The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space. Using the approach of Dijkgraaf and …
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48 results for “phase spaces”
Symplectic forms from two phase spaces are proven equivalent.
problem Equivalence of symplectic forms from different phase spaces.
method Proof of equivalence for theories over space-time with boundary.
result Symplectic forms derived from canonical and covariant phase spaces are equivalent.
The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the odd-dimensional phase space a generalized contact structure. In the paper infinitesimal sy…
Classifies symplectic phase space deformations preserving angular momentum symmetry.
problem Preserving symplectic -symmetry in phase space deformations.
method Classifying linear deformations of phase space that preserve symplectic -symmetry.
result Standard phase space and related manifolds as degenerations of a 3-dimensional family of coadjoint orbits.
New method for flux quantization on phase space stacks.
problem Defining and constructing flux-quantized phase space stacks.
method Observation of flux densities and characterization of Cauchy data.
result Flux-quantized phase space stacks have classifying spaces with rational Whitehead L-infinity algebra.
Introduces a new phase space for 2D supersymmetric sigma models.
problem Developing a new Hamiltonian formulation for 2D supersymmetric sigma models.
method Introduces a phase space with spinorial momenta and derives a covariant Hamiltonian formulation.
result Shows the existence of additional supersymmetries in the new formulation.
The paper explores the geometrical structures of phase spaces for controlled Hamiltonian systems with symmetry.
problem Understanding the dynamics and phase spaces of controlled Hamiltonian systems with symmetry.
method The paper uses Marsden-Weinstein reduction to define and analyze CH systems and their dynamics, focusing on the geometrical and topological structures of phase spaces.
result The paper reveals the relationships between the geometrical structures, dynamical vector fields, and controls of CH systems with symmetry.
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of spacetime. This setting allows us to skip constraints. Our main goal is to determine the…
Para-Kahler hom-Lie algebrasmath.DG
The paper defines and characterizes para-Kahler structures on hom-Lie algebras.
problem Defining and characterizing para-Kahler structures on hom-Lie algebras.
method Introducing pseudo-Riemannian, para-Hermitian, and para-Kahler structures on hom-Lie algebras, providing examples, and defining phase spaces.
result Para-Kahler hom-Lie algebras give phase spaces and conversely, can be constructed from phase spaces.
The covariant phase space of a Lagrangian field theory is the solution space of the associated Euler-Lagrange equations. It is, in principle, a nice environment for covariant quantization of a Lagrangian field theory. Indeed, it is manifestly covariant and possesses a canonical (functional) "presymplectic structure" w …
Neural networks improve efficiency in integrating multi-dimensional phase spaces in particle physics.
problem Efficiently integrating multi-dimensional phase spaces in particle physics.
method Optimized Neural Network (NN) algorithm for phase space integration.
result NN-based approach achieves unweighting efficiencies of 30-75% in various particle physics examples.
A neural network learns phase space properties for time series analysis.
problem Lack of consistency and robustness in estimating embedding parameters.
method Forgetting mechanism neural network to learn phase space properties.
result Neural network approach is competitive or superior to state-of-the-art strategies.
Paper predicts GNSS phase scintillations with machine learning.
problem Predicting phase scintillations due to ionosphere disturbances.
method Proposes a novel machine learning architecture and loss function.
result Achieves state-of-the-art prediction of phase scintillations 1 hour in advance.
Geometric phases in stock trading show profits/losses without price changes.
problem Applying geometric phases to stock trading dynamics.
method Discrete-time systems analysis with zero-area cycles.
result Zero-area cycles in shape space represent high-frequency trading operations.
Berry phases and connection matrices defined on homogeneous spaces attached to Siegel-Jacobi groupsmath.DG
Analyzes Berry phases and connection matrices on Siegel-Jacobi spaces.
problem Understanding Berry phases and connection matrices on Siegel-Jacobi spaces.
method Examines the Siegel-Jacobi disk and upper half-plane, calculates connection matrices and covariant derivatives.
result Calculates the connection matrix and covariant derivatives on the extended Siegel-Jacobi upper half-plane.
Convolutional neural networks learn phase-dependent frequency representations.
problem Capturing phase dependence in frequency representations for better signal analysis.
method Convolutional neural networks learn filters with different phases, which rectify to phase-dependent descriptors.
result Phase harmonics correlations can compressively represent signals with sparse wavelet coefficients.
Chirped sinosoids and interferometric phase plots are functions that are not periodic, but are the composition of a smooth function and a periodic function. These functions functions factor into a pair of maps: from their domain to a circle, and from a circle to their codomain. One can easily imagine replacing the circ…
Discovering Phase Transitions with Unsupervised Learningcond-mat.stat-mech
Unsupervised learning identifies phases and transitions in complex systems.
problem Discovering hidden patterns and phases in large datasets.
method Raw spin configurations were analyzed using principal component analysis and clustering.
result Unsupervised learning successfully identifies physical concepts like order parameter and structure factor.
Paper analyzes latent space geometry in generative models using Fisher information.
problem Understanding the structure of latent spaces in generative models.
method Reconstructs Fisher information metric from generated samples and posterior distribution.
result Reveals fractal structure and abrupt changes in Fisher metric at phase boundaries.
New theorem links tropical phased matroids to higher-dimensional spheres.
problem Understanding topological properties of tropical phased matroids.
method Proving homeomorphism between topological order complex and a sphere.
result Topological order complex of tropical phased matroids is a -sphere.
In this paper we study vector fields on the big phase space of Gromov-Witten theory which are idempotents of the quantum product. Such vector fields can be used to simplify universal equations for higher genus Gromov-Witten invariants.
Unified geometric framework for adiabatic quantum mechanics.
problem Understanding geometric phases and exceptional points in quantum mechanics.
method Formal geometric framework for arbitrary non-degenerate Hamiltonians.
result Generalization of geometric phase to non-Hermitian Hamiltonians.
This thesis revises phase space concepts in physics, incorporating physical dimensions.
problem Disconnection between theoretical models and units of measurement.
method Introducing unit-free manifolds and dimensioned algebraic structures.
result Reinterpretation of Jacobi manifolds as unit-free analogues of Poisson manifolds.
The paper connects -manifolds to Coulomb and Higgs phases of gauge theories.
problem Exploring the physical interpretation of special singularities in -holonomy manifolds.
method Analyzing desingularizations of orbifold singularities and relating them to gauge theories.
result Shows an isomorphism between moduli spaces of Ricci flat metrics and flat ADE-connections.
We generalize the observable diameter and the separation distance for metric measure spaces to those for pyramids, and prove some limit formulas for these invariants for a convergent sequence of pyramids. We obtain various applications of our limit formulas as follows. We have a criterion of the phase transition proper…
Complex and Kahler structures defined on hom-Lie algebras.
problem Defining structures on hom-Lie algebras.
method Introducing complex and Hermitian structures on hom-Lie algebras, providing examples, and constructing phase spaces.
result No proper complex (Hermitian) hom-Lie algebra of dimension two exists.
The study finds all possible heights for transformation groups on graphs.
problem Determining the possible heights of transformation groups on graphs.
method Proved the existence of a topological graph for all finite .
result For all finite , there exists a graph such that the set of heights is .
DCTR uses neural networks to improve particle physics simulations and parameter tuning.
problem High computational cost limits precise scientific analysis in particle physics.
method Deep neural networks for reweighting and parameter tuning of simulations.
result DCTR enables precise simulations and parameter tuning, improving model accuracy.
On Quantum Indeterminacyquant-ph
Unified geometric approach to quantum indeterminacy.
problem Quantum indeterminacy and uncertainty principles.
method Geometric formulation using convex geometry and symplectic topology.
result Robertson-Schrodinger inequalities emerge as geometric principles.
3D gravity shows phase transitions with scalar condensation.
problem Phase transitions in 3D gravity with higher genus boundaries.
method Analytical and numerical computations of Rényi entropies and critical dimensions.
result Rényi entropies of holographic CFTs undergo phase transitions.
New geometrization of gravitational wave phase space.
problem Understanding the geometry of null-infinity in asymptotically flat space-times.
method Proposes a new geometrization using tractor calculus adapted to degenerate conformal metrics.
result Gravitational waves correspond to a class of tractor connections called 'null-normal'.
On the basis of Liouville theorem the generalization of the Nambu mechanics is considered. For three-dimensional phase space the concept of vector hamiltonian and vector lagrangian is entered.
Study of trapped photons in Kerr spacetime's phase space.
problem Characterize trapped photons in Kerr spacetime.
method Explicit proof and new proof of trapped photons' set as a smooth 5D submanifold.
result Set of trapped photons forms a smooth 5D submanifold with topology .
Paper uses TDA to assess cryptocurrency risk by measuring phase space instability.
problem Traditional risk measures fail to capture market dynamics' geometric structure.
method Applied Takens' Delay Embedding Theorem to generate point cloud, computed persistent homology groups, defined Topological Persistence Norm.
result Proposed leverage calibration heuristic based on persistence of 1-dimensional cycles.
PDE-Foam - a probability-density estimation method using self-adapting phase-space binningphysics.data-an
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this paper, we present a modification of the PDE method that uses a self-adapting bi…
We study the indefinite metric in the contact phase space of a homogeneous thermodynamical system introduced by R. Mrugala. We calculate the curvature tensor, Killing vector fields, second fundamental form of Legendre submanifolds of - constitutive surfaces of different homogeneous thermodynamical syste…
A new geometric approach to identify slow invariant manifolds in complex systems.
problem The mathematical definition of slow invariant manifolds is unsatisfactory and limited to slow-fast systems.
method Formulate slow invariant manifolds geometrically within the context of differential geometry, focusing on covariant formulations.
result A more general definition of slow invariant manifolds is provided, independent of coordinate choice.
The problem of optimizing unknown costly-to-evaluate functions has been studied for a long time in the context of Bayesian Optimization. Algorithms in this field aim to find the optimizer of the function by asking only a few function evaluations at locations carefully selected based on a posterior model. In this paper,…
New K-theory approach classifies anyonic topological phases in 2D semimetals.
problem Classifying interacting topological phases remains open.
method TED K-theory of configuration spaces of points in the Brillouin torus.
result Classifies su(2)-anyonic topological order in 2D semimetals.
Describes reconstructing Poisson structures from Lie group actions.
problem Reconstructing invariant Poisson structures from Lie group actions.
method Describes reconstruction of invariant Poisson structures from canonical actions of compact Lie groups on fibered phase spaces.
result Derives symmetry properties of Wong's type equations from main results.
Geometric phase and modulus relations for SU(n) matrix elements in the defining representationmath-ph
A set of relations between the modulus and phase is derived for amplitudes of the form $\mels{\hatu(x)}$ where in the fundamental representation and denotes the coordinates on the group manifold. An illustration is given for the case as well as a brief discussion of phase singularities …
In differential-geometric language, vortex-lines equations on extended phase space of a system may be written as , where is a differential 1-form. This is the structure, to give a paradigmatic example, of the Hamilton equations. Here, we study equations of the same structure, where is a differen…
New tan-concavity property for Lagrangian phase operators helps in studying dHYM metrics.
problem Lack of concavity in Lagrangian phase operator for dHYM metrics.
method Introduce tangent Lagrangian phase flow (TLPF) on almost calibrated (1,1)-forms.
result TLPF exists for all positive time and converges to dHYM metrics under certain conditions.
Due to space limitations, our submission "Source Separation and Clustering of Phase-Locked Subspaces", accepted for publication on the IEEE Transactions on Neural Networks in 2011, presented some results without proof. Those proofs are provided in this paper.
We identify the leading order term of the asymptotic expansion of the Witten-Reshetikhin-Turaev invariants for finite order mapping tori with classical invariants for all simple and simply-connected compact Lie groups. The square root of the Reidemeister torsion is used as a density on the moduli space of flat connecti…
We present a generalization of the Nambu mechanics on the base of Liouville's theorem. We prove that the Poisson structure of an n-dimensional multisymplectic phase space is induced by (n-1)-Hamiltonian k-vector field seach of which requires introduction of k-Hamiltonians.
Visualizes functions on hyperbolic geometry surfaces.
problem Visualizing functions on hyperbolic geometry surfaces.
method Reinvented phase plotting for hyperbolic geometry using conformal maps.
result Illustrates direct motions on geodesics.
Nonconcentration of eigenfunctions in Microlocal Kakeya-Nikodym norms: a phase space approachmath.AP
Improves bounds on eigenfunctions using microlocal averages in phase space.
problem Improving bounds on eigenfunctions in high frequency limit.
method Develops sufficient conditions for microlocal averages in nonpositive curvature and partially hyperbolic flows.
result Improves microlocal averages for eigenfunctions in more general settings.