1-form and the Wess-Zumiono-Witten term as the superpotentials, respectively, and an anisotropic generalized Yang-Mills instanton in 4 + 1 dimensions, for which we take the Chern-Simons term as the superpotential.
Non-Perturbative Field Theories.
NASA Astrophysics Data System (ADS)
Stephenson, David
Available from UMI in association with The British Library. Requires signed TDF. Some non-perturbative aspects of field theories are studied by applying lattice gauge theory techniques. The low-lying hadronic mass spectrum is calculated numerically using quenched lattice quantum chromodynamics. The results of large numerical simulations performed on a distributed array processor are presented and analysed. Particular emphasis is stressed upon the understanding of systematic and statistical errors in the calculation. In addition, the pion decay constant and the chiral condensate are evaluated. An attempt is made to relate the numerical findings to the experimentally measured quantities. A pioneering attempt to understand Yukawa couplings is discussed. A toy Fermion-Higgs system is studied numerically on a transputer array. Dynamical fermions are included in the investigation of the behavior of the system over a wide range of Yukawa couplings. A phase diagram is found for the model which shows evidence of spontaneous chiral symmetry breaking transitions. Extensions of the model are discussed together some speculations concerning the behaviour of Yukawa couplings in general. The possibility of using the lattice as a model for space-time is investigated by studying the propagation of particles on a fractal lattice. In addition, the use of truncated fractals as novel regulators is studied numerically in the hope that the problem of fermion doubling will be alleviated.
Group field theory with noncommutative metric variables.
Baratin, Aristide; Oriti, Daniele
2010-11-26
We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action. PMID:21231377
Diffusion and stochastic island generation in the magnetic field line random walk
Vlad, M.; Spineanu, F.
2014-08-10
The cross-field diffusion of field lines in stochastic magnetic fields described by the 2D+slab model is studied using a semi-analytic statistical approach, the decorrelation trajectory method. We show that field line trapping and the associated stochastic magnetic islands strongly influence the diffusion coefficients, leading to dependences on the parameters that are different from the quasilinear and Bohm regimes. A strong amplification of the diffusion is produced by a small slab field in the presence of trapping. The diffusion regimes are determined and the corresponding physical processes are identified.
Stochastic perturbed systems: Theory and practice of Karman vortex streets
NASA Astrophysics Data System (ADS)
Holtfort, Joerg
1991-05-01
In the theory of randomly perturbed dynamical systems developed by Friedlin and Wentzell, the potential of a vectorfield is generalized to the so called quasipotential. For general nonlinear systems, the quasipotential turns out to be nondifferentiable along certain lines. These lines are investigated numerically for bistable systems with at least one limit cycle. It is found that even for strong nonlinearity, the quasipotential remains smooth in a finite neighborhood of the stable limit cycle. This formalism is used for the reconstruction of dynamical systems for measured time series. The method is successfully applied to velocity measurements in a Karman vortex street at Reynolds numbers 60 to 150.
Traveling wave solution of the Reggeon field theory
Peschanski, Robi
2009-05-15
We identify the nonlinear evolution equation in impact-parameter space for the 'Supercritical Pomeron' in Reggeon field theory as a two-dimensional stochastic Fisher-Kolmogorov-Petrovski-Piscounov equation. It exactly preserves unitarity and leads in its radial form to a high-energy traveling wave solution corresponding to a 'universal' behavior of the impact-parameter front profile of the elastic amplitude; its rapidity dependence and form depend only on one parameter, the noise strength, independently of the initial conditions and of the nonlinear terms restoring unitarity. Theoretical predictions are presented for the three typical distinct regimes corresponding to zero, weak, and strong noise.
Perturbative double field theory on general backgrounds
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Marques, Diego
2016-01-01
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the field fluctuations. We expand the generalized curvature scalar to cubic order in fluctuations and thereby determine the cubic action in a manifestly background covariant form. As a first application we specialize this theory to group manifold backgrounds, such as S U (2 )≃S3 with H -flux. In the full string theory this corresponds to a Wess-Zumino-Witten background CFT. Starting from closed string field theory, the cubic action around such backgrounds has been computed before by Blumenhagen, Hassler, and Lüst. We establish precise agreement with the cubic action derived from double field theory. This result confirms that double field theory is applicable to arbitrary curved background solutions, disproving assertions in the literature to the contrary.
Extension of Nelson's stochastic quantization to finite temperature using thermo field dynamics
NASA Astrophysics Data System (ADS)
Kobayashi, K.; Yamanaka, Y.
2011-08-01
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfies the position-momentum uncertainty relation at finite temperature.
Toward a gauge field theory of gravity.
NASA Astrophysics Data System (ADS)
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Effect of a stochastic electric field on plasma confinement in FTU
NASA Astrophysics Data System (ADS)
Martorelli, Roberto; Montani, Giovanni; Carlevaro, Nakia
2016-01-01
We discuss a stochastic model for the behavior of electrons in a magnetically confined plasma having axial symmetry. The aim of the work is to provide an explanation for the density limit observed in the Frascati Tokamak Upgrade (FTU) machine. The dynamical framework deals with an electron embedded in a stationary and uniform magnetic field and affected by an orthogonal random electric field. The behavior of the average plasma profile is determined by the appropriate Fokker-Planck equation associated to the considered model and the disruptive effects of the stochastic electric field are shown. The comparison between the addressed model and the experimental data allows to fix the relevant spatial scale of such a stochastic field. It is found to be of the order of the Tokamak micro-physics scale, i.e. few millimeters. Moreover, it is clarified how the diffusion process outlines a dependence on the magnetic field as ˜ B-3/2.
Homotopy Classification of Bosonic String Field Theory
NASA Astrophysics Data System (ADS)
Münster, Korbinian; Sachs, Ivo
2014-09-01
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories.
Towards weakly constrained double field theory
NASA Astrophysics Data System (ADS)
Lee, Kanghoon
2016-08-01
We show that it is possible to construct a well-defined effective field theory incorporating string winding modes without using strong constraint in double field theory. We show that X-ray (Radon) transform on a torus is well-suited for describing weakly constrained double fields, and any weakly constrained fields are represented as a sum of strongly constrained fields. Using inverse X-ray transform we define a novel binary operation which is compatible with the level matching constraint. Based on this formalism, we construct a consistent gauge transform and gauge invariant action without using strong constraint. We then discuss the relation of our result to the closed string field theory. Our construction suggests that there exists an effective field theory description for massless sector of closed string field theory on a torus in an associative truncation.
Singularity theory and N = 2 superconformal field theories
Warner, N.P.
1989-01-01
The N = 2 superconformal field theories that appear at the fixed points of the renormalization group flows of Landau-Ginsburg models are discussed. Some of the techniques of singularity theory are employed to deduce properties of these superconformal theories. These ideas are then used to deduce the relationship between Calabi-Yau compactifications and tensored discrete series models. The chiral rings of general N = 2 superconformal theories are also described. 14 refs.
Gauge anomalies in an effective field theory
Preskill, J. )
1991-09-01
A four-dimensional gauge theory with anomalous fermion content can be consistently quantized, provided that at least some gauge fields are permitted to have nonvanishing masses. Such a theory is nonrenormalizable; there is a maximal value of the ultraviolet cutoff {Lambda}, beyond which the locality of the theory breaks down. The maximal {Lambda} can be estimated in perturbation theory and has a qualitatively different character in Abelian and non-Abelian anomalous gauge theories.
Stochastic Ion Heating in a Field-reversed Configuration Geometry by Rotating Magnetic Fields
S.A. Cohen, A.S. Landsman, and A.H. Glasser
2007-06-25
Ion heating by application of rotating magnetic fields (RMF) to a prolate field-reversed configuration(FRC) is explored by analytical and numerical techniques. For odd-parity RMF (RMFo), perturbation analysis shows ions in figure-8 orbits gain energy at resonances of the RMFo frequency, ωR, with the figure-8 orbital frequency, ω. Since figure-8 orbits tend to gain the most energy from the RMF and are unlikely to escape in the cusp region (where most losses occur), they are optimal candidates for rapid stochastic heating, as compared to cyclotron and betatron orbits. Comparisons are made between heating caused by even- and odd-parity RMFs and between heating in currently operating and in reactor-scale FRC devices.
Two-point functions of quenched lattice QCD in Numerical Stochastic Perturbation Theory
Di Renzo, F.; Ilgenfritz, E.-M.; Perlt, H.; Schiller, A.; Torrero, C.
2011-05-23
We summarize the higher-loop perturbative computation of the ghost and gluon propagators in SU(3) Lattice Gauge Theory. Our final aim is to compare with results from lattice simulations in order to expose the genuinely non-perturbative content of the latter. By means of Numerical Stochastic Perturbation Theory we compute the ghost and gluon propagators in Landau gauge up to three and four loops. We present results in the infinite volume and a{yields}0 limits, based on a general fitting strategy.
Fluorescence microscopy image noise reduction using a stochastically-connected random field model
Haider, S. A.; Cameron, A.; Siva, P.; Lui, D.; Shafiee, M. J.; Boroomand, A.; Haider, N.; Wong, A.
2016-01-01
Fluorescence microscopy is an essential part of a biologist’s toolkit, allowing assaying of many parameters like subcellular localization of proteins, changes in cytoskeletal dynamics, protein-protein interactions, and the concentration of specific cellular ions. A fundamental challenge with using fluorescence microscopy is the presence of noise. This study introduces a novel approach to reducing noise in fluorescence microscopy images. The noise reduction problem is posed as a Maximum A Posteriori estimation problem, and solved using a novel random field model called stochastically-connected random field (SRF), which combines random graph and field theory. Experimental results using synthetic and real fluorescence microscopy data show the proposed approach achieving strong noise reduction performance when compared to several other noise reduction algorithms, using quantitative metrics. The proposed SRF approach was able to achieve strong performance in terms of signal-to-noise ratio in the synthetic results, high signal to noise ratio and contrast to noise ratio in the real fluorescence microscopy data results, and was able to maintain cell structure and subtle details while reducing background and intra-cellular noise. PMID:26884148
Logarithmic operators and logarithmic conformal field theories
NASA Astrophysics Data System (ADS)
Gurarie, Victor
2013-12-01
Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c = -2 and c = 0 logarithmic conformal field theories. c = 0 logarithmic conformal field theories are especially interesting since they describe some of the critical points of a variety of longstanding problems involving a two dimensional quantum particle moving in a spatially random potential, as well as critical two dimensional self-avoiding random walks and percolation. Lack of classification of logarithmic conformal field theories remains a major impediment to progress towards finding complete solutions to these problems.
Continuum regularization of quantum field theory
Bern, Z.
1986-01-01
Breit, Gupta, and Zaks made the first proposal for new gauge invariant nonperturbative regularization. The scheme is based on smearing in the fifth-time of the Langevin equation. An analysis of their stochastic regularization scheme for the case of scalar electrodynamics with the standard covariant gauge fixing is given. Their scheme is shown to preserve the masslessness of the photon and the tensor structure of the photon vacuum polarization at the one-loop level. Although stochastic regularization is viable in one-loop electrodynamics, difficulties arise which, in general, ruins the scheme. A successful covariant derivative scheme is discussed which avoids the difficulties encountered with the earlier stochastic regularization by fifth-time smearing. For QCD the regularized formulation is manifestly Lorentz invariant, gauge invariant, ghost free and finite to all orders. A vanishing gluon mass is explicitly verified at one loop. The method is designed to respect relevant symmetries, and is expected to provide suitable regularization for any theory of interest.
Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics
Burić, Nikola Popović, Duška B.; Radonjić, Milan; Prvanović, Slobodan
2014-04-15
A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. -- Highlights: •A novel theory of quantum–classical systems is developed. •Framework of quantum constrained dynamical systems is used. •A dynamical description of the measurement induced collapse is obtained.
One-dimensional random field Ising model and discrete stochastic mappings
Behn, U.; Zagrebnov, V.A.
1987-06-01
Previous results relating the one-dimensional random field Ising model to a discrete stochastic mapping are generalized to a two-valued correlated random (Markovian) field and to the case of zero temperature. The fractal dimension of the support of the invariant measure is calculated in a simple approximation and its dependence on the physical parameters is discussed.
Spencer, James S; Thom, Alex J W
2016-02-28
We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to r(s) = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities. PMID:26931682
Butler, T.; Graham, L.; Estep, D.; Westerink, J.J.
2015-01-01
The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed. PMID:25937695
Boson formulation of fermion field theories
Ha, Y.K.
1984-04-15
The nonperturbative connection between a canonical Fermi field and a canonical Bose field in two dimensions is developed and its validity verified according to the tenets of quantum field theory. We advocate the point of view that a boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. Many features of the massless theory, such as dynamical mass generation with asymptotic-freedom behavior, hidden chiral symmetry, and connections with models of apparently different internal symmetries, are readily transparent through such fermion-boson metamorphosis.
Three approaches to classical thermal field theory
NASA Astrophysics Data System (ADS)
Gozzi, E.; Penco, R.
2011-04-01
In this paper we study three different functional approaches to classical thermal field theory, which turn out to be the classical counterparts of three well-known different formulations of quantum thermal field theory: the closed-time path (CTP) formalism, the thermofield dynamics (TFD) and the Matsubara approach.
Descent relations in cubic superstring field theory
NASA Astrophysics Data System (ADS)
Aref'eva, I. Y.; Gorbachev, R.; Medvedev, P. B.; Rychkov, D. V.
2008-01-01
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations langleV2|V1rangle and langleV3|V1rangle in the NS fermionic string field theory in the κ and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
Observation of energetic electron confinement in a largely stochastic reversed-field pinch plasma
NASA Astrophysics Data System (ADS)
Clayton, D. J.; Chapman, B. E.; O'Connell, R.; Almagri, A. F.; Burke, D. R.; Forest, C. B.; Goetz, J. A.; Kaufman, M. C.; Bonomo, F.; Franz, P.; Gobbin, M.; Piovesan, P.
2010-01-01
Runaway electrons with energies >100 keV are observed with the appearance of an m =1 magnetic island in the core of otherwise stochastic Madison Symmetric Torus [Dexter et al., Fusion Technol. 19, 131 (1991)] reversed-field-pinch plasmas. The island is associated with the innermost resonant tearing mode, which is usually the largest in the m =1 spectrum. The island appears over a range of mode spectra, from those with a weakly dominant mode to those, referred to as quasi single helicity, with a strongly dominant mode. In a stochastic field, the rate of electron loss increases with electron parallel velocity. Hence, high-energy electrons imply a region of reduced stochasticity. The global energy confinement time is about the same as in plasmas without high-energy electrons or an island in the core. Hence, the region of reduced stochasticity must be localized. Within a numerical reconstruction of the magnetic field topology, high-energy electrons are substantially better confined inside the island, relative to the external region. Therefore, it is deduced that the island provides a region of reduced stochasticity and that the high-energy electrons are generated and well confined within this region.
E11 and exceptional field theory
NASA Astrophysics Data System (ADS)
Tumanov, Alexander G.; West, Peter
2016-04-01
We argue that the exceptional field theory is a truncation of the nonlinear realisation of the semi-direct product of E11 and its first fundamental as proposed in 2003. Evaluating the simple equations of the E11 approach, and using the commutators of the E11 algebra, we find the local variations of the fields of exceptional field theory after making a radical truncation. This procedure does not respect any of the higher level E11 symmetries and so these are lost. We suggest that the need for the section condition in the exceptional field theory could be a consequence of the truncation.
Introduction to conformal field theory and string theory
Dixon, L.J.
1989-12-01
These lectures are meant to provide a brief introduction to conformal field theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available, and most of these go in to much more detail than I will be able to here. 52 refs., 11 figs.
A Simple Stochastic Model for Generating Broken Cloud Optical Depth and Top Height Fields
NASA Technical Reports Server (NTRS)
Prigarin, Sergei M.; Marshak, Alexander
2007-01-01
A simple and fast algorithm for generating two correlated stochastic twodimensional (2D) cloud fields is described. The algorithm is illustrated with two broken cumulus cloud fields: cloud optical depth and cloud top height retrieved from Moderate Resolution Imaging Spectrometer (MODIS). Only two 2D fields are required as an input. The algorithm output is statistical realizations of these two fields with approximately the same correlation and joint distribution functions as the original ones. The major assumption of the algorithm is statistical isotropy of the fields. In contrast to fractals and the Fourier filtering methods frequently used for stochastic cloud modeling, the proposed method is based on spectral models of homogeneous random fields. For keeping the same probability density function as the (first) original field, the method of inverse distribution function is used. When the spatial distribution of the first field has been generated, a realization of the correlated second field is simulated using a conditional distribution matrix. This paper is served as a theoretical justification to the publicly available software that has been recently released by the authors and can be freely downloaded from http://i3rc.gsfc.nasa.gov/Public codes clouds.htm. Though 2D rather than full 3D, stochastic realizations of two correlated cloud fields that mimic statistics of given fields have proved to be very useful to study 3D radiative transfer features of broken cumulus clouds for better understanding of shortwave radiation and interpretation of the remote sensing retrievals.
Understanding conformal field theory through parafermions and Chern Simons theory
Hotes, S.A.
1992-11-19
Conformal field theories comprise a vast class of exactly solvable two dimensional quantum field theories. Conformal theories with an enlarged symmetry group, the current algebra symmetry, axe a key ingredient to possible string compactification models. The following work explores a Lagrangian approach to these theories. In the first part of this thesis, a large class of conformal theories, the so-called coset models, are derived semi-classically from a gauged version Of the Wess-Zumino-Witten functional. A non-local field transformation to the parafermionic field description is employed in the quantization procedure. Classically, these parafermionic fields satisfy non-trivial Poisson brackets, providing insight into the fractional spin nature of the conformal theory. The W-algebra symmetry is shown to appear naturally in this approach. In the second part of this thesis, the connection between the fusion algebra structure of Wess-Zumino-Witten models and the quantization of the Chern-Simons action on the torus is made explicit. The modular properties of the conformal model are also derived in this context, giving a natural demonstration of the Verlinde conjecture. The effects of background gauge fields and monopoles are also discussed.
Diffusion of test particles in stochastic magnetic fields in the percolative regime
Neuer, Marcus; Spatschek, Karl H.
2006-09-15
For stochastic magnetic flux functions with percolative contours the test particle transport is investigated. The calculations make use of the stochastic Liouville approach. They start from the so-called A-Langevin equations, including stochastic magnetic field components and binary collisions. Using the decorrelation trajectory method, a relation between the Lagrangian velocity correlation function and the Eulerian magnetic field correlation is derived and introduced into the Green-Kubo formalism. Finite Larmor radius effects are included. Interesting results are presented in the percolation regime corresponding to high Kubo numbers. Previous results are found to be limiting cases for small Kubo numbers. For different percolative scenarios the diffusion is analyzed and strong influences of the percolative structures on the transport scaling are found. The finite Larmor radius effects are discussed in detail. Numerical simulations of the A-Langevin equation confirm the semianalytical predictions.
Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.
Szabó-Solticzky, András; Berthouze, Luc; Kiss, Istvan Z; Simon, Péter L
2016-04-01
An adaptive network model using SIS epidemic propagation with link-type-dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models. PMID:26063525
Self-Averaging Stochastic Kohn-Sham Density-Functional Theory
NASA Astrophysics Data System (ADS)
Baer, Roi; Neuhauser, Daniel; Rabani, Eran
2013-09-01
We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. The fluctuations in the total energy per electron are guaranteed to decay to zero as the system size increases. This facilitates “self-averaging” which leads to the first ever report of sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus, is insensitive to its evasive sparseness, as demonstrated here for silicon nanocrystals. The formalism is not only appealing in terms of its promise to far push the limits of application of KS-DFT, but also represents a cognitive change in the way we think of electronic structure calculations as this stochastic theory seamlessly converges to the thermodynamic limit.
Failure of classical traffic flow theories: Stochastic highway capacity and automatic driving
NASA Astrophysics Data System (ADS)
Kerner, Boris S.
2016-05-01
In a mini-review Kerner (2013) it has been shown that classical traffic flow theories and models failed to explain empirical traffic breakdown - a phase transition from metastable free flow to synchronized flow at highway bottlenecks. The main objective of this mini-review is to study the consequence of this failure of classical traffic-flow theories for an analysis of empirical stochastic highway capacity as well as for the effect of automatic driving vehicles and cooperative driving on traffic flow. To reach this goal, we show a deep connection between the understanding of empirical stochastic highway capacity and a reliable analysis of automatic driving vehicles in traffic flow. With the use of simulations in the framework of three-phase traffic theory, a probabilistic analysis of the effect of automatic driving vehicles on a mixture traffic flow consisting of a random distribution of automatic driving and manual driving vehicles has been made. We have found that the parameters of automatic driving vehicles can either decrease or increase the probability of the breakdown. The increase in the probability of traffic breakdown, i.e., the deterioration of the performance of the traffic system can occur already at a small percentage (about 5%) of automatic driving vehicles. The increase in the probability of traffic breakdown through automatic driving vehicles can be realized, even if any platoon of automatic driving vehicles satisfies condition for string stability.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Fermion boson metamorphosis in field theory
Ha, Y.K.
1982-01-01
In two-dimensional field theories many features are especially transparent if the Fermi fields are represented by non-local expressions of the Bose fields. Such a procedure is known as boson representation. Bilinear quantities appear in the Lagrangian of a fermion theory transform, however, as simple local expressions of the bosons so that the resulting theory may be written as a theory of bosons. Conversely, a theory of bosons may be transformed into an equivalent theory of fermions. Together they provide a basis for generating many interesting equivalences between theories of different types. In the present work a consistent scheme for constructing a canonical Fermi field in terms of a real scalar field is developed and such a procedure is valid and consistent with the tenets of quantum field theory is verified. A boson formulation offers a unifying theme in understanding the structure of many theories. This is illustrated by the boson formulation of a multifermion theory with chiral and internal symmetries. The nature of dynamical generation of mass when the theory undergoes boson transmutation and the preservation of continuous chiral symmetry in the massive case are examined. The dynamics of the system depends to a great extent on the specific number of fermions and different models of the same system can have very different properties. Many unusual symmetries of the fermion theory, such as hidden symmetry, duality and triality symmetries, are only manifest in the boson formulation. The underlying connections between some models with U(N) internal symmetry and another class of fermion models built with Majorana fermions which have O(2N) internal symmetry are uncovered.
The Idea of a Stochastic Space-Time: Theory and Experiments
NASA Astrophysics Data System (ADS)
Consoli, Maurizio; Pluchino, Alessandro
Basic foundational aspects of both quantum physics and relativity suggest that space-time may have the fundamental stochastic nature of a turbulent fluid. After reviewing the basic theoretical motivations, we have compared this picture with the phenomenological pattern observed in the ether-drift experiments. To this end, we have performed numerical simulations in which the parameters of the oscopic Earth's cosmic motion are only used to fix the limiting boundaries for a microscopic velocity field which has instead an intrinsic stochastic nature. In this framework, both classical and modern experiments become consistent with the type of cosmic Earth's motion which today is used to describe the CMB anisotropy. The need for confirmations with a new generation of dedicated experiments is finally emphasized.
Temporal variability in a stochastic precipitation field simulator
NASA Astrophysics Data System (ADS)
Kolberg, Sjur
2016-04-01
The space-time statistics of short-term precipitation is studied for two cities in northern Europe, and related to radiosonde observations. The motivation is to construct the temporally varying parameters needed to drive a stochastic short-term precipitation generator. Moments, intermittency, semivariograms, temporal covariance and advection parameters need to be characterised in order to produce realistic scenario simulations for extreme value estimation at different scales. It is hoped that the temporal variability in these parameters can be related to radiosonde data. Hourly values from 46 precipitation stations within a 100*130 km2 region around Copenhagen during the period 1979-2012 is analysed. Bi-daily radiosonde profiles are present from 1969 to 2006. These soundings (vertical profiles of temperature, dew point and wind vector) describe the atmospheric moisture content and convective potential of the current weather situation. Preliminary analysis show that some of the indices extracted from the 12h radiosonde data show good temporal autocorrelation, supporting interpolation to match the 1-hour precipitation data. The precipitation data show a rapidly decreasing temporal autocorrelation function (typically below 0.5 above approx. 12 km), indicating that there is a high variance fraction below scales that the station network is able to reveal. The second data set consists of 7.5-minute C-band radar data from Trondheim, available from June 2013 to October 2015. During the 2014 and 2015 summer seasons, around 25 tipping-bucket precipitation gauges within a 15*20 km area supply observations with temporal resolution down to minute-scale. Nearby radiosonde data are available bi-daily from 1963 to 2015. These data will be explored to provide insight in high-frequency spatial and temporal variability not detectable from the long-term Copenhagen data set. The analysis is a part of the EU-7FP project "Pearl" (http://www.pearl-fp7.eu/, Greve case study), the Norwegian
On causality in polymer scalar field theory
NASA Astrophysics Data System (ADS)
García-Chung, Angel A.; Morales-Técotl, Hugo A.
2011-10-01
The properties of spacetime corresponding to a proposed quantum gravity theory might modify the high energy behavior of quantum fields. Motivated by loop quantum gravity, recently, Hossain et al [1] have considered a polymer field algebra that replaces the standard canonical one in order to calculate the propagator of a real scalar field in flat spacetime. This propagator features Lorentz violations. Motivated by the relation between Lorentz invariance and causality in standard Quantum Field Theory, in this work we investigate the causality behavior of the polymer scalar field.
Ostrogradsky in theories with multiple fields
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Matas, Andrew
2016-06-01
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
NASA Astrophysics Data System (ADS)
Kotchenova, Svetlana Y.; Shabanov, Nikolay V.; Knyazikhin, Yuri; Davis, Anthony B.; Dubayah, Ralph; Myneni, Ranga B.
2003-08-01
Large footprint waveform-recording laser altimeters (lidars) have demonstrated a potential for accurate remote sensing of forest biomass and structure, important for regional and global climate studies. Currently, radiative transfer analyses of lidar data are based on the simplifying assumption that only single scattering contributes to the return signal, which may lead to errors in the modeling of the lower portions of recorded waveforms in the near-infrared spectrum. In this study we apply time-dependent stochastic radiative transfer (RT) theory to model the propagation of lidar pulses through forest canopies. A time-dependent stochastic RT equation is formulated and solved numerically. Such an approach describes multiple scattering events, allows for realistic representation of forest structure including foliage clumping and gaps, simulates off-nadir and multiangular observations, and has the potential to provide better approximations of return waveforms. The model was tested with field data from two conifer forest stands (southern old jack pine and southern old black spruce) in central Canada and two closed canopy deciduous forest stands (with overstory dominated by tulip poplar) in eastern Maryland. Model-simulated signals were compared with waveforms recorded by the Scanning Lidar Imager of Canopies by Echo Recovery (SLICER) over these regions. Model simulations show good agreement with SLICER signals having a slow decay of the waveform. The analysis of the effects of multiple scattering shows that multiply scattered photons magnify the amplitude of the reflected signal, especially that originating from the lower portions of the canopy.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
Eddy current in a rotating cylinder in a static field by a stochastic method
NASA Astrophysics Data System (ADS)
Lévêque, J.; Lubin, T.; Mezani, S.; Rezzoug, A.
2012-02-01
This paper deals with the calculation of eddy current in a copper cylinder. This cylinder rotates in an applied static magnetic field. The electromagnetic problem is solved in two-dimension by considering transient motion. Two methods for eddy current computation are compared: stochastic method and classical finite element method. The main goal of this paper is to compare these methods.
An introduction to conformal field theory
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.
2000-04-01
A comprehensive introduction to two-dimensional conformal field theory is given. The structure of the meromorphic subtheory is described in detail, and a number of examples are presented explicitly. Standard constructions such as the coset and the orbifold construction are explained. The concept of a representation of the meromorphic theory is introduced, and the role of Zhu's algebra in classifying highest weight representations is elucidated. The fusion product of two representations and the corresponding fusion rules are defined, and Verlinde's formula is explained. Finally, higher correlation functions are considered, and the polynomial relations of Moore and Seiberg and the quantum group structure of chiral conformal field theory are discussed. The treatment is relatively general and also allows for a description of less well known classes of theories such as logarithmic conformal field theories.
Relativistic mean-field theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Ring, Peter; Zhao, Pengwei
In this chapter, the covariant energy density functional is constructed with both the meson-exchange and the point-coupling pictures. Several widely used functionals with either nonlinear or density-dependent effective interactions are introduced. The applications of covariant density functional theory are demonstrated for infinite nuclear matter and finite nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes. Finally, a relativistic description of the nuclear landscape has been discussed, which is not only important for nuclear structure, but also important for nuclear astrophysics, where we are facing the problem of a reliable extrapolation to the very neutron-rich nuclei.
A nonlinear field theory of deformable dielectrics
NASA Astrophysics Data System (ADS)
Suo, Zhigang; Zhao, Xuanhe; Greene, William H.
Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.
Quantum statistical correlations in thermal field theories: Boundary effective theory
Bessa, A.; Brandt, F. T.; Carvalho, C. A. A. de; Fraga, E. S.
2010-09-15
We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field {phi}{sub c}, and if we trade free propagators at zero temperature for their finite-temperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schroedinger field representation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle point for fixed boundary fields, which is the classical field {phi}{sub c}, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally reduced effective theory for the thermal system. We calculate the two-point correlation as an example.
Stochastic Modeling of the Residual Acceleration Field in a Microgravity Environment
NASA Astrophysics Data System (ADS)
Casademunt, Jaume; Viñals, Jorge
2001-03-01
We discuss fluid flows induced by the high-frequency components of the residual acceleration field onboard spacecraft (g-jitter) on representative experimental configurations. We study the statistics of g-jitter time series data from the NASA SL-J mission (SAMS-258), and discuss a recently introduced stochastic model of g-jitter. The examples studied are chosen to highlight intrinsically stochastic effects of g-jitter. They include free surface resonances, cavity flow, and inertial Brownian motion in suspensions. The latter is relevant for coarsening experiments in solid-liquid mixtures.
Weyl's Abandonment of Unified Field Theory
NASA Astrophysics Data System (ADS)
Sieroka, Norman
2015-01-01
In 1918, Hermann Weyl proposed a generalisation of Riemannian geometry, in order to unify general relativity and electrodynamics. This paper investigates the physical, mathematical and philosophical reasons for his subsequent abandonment of any such attempt towards a unified field theory.
Pure field theories and MACSYMA algorithms
NASA Technical Reports Server (NTRS)
Ament, W. S.
1977-01-01
A pure field theory attempts to describe physical phenomena through singularity-free solutions of field equations resulting from an action principle. The physics goes into forming the action principle and interpreting specific results. Algorithms for the intervening mathematical steps are sketched. Vacuum general relativity is a pure field theory, serving as model and providing checks for generalizations. The fields of general relativity are the 10 components of a symmetric Riemannian metric tensor; those of the Einstein-Straus generalization are the 16 components of a nonsymmetric. Algebraic properties are exploited in top level MACSYMA commands toward performing some of the algorithms of that generalization. The light cone for the theory as left by Einstein and Straus is found and simplifications of that theory are discussed.
Giordano, Peter J
2014-06-01
An important objective of personality psychology is to provide compelling descriptions and explanations of intraindividual personality dynamics that capture the unique qualities of persons. Among contemporary Western personality theories, the Five-Factor Model enjoys prominence in describing individual differences in personality traits. It falls short, however, in its ability to work with intraindividual personality function. This article argues that classical Confucianism, originating 2500 years ago in mainland China, offers Western personality psychologists important theoretical resources for capturing the complex and dynamic processes inherent in human personality. The Confucian perspective emphasizes a behaviorally anchored, continuous, stochastic, process-oriented understanding of the self as relationally constructed and proposes an elegant description of the relational virtuosity of exemplary persons. The article concludes with five characteristics of a Confucian inspired model of personality and questions the viability of a universal theory of personality. PMID:24101234
Stochastic theory of interfacial enzyme kinetics: A kinetic Monte Carlo study
NASA Astrophysics Data System (ADS)
Das, Biswajit; Gangopadhyay, Gautam
2012-01-01
In the spirit of Gillespie's stochastic approach we have formulated a theory to explore the advancement of the interfacial enzyme kinetics at the single enzyme level which is ultimately utilized to obtain the ensemble average macroscopic feature, lag-burst kinetics. We have provided a theory of the transition from the lag phase to the burst phase kinetics by considering the gradual development of electrostatic interaction among the positively charged enzyme and negatively charged product molecules deposited on the phospholipid surface. It is shown that the different diffusion time scales of the enzyme over the fluid and product regions are responsible for the memory effect in the correlation of successive turnover events of the hopping mode in the single trajectory analysis which again is reflected on the non-Gaussian distribution of turnover times on the macroscopic kinetics in the lag phase unlike the burst phase kinetics.
Constraining Modified Theories of Gravity with Gravitational-Wave Stochastic Backgrounds.
Maselli, Andrea; Marassi, Stefania; Ferrari, Valeria; Kokkotas, Kostas; Schneider, Raffaella
2016-08-26
The direct discovery of gravitational waves has finally opened a new observational window on our Universe, suggesting that the population of coalescing binary black holes is larger than previously expected. These sources produce an unresolved background of gravitational waves, potentially observable by ground-based interferometers. In this Letter we investigate how modified theories of gravity, modeled using the parametrized post-Einsteinian formalism, affect the expected signal, and analyze the detectability of the resulting stochastic background by current and future ground-based interferometers. We find the constraints that Advanced LIGO would be able to set on modified theories, showing that they may significantly improve the current bounds obtained from astrophysical observations of binary pulsars. PMID:27610838
Reductionism, emergence, and effective field theories
NASA Astrophysics Data System (ADS)
Castellani, Elena
In recent years, a "change in attitude" in particle physics has led to our understanding current quantum field theories as effective field theories (EFTs). The present paper is concerned with the significance of this EFT approach, especially from the viewpoint of the debate on reductionism in science. In particular, I shall show how EFTs provide a new and interesting case study in current philosophical discussion on reduction, emergence, and inter-level relationships in general.
Conserved currents of double field theory
NASA Astrophysics Data System (ADS)
Blair, Chris D. A.
2016-04-01
We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.
Effective field theory out of equilibrium: Brownian quantum fields
NASA Astrophysics Data System (ADS)
Boyanovsky, D.
2015-06-01
The emergence of an effective field theory out of equilibrium is studied in the case in which a light field—the system—interacts with very heavy fields in a finite temperature bath. We obtain the reduced density matrix for the light field, its time evolution is determined by an effective action that includes the influence action from correlations of the heavy degrees of freedom. The non-equilibrium effective field theory yields a Langevin equation of motion for the light field in terms of dissipative and noise kernels that obey a generalized fluctuation dissipation relation. These are completely determined by the spectral density of the bath which is analyzed in detail for several cases. At T = 0 we elucidate the effect of thresholds in the renormalization aspects and the asymptotic emergence of a local effective field theory with unitary time evolution. At T\
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
"Quantum Field Theory and QCD"
Jaffe, Arthur M.
2006-02-25
This grant partially funded a meeting, "QFT & QCD: Past, Present and Future" held at Harvard University, Cambridge, MA on March 18-19, 2005. The participants ranged from senior scientists (including at least 9 Nobel Prize winners, and 1 Fields medalist) to graduate students and undergraduates. There were several hundred persons in attendance at each lecture. The lectures ranged from superlative reviews of past progress, lists of important, unsolved questions, to provocative hypotheses for future discovery. The project generated a great deal of interest on the internet, raising awareness and interest in the open questions of theoretical physics.
Entanglement entropy in warped conformal field theories
NASA Astrophysics Data System (ADS)
Castro, Alejandra; Hofman, Diego M.; Iqbal, Nabil
2016-02-01
We present a detailed discussion of entanglement entropy in (1+1)-dimensional Warped Conformal Field Theories (WCFTs). We implement the Rindler method to evaluate entanglement and Renyi entropies for a single interval and along the way we interpret our results in terms of twist field correlation functions. Holographically a WCFT can be described in terms of Lower Spin Gravity, a SL (2, ℝ) × U (1) Chern-Simons theory in three dimensions. We show how to obtain the universal field theory results for entanglement in a WCFT via holography. For the geometrical description of the theory we introduce the concept of geodesic and massive point particles in the warped geometry associated to Lower Spin Gravity. In the Chern-Simons description we evaluate the appropriate Wilson line that captures the dynamics of a massive particle.
Stochastic geometry and topology of non-Gaussian fields.
Beuman, Thomas H; Turner, Ari M; Vitelli, Vincenzo
2012-12-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. PMID:23169625
Stochastic geometry and topology of non-Gaussian fields
Beuman, Thomas H.; Turner, Ari M.; Vitelli, Vincenzo
2012-01-01
Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher-order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion. PMID:23169625
The Theory of Quantized Fields. II
DOE R&D Accomplishments Database
Schwinger, J.
1951-01-01
The arguments leading to the formulation of the Action Principle for a general field are presented. In association with the complete reduction of all numerical matrices into symmetrical and anti-symmetrical parts, the general field is decomposed into two sets, which are identified with Bose-Einstein and Fermi-Dirac fields. The spin restriction on the two kinds of fields is inferred from the time reflection invariance requirement. The consistency of the theory is verified in terms of a criterion involving the various generators of infinitesimal transformations. Following a discussion of charged fields, the electromagnetic field is introduced to satisfy the postulate of general gauge invariance. As an aspect of the latter, it is recognized that the electromagnetic field and charged fields are not kinematically independent. After a discussion of the field-strength commutation relations, the independent dynamical variable of the electromagnetic field are exhibited in terms of a special gauge.
From theory to field experiments
NASA Astrophysics Data System (ADS)
de Vos, Bram
2016-04-01
Peter Raats' achievements in Haren (NL) 1986-1997 were based on a solid theoretical insight in hydrology and transport process in soil. However, Peter was also the driving force behind many experimental studies and applied research. This will be illustrated by a broad range of examples ranging from the dynamics of composting processes of organic material; modelling and monitoring nutrient leaching at field-scale; wind erosion; water and nutrient dynamics in horticultural production systems; oxygen diffusion in soils; and processes of water and nutrient uptake by plant roots. Peter's leadership led to may new approaches and the introduction of innovative measurement techniques in Dutch research; ranging from TDR to nutrient concentration measurements in closed fertigation systems. This presentation will give a brief overview how Peter's theoretical and mathematical insights accelerated this applied research.
Laws of Large Numbers and Langevin Approximations for Stochastic Neural Field Equations
2013-01-01
In this study, we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson–Cowan equation can be obtained as the limit in uniform convergence on compacts in probability for a sequence of microscopic models when the number of neuron populations distributed in space and the number of neurons per population tend to infinity. This result also allows to obtain limits for qualitatively different stochastic convergence concepts, e.g., convergence in the mean. Further, we present a central limit theorem for the martingale part of the microscopic models which, suitably re-scaled, converges to a centred Gaussian process with independent increments. These two results provide the basis for presenting the neural field Langevin equation, a stochastic differential equation taking values in a Hilbert space, which is the infinite-dimensional analogue of the chemical Langevin equation in the present setting. On a technical level, we apply recently developed law of large numbers and central limit theorems for piecewise deterministic processes taking values in Hilbert spaces to a master equation formulation of stochastic neuronal network models. These theorems are valid for processes taking values in Hilbert spaces, and by this are able to incorporate spatial structures of the underlying model. Mathematics Subject Classification (2000): 60F05, 60J25, 60J75, 92C20. PMID:23343328
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
Phase-space quantization of field theory.
Curtright, T.; Zachos, C.
1999-04-20
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999.
Stochastic Motion of Relativistic Particles in the Field of a Wide Wave Packet
NASA Astrophysics Data System (ADS)
Nagornykh, E.; Tel'nikhin, A.
2003-06-01
Stochastic motion of relativistic particles in the field of a wave packet propagating under an angle to the external magnetic field are investigated. The interplay of the dynamical and statistical aspects of the behavior of the relativistic particle-potential wave packet system is considered. Dynamics of this system are described by nonlinear mapping and corresponding Fokker-Planck-Kolmogorov equation in phase space possesses canonical Hamiltonian structure. The following general problems of stochastic motion are disscussed: local instability and the Lyapunov exponents and the Kolmogorov entropy; a fractal structures and its dimension; bifurcations of a vector fields and the boundaries of the region of dynamical chaos. The results of numerical simulation are presented. A possible astrophysical application of the results obtained is discussed.
Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach
NASA Astrophysics Data System (ADS)
Lacroix, Denis; Hermanns, S.; Hinz, C. M.; Bonitz, M.
2014-09-01
Finite lattice models are a prototype for interacting quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is—for not too large two-body interaction strength—found to be much more accurate than time-dependent mean-field at the same order of numerical costs. Furthermore, it can well compete with recent nonequilibrium Green function approaches using second-order Born approximation, which are of substantially larger complexity. The performance of the stochastic mean-field approach is demonstrated for Hubbard clusters with up to 512 particles in one, two, and three dimensions.
Mean-field theory of four species in cyclic competition
NASA Astrophysics Data System (ADS)
Durney, C. H.; Case, S. O.; Pleimling, M.; Zia, R. K. P.
2011-03-01
We consider a simple model of cyclic competition of M species: When a pair of individuals from species k and k + 1 interact, the latter transforms into the former. Even with no spatial structure, such systems often display interesting and counterintuitive behavior. With possible applications in both biological systems (e.g., Min proteins, E. Coli, lizards) and game theory (e.g., rock-paper-scissors), the M = 3 case has attracted considerable recent attention. We study a M = 4 system (with no spatial structure) and find major differences, e.g., (1) the presence of macroscopically many absorbing states, (2) coexistence of species, and (3) violation of the ``law'' of survival of the weakest - a central theme in the M = 3 case. Like the game of Bridge, the system typically ends with ``partner pairs.'' After describing the full stochastic model and its master equation, we present the mean-field approximation. Several exact, analytic predictions will be shown. Their limitations and implications for the stochastic system will also be discussed. Supported in part by NSF-DMR-0705152, 0904999, 1005417.
Nonequilibrium statistical field theory for classical particles: Basic kinetic theory
NASA Astrophysics Data System (ADS)
Viermann, Celia; Fabis, Felix; Kozlikin, Elena; Lilow, Robert; Bartelmann, Matthias
2015-06-01
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010), 10.1103/PhysRevE.81.061102; J. Stat. Phys. 149, 643 (2012), 10.1007/s10955-012-0610-y; J. Stat. Phys. 152, 159 (2013), 10.1007/s10955-013-0755-3; Phys. Rev. E 83, 041125 (2011), 10.1103/PhysRevE.83.041125] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
Fluctuation-Induced Particle Transport and Density Relaxation in a Stochastic Magnetic Field
NASA Astrophysics Data System (ADS)
Brower, David L.
2009-11-01
Particle transport and density relaxation associated with electromagnetic fluctuations is an unresolved problem of long standing in plasma physics and magnetic fusion research. In toroidal fusion plasmas, magnetic field fluctuations can arise spontaneously from global MHD instabilities, e.g., tearing fluctuations associated with sawtooth oscillations. Resonant magnetic perturbations (RMP) have also been externally imposed to mitigate the effect of edge localized modes (ELMs) by locally enhancing edge transport in Tokamaks. Understanding stochastic-field-driven transport processes is thus not only of basic science interest but possibly critical to ELM control in ITER. We report on the first direct measurement of magnetic fluctuation-induced particle transport in the core of a high-temperature plasma, the MST reversed field pinch. Measurements focus on the sawtooth crash, when the stochastic field resulting from tearing reconnection is strongest, and are accomplished using newly developed, laser-based, differential interferometry and Faraday rotation techniques. The measured electron particle flux, resulting from the correlated product of electron density (δn) and radial magnetic fluctuations (δbr), accounts for density profile relaxation during these magnetic reconnection events. Surprisingly, the electron diffusion is 30 times larger than estimates of ambipolarity-constrained transport in a stochastic magnetic field. A significant ion flux associated with parallel ion flow velocity fluctuations (δvi,//) correlated with δbr appears responsible for transport larger than predictions from the quasi-linear test particle model. These results indicate the need for improved understanding of particle transport in a stochastic magnetic field. Work performed in collaboration with W.X. Ding, W.F. Bergerson, T.F. Yates, UCLA; D.J. Den Hartog, G. Fiksel, S.C. Prager, J.S. Sarff and the MST Group, University of Wisconsin-Madison.
Intrinsic trapping of stochastic sheared magnetic field lines
Negrea, M.; Petrisor, I.; Balescu, R.
2004-10-01
The decorrelation trajectory method is applied to the diffusion of magnetic field lines in a perturbed sheared slab magnetic configuration. Some interesting decorrelation trajectories for several values of the magnetic Kubo number and of the shear parameter are exhibited. The asymmetry of the decorrelation trajectories appears in comparison with those obtained in the purely electrostatic case studied in earlier work. The running and asymptotic diffusion tensor components are calculated and displayed.
Effective Field Theories, Reductionism and Scientific Explanation
NASA Astrophysics Data System (ADS)
Hartmann, Stephan
Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effective field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispensable. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation.
Unification of classical nucleation theories via a unified Itô-Stratonovich stochastic equation.
Durán-Olivencia, Miguel A; Lutsko, James F
2015-09-01
Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J. F. Lutsko and M. A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)10.1063/1.4811490] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer. PMID:26465482
Quantum Cylindrical Waves and Parametrized Field Theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space-time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space-time and review the relevant results for unitary implementability.
Field Theory for Multi-Particle System
NASA Astrophysics Data System (ADS)
Wang, Shouhong; Ma, Tian
2016-03-01
The main objectives of this talk are 1) to introduce some basic postulates for quantum multi-particle systems, and 2) to develop a universal field theory for interacting multi-particle systems coupling both particle fields and interacting fields. By carefully examining the nature of interactions between multi-particles, we conclude that multi-particle systems must obey i) the gauge symmetry, ii) the principle of interaction dynamics (PID), and iii) the principle of representation invariance (PRI). Intuitively, PID takes the variation of the action functional under energy-momentum conservation constraint, offers a different and natural way of introducing Higgs fields, and is also required by the presence of dark matter and dark energy and the quark confinement. PRI requires that the SU(N) gauge theory be independent of representations of SU(N). Based on these principles, a few basic postulates for multi-particle systems are introduced in this talk, leading to a field theory for interacting multi-particle systems. A direct consequence of the field theory is the derivation of general atomic spectrum equations. Supported in Part by the Office of Naval Research, by the US National Science Foundation, and by the Chinese National Science Foundation.
Non Perturbative Aspects of Field Theory
Bashir, A.
2009-04-20
For any quantum field theory (QFT), there exists a set of Schwinger-Dyson equations (SDE) for all its Green functions. However, it is not always straight forward to extract quantitatively exact physical information from this set of equations, especially in the non perturbative regime. The situation becomes increasingly complex with growing number of external legs. I give a qualitative account of the hunt for the non perturbative Green functions in gauge theories.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Noncommutative Geometry in M-Theory and Conformal Field Theory
Morariu, Bogdan
1999-05-01
In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U{sub q}(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun{sub q} (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.
Mean Field Analysis of Stochastic Neural Network Models with Synaptic Depression
NASA Astrophysics Data System (ADS)
Yasuhiko Igarashi,; Masafumi Oizumi,; Masato Okada,
2010-08-01
We investigated the effects of synaptic depression on the macroscopic behavior of stochastic neural networks. Dynamical mean field equations were derived for such networks by taking the average of two stochastic variables: a firing-state variable and a synaptic variable. In these equations, the average product of thesevariables is decoupled as the product of their averages because the two stochastic variables are independent. We proved the independence of these two stochastic variables assuming that the synaptic weight Jij is of the order of 1/N with respect to the number of neurons N. Using these equations, we derived macroscopic steady-state equations for a network with uniform connections and for a ring attractor network with Mexican hat type connectivity and investigated the stability of the steady-state solutions. An oscillatory uniform state was observed in the network with uniform connections owing to a Hopf instability. For the ring network, high-frequency perturbations were shown not to affect system stability. Two mechanisms destabilize the inhomogeneous steady state, leading to two oscillatory states. A Turing instability leads to a rotating bump state, while a Hopf instability leads to an oscillatory bump state, which was previously unreported. Various oscillatory states take place in a network with synaptic depression depending on the strength of the interneuron connections.
NASA Astrophysics Data System (ADS)
Touboul, Jonathan
2012-08-01
In this manuscript we analyze the collective behavior of mean-field limits of large-scale, spatially extended stochastic neuronal networks with delays. Rigorously, the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro-differential McKean-Vlasov equation that remain impenetrable, leaving the stochastic collective dynamics of such networks poorly understood. In order to study these macroscopic dynamics, we analyze networks of firing-rate neurons, i.e. with linear intrinsic dynamics and sigmoidal interactions. In that case, we prove that the solution of the mean-field equation is Gaussian, hence characterized by its two first moments, and that these two quantities satisfy a set of coupled delayed integro-differential equations. These equations are similar to usual neural field equations, and incorporate noise levels as a parameter, allowing analysis of noise-induced transitions. We identify through bifurcation analysis several qualitative transitions due to noise in the mean-field limit. In particular, stabilization of spatially homogeneous solutions, synchronized oscillations, bumps, chaotic dynamics, wave or bump splitting are exhibited and arise from static or dynamic Turing-Hopf bifurcations. These surprising phenomena allow further exploring the role of noise in the nervous system.
Global anomalies and effective field theory
NASA Astrophysics Data System (ADS)
Golkar, Siavash; Sethi, Savdeep
2016-05-01
We show that matching anomalies under large gauge transformations and large diffeomorphisms can explain the appearance and non-renormalization of couplings in effective field theory. We focus on thermal effective field theory, where we argue that the appearance of certain unusual Chern-Simons couplings is a consequence of global anomalies. As an example, we show that a mixed global anomaly in four dimensions fixes the chiral vortical effect coefficient (up to an overall additive factor). This is an experimentally measurable prediction from a global anomaly. For certain situations, we propose a simpler method for calculating global anomalies which uses correlation functions rather than eta invariants.
Effective field theory for deformed atomic nuclei
Papenbrock, Thomas F.; Weidenmüller, H. A.
2016-04-13
In this paper, we present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. Finally, for rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Effective field theory for deformed atomic nuclei
NASA Astrophysics Data System (ADS)
Papenbrock, T.; Weidenmüller, H. A.
2016-05-01
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order corrections are computed, the EFT accounts for finer details such as the variation of the moment of inertia with the band head and the small magnitudes of interband E2 transitions. For rotational bands with a finite spin of the band head, the EFT is equivalent to the theory of a charged particle on the sphere subject to a magnetic monopole field.
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.