We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provid…
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48 results for “Einstein-Dirac system”
The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.
problem Finding exact solutions to an Einstein-Dirac-Maxwell system with Sasakian quasi-Killing spinors.
method Constructing a family of exact solutions on four-dimensional static Sasakian spacetimes using the Sasakian frame.
result Closed and open universe models are found with specific energy conditions.
This paper studies Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
problem Characterizing Sasakian quasi-Killing spinors on 3D Sasakian manifolds.
method Detailed analysis and geometric properties of Sasakian quasi-Killing spinors.
result Almost all Sasakian quasi-Killing spinors solve the Einstein-Dirac system with a non-zero cosmological constant.
The paper proves compactness for Dirac-Einstein spin manifolds.
problem Compactness of Dirac-Einstein spin manifolds under specific conditions.
method Study of the Hilbert-Einstein-Dirac functional, proving compactness for critical points.
result Compactness result for Dirac-Einstein spin manifolds in dimensions three and four.
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the notion of Killing spinors. The solutions of this spinorial field equation are c…
Solutions of the Einstein-Dirac Equation on Riemannian 3-Manifolds with Constant Scalar Curvaturemath.DG
This paper contains a classification of all 3-dimensional manifolds with constant scalar curvature that carry a non-trivial solution of the Einstein-Dirac equation.
New flow deforms Riemannian metrics smoothly.
problem Deforming Riemannian metrics on spin manifolds.
method Parabolic flow based on Dirac-Einstein functional.
result Local well-posedness of smooth solutions proved.
We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics on such that $(M^n \ti…
Not only the Dirac operator, but also the spinor bundle of a pseudo-Riemannian manifold depends on the underlying metric. This leads to technical difficulties in the study of problems where many metrics are involved, for instance in variational theory. We construct a natural finite dimensional bundle, from which all th…
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. hep-th/0501217. Such Einstein-Dirac spacetimes are parametrized by gene…
We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in t…
We characterize the Lie derivative of spinor fields from a variational point of view by resorting to the theory of the Lie derivative of sections of gauge-natural bundles. Noether identities from the gauge-natural invariance of the first variational derivative of the Einstein(--Cartan)--Dirac Lagrangian provide restric…
We study the geometry of families of hypersurfaces in Eguchi-Hanson space that arise as complex line bundles over curves in and are three-dimensional, non-compact Riemannian manifolds, which are foliated in Hopf tori for closed curves. They are negatively curved, asymptotically flat spaces, and we compute the com…
The aim of this short note is to announce the existence of a one-parameter family of left-invariant metrics on admitting WK-spinors. This family contains the two non-Einstein Sasakian metrics with WK-spinors on , but does not contain the standard sphere with Killing spinors. Moreover, any simply-connec…
Some Remarks on the Hijazi Inequality and Generalizations of the Killing Equation for Spinorsmath.DG
We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Th. Friedrich (1980) and O. Hijazi (1986, 1992). The special solutions of the Einstein-Dirac equation constructed recently by Friedrich/Kim are examples for the limiting case of th…
We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal metrics and linear and nonlinear connections define different types of Finsler, …
Overview of integrable systems with symmetries, focusing on toric and semitoric systems.
problem Classifying and understanding integrable systems with symmetries.
method Using decorated polygons and controlled bifurcations in one-parameter families of systems.
result Construction of explicit semitoric systems with prescribed invariants.
New method to derive integrable systems from existing Lax systems.
problem Deriving new integrable systems from existing ones.
method Systematic method of deriving new integrable systems from a given one.
result Examples of new integrable systems derived, including the dispersionless Hirota equation, the general heavenly equation, and the web equations.
Learning to control linear systems is statistically hard, especially for underactuated systems.
problem Statistical difficulty of learning to control linear systems, especially underactuated ones.
method Utilized minimax lower bounds and structural assumptions to prove learning complexity can be exponential.
result Learning complexity can be at most exponential with the controllability index of the system.
Discrete-time systems can be characterized by simple flat coordinates and their shifts.
problem Characterizing flatness of discrete-time systems.
method Developed a map from flat coordinates and their shifts to system state and input, fulfilling system equations identically.
result Derived necessary conditions for a system to be flat, without requiring differential geometry methods.
The paper explores when linear system identification is hard or easy, especially for under-actuated systems.
problem Statistical hardness of learning linear systems, especially under-actuated or under-excited systems.
method Using tools from minimax theory and recent statistical tools for finite sample analysis of system identification.
result The controllability index of linear systems affects the sample complexity of identification, making some systems hard to learn.
This paper improves system identification by reducing sample complexity for high-dimensional linear dynamical systems.
problem High sample complexity for learning partially observed linear dynamical systems in high dimensions.
method Introduces an -regularized estimation method that reduces sample complexity from linear to logarithmic with system dimension.
result Markov parameters can be learned with logarithmic number of samples relative to system dimension, improving sample complexity.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
problem Existence of Riemannian invariants for integrable systems of hydrodynamic type.
method Finding coordinates where the generator and all symmetries are diagonal.
result In integrable hydrodynamic systems, there exist coordinates where the generator and all symmetries are diagonal.
Nonholonomic Controlled Hamiltonian System: Symmetric Reduction and Hamilton-Jacobi Equationsmath.SG
This paper studies nonholonomic constraints in Hamiltonian systems, deriving equations and theorems.
problem Analyzing nonholonomic constraints in Hamiltonian systems.
method Deriving distributional RCH systems, geometric constraint conditions, and Hamilton-Jacobi theorems.
result Derives precise geometric constraint conditions and Hamilton-Jacobi theorems for nonholonomic systems.
New method models unknown systems with hidden parameters using neural networks.
problem Modeling unknown dynamical systems with hidden parameters.
method Training a deep neural network (DNN) model using trajectory data of the unknown system.
result DNN model accurately predicts unknown dynamical systems with new initial conditions.
Study absolute equivalence for Pfaffian systems, applying to control systems.
problem Absolute equivalence of Pfaffian systems with specific independence conditions.
method Structural results for Pfaffian systems of corank 3, applied to control systems.
result Dynamic feedback linearization of control systems with 2 inputs.
Solves selecting the best optimizing system problems.
problem Selecting the best system among contenders with unknown performance.
method Adaptive algorithms integrating stochastic gradient descent and sequential elimination.
result Exponential rates of convergence to zero for false selection probability.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Superintegrable systems on curved manifolds found to have Hessian structures.
problem Characterizing superintegrable systems on curved manifolds.
method Identifying and computing Hessian coordinates for superintegrable systems.
result Examples of superintegrable systems in 2D and 3D have natural Hessian coordinates.
Measures of Systemic Riskq-fin.RM
Systemic risk refers to the risk that the financial system is susceptible to failures due to the characteristics of the system itself. The tremendous cost of systemic risk requires the design and implementation of tools for the efficient macroprudential regulation of financial institutions. The current paper proposes a…
Researchers solve boundary and scattering rigidity problems for magnetic systems.
problem Recovering magnetic systems from boundary or scattering data.
method Reduced to magnetic systems and applied results from [DPSU07].
result Recovering -system up to a gauge.
The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.
problem Finding general solutions for Lie systems.
method Develops mixed superposition rules for Lie systems with imprimitive Lie algebras and semidirect sums.
result Extends coalgebra method to Lie systems of partial differential equations.
Paper develops reduction theory for controlled Lagrangian systems with symmetry and momentum map.
problem Reduction of controlled Lagrangian systems with symmetry and momentum map.
method Using Legendre transformation and Euler-Lagrange vector field, the paper extends symmetric reduction theory.
result Established regular reduction theory for RCL systems with symmetry and momentum map.
The paper studies connections in superintegrable systems, revealing geometric insights.
problem Understanding non- and semi-degenerate superintegrable systems.
method Analyzes two torsion-free connections associated with superintegrable systems.
result Semi-degenerate secondary structure tensor is the Ricci curvature of a natural torsion-free connection.
This paper proposes a system-agnostic policy for dynamic scheduling.
problem Dynamic scheduling in changing systems is challenging due to system-specific optimal policies.
method Descriptive policy that learns a system-agnostic scheduling principle.
result System-agnostic meta-learning enables adaptation to unseen system characteristics.
Learn dynamics of a system using auxiliary data from similar systems.
problem Learning dynamics of a linear system with limited data.
method Weighted least squares approach, incorporating auxiliary data.
result Auxiliary data can help reduce intrinsic error due to noise.
The inability to see and quantify systemic financial risk comes at an immense social cost. Systemic risk in the financial system arises to a large extent as a consequence of the interconnectedness of its institutions, which are linked through networks of different types of financial contracts, such as credit, derivativ…
Smooth and F--smooth systemsmath.DG
Abstract reviews geometric theories of smooth and F-smooth systems.
problem Geometric theories of smooth and F-smooth systems.
method Reviews geometric theories of smooth and F-smooth systems.
result Discusses geometric theories of smooth and F-smooth systems.
New Lie systems derived from Goursat distributions with applications to differential equations.
problem Analyzing Lie systems associated with Goursat distributions and their applications.
method Analyzing bracket-generating distributions and their relation to Lie systems, focusing on reductions and reconstructions.
result Lie systems associated with Goursat distributions can be reduced and solutions reconstructed from reduced systems.
Elliptic systems are characterized by Darboux integrability.
problem Characterizing elliptic differential systems with holomorphic solutions.
method Using a complex manifold and associated holomorphic Pfaffian system.
result Elliptic systems are Darboux integrable under generic conditions.
The study analyzes stochastic Lie systems and their applications in various models.
problem Analyzing stochastic differential equations on manifolds.
method Coalgebra method for Hamiltonian stochastic Lie systems.
result New examples of stochastic Lie systems and Hamiltonian stochastic Lie systems are analyzed.
Reduces multisymplectic Lie systems through symmetry analysis.
problem Solving multisymplectic Lie systems using symmetry reduction.
method Using momentum maps for reduction and reconstruction of multisymplectic Lie systems.
result Solves the original problem by analyzing simpler multisymplectic Lie systems.
Study integrable discretizations of cyclic systems with circular coordinate lines.
problem Integrable discretizations of 3D cyclic systems with circular coordinate lines.
method Investigate circle congruences and flat connections in the context of discrete cyclic systems.
result Characterization of circle congruences and existence of certain flat connections.
A new chaotic financial system is proposed by considering ethics involvement in a four-dimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integer-order system. A discretization scheme is propo…
A distributed system identification method for LTI systems using reverse experience replay.
problem Online system identification of LTI systems over multi-agent networks.
method DSGD-RER, a distributed variant of SGD-RER with backward updates.
result The estimation error decreases as the network size grows.
This work extends reduction processes for nonholonomic discrete mechanical systems.
problem Nonholonomic discrete mechanical systems and their reductions.
method Introduces a category of discrete-time dynamical systems and a two-stage reduction process.
result Two-stage reduction process produces systems isomorphic to one-stage reduction.
Unified approach to deform Lie-Hamilton systems using Poisson-Hopf algebra.
problem Deforming Lie systems with quantum algebras.
method Poisson-Hopf algebra deformations applied to Lie-Hamilton systems.
result Unified approach to deformations of Lie-Hamilton systems on the real plane.