Search results for "Geometric"

showing 10 items of 652 documents

A closed formula for the evaluation of foams

2020

International audience; We give a purely combinatorial formula for evaluating closed, decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral, equivariant version of colored Khovanov-Rozansky link homology categorifying the sl(N) link polynomial. We also provide connections to the equivariant cohomology rings of partial flag varieties.

Pure mathematicscoherent sheaveskhovanov-rozansky homology01 natural sciencesMathematics::Algebraic Topologylink homologiesMathematics::K-Theory and HomologyMathematics::Quantum Algebra[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences[MATH]Mathematics [math]010306 general physicsMathematics::Symplectic GeometryMathematical PhysicsMathematicswebsmodel010308 nuclear & particles physicsmodulesmatrix factorizationscategoriesFoamsMathematics::Geometric TopologyTQFTknot floer homologyholomorphic disksGeometry and Topologyinvariantstangle
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Anomalous Anosov flows revisited

2017

This paper is devoted to higher dimensional Anosov flows and consists of two parts. In the first part, we investigate fiberwise Anosov flows on affine torus bundles which fiber over 3-dimensional Anosov flows. We provide a dichotomy result for such flows --- they are either suspensions of Anosov diffeomorphisms or the stable and unstable distributions have equal dimensions. In the second part, we give a new surgery type construction of Anosov flows, which yields non-transitive Anosov flows in all odd dimensions.

Pure mathematicsdiffeomorphismsMathematics::Dynamical Systems37D30Fiber (mathematics)General Mathematics010102 general mathematics37D30 (primary)TorusGeometric Topology (math.GT)Dynamical Systems (math.DS)Type (model theory)01 natural sciencesMathematics::Geometric TopologyPhysics::Fluid DynamicsMathematics - Geometric Topology0103 physical sciencesFOS: Mathematics010307 mathematical physicsAffine transformation0101 mathematics[MATH]Mathematics [math]Mathematics - Dynamical SystemsMathematics::Symplectic GeometryMathematics
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Assouad dimension, Nagata dimension, and uniformly close metric tangents

2013

We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…

Pure mathematicssub-Riemannian manifoldsGeneral Mathematics54F45 (Primary) 53C23 54E35 53C17 (Secondary)01 natural sciencessymbols.namesakeMathematics - Geometric TopologyDimension (vector space)Mathematics - Metric Geometry0103 physical sciencesFOS: MathematicsMathematics (all)assouad dimensionMathematics::Metric GeometryPoint (geometry)0101 mathematicsMathematics010102 general mathematicsta111TangentMetric Geometry (math.MG)Geometric Topology (math.GT)16. Peace & justiceMetric dimensionAssouad dimension; Metric tangents; Nagata dimension; Sub-Riemannian manifolds; Mathematics (all)Metric spaceBounded functionNagata dimensionMetric (mathematics)symbols010307 mathematical physicsMathematics::Differential Geometrymetric tangentsLebesgue covering dimension
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Geometrical control of pure spin current induced domain wall depinning.

2017

[EN] We investigate the pure spin-current assisted depinning of magnetic domain walls in half ring based Py/Al lateral spin valve structures. Our optimized geometry incorporating a patterned notch in the detector electrode, directly below the Al spin conduit, provides a tailored pinning potential for a transverse domain wall and allows for a precise control over the magnetization configuration and as a result the domain wall pinning. Due to the patterned notch, we are able to study the depinning field as a function of the applied external field for certain applied current densities and observe a clear asymmetry for the two opposite field directions. Micromagnetic simulations show that this …

Pure spin currentField (physics)Magnetic domainGeometrical constrictions in nanostructuresSpin valve02 engineering and technology01 natural sciencesMagnetization0103 physical sciencesComputational physicsGeneral Materials Science[PHYS.COND]Physics [physics]/Condensed Matter [cond-mat]010306 general physicsComputingMilieux_MISCELLANEOUSSpin-½PhysicsCondensed matter physicsMagnetismSpin-transfer torque021001 nanoscience & nanotechnologyCondensed Matter PhysicsDomain wall motionDomain wall (magnetism)Spin Hall effect0210 nano-technologyJournal of physics. Condensed matter : an Institute of Physics journal
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"Table 4" of "Probing the quantum interference between singly and doubly resonant top-quark production in $pp$ collisions at $\sqrt{s}=13$ TeV with t…

2019

The systematic uncertainty on the unfolded distribution as a function of minimax-mbl, broken down by components.

Quantitative Biology::BiomoleculesStatistics::TheoryMathematics::Algebraic Geometry13000.0Proton-Proton ScatteringCross SectionSIGMathematics::Geometric TopologyComputer Science::DatabasesP P --> W W b b
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A Monte Carlo Study of Knots in Long Double-Stranded DNA Chains.

2016

We determine knotting probabilities and typical sizes of knots in double-stranded DNA for chains of up to half a million base pairs with computer simulations of a coarse-grained bead-stick model: Single trefoil knots and composite knots which include at least one trefoil as a prime factor are shown to be common in DNA chains exceeding 250,000 base pairs, assuming physiologically relevant salt conditions. The analysis is motivated by the emergence of DNA nanopore sequencing technology, as knots are a potential cause of erroneous nucleotide reads in nanopore sequencing devices and may severely limit read lengths in the foreseeable future. Even though our coarse-grained model is only based on …

Quantitative Biology::Biomoleculessurgical procedures operativestomatognathic systemlcsh:Biology (General)530 Physicsfood and beverages530 PhysikMathematics::Geometric Topologylcsh:QH301-705.5PLoS Computational Biology
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New approach to describe two coupled spins in a variable magnetic field

2021

We propose a method to describe the evolution of two spins coupled by hyperfine i nteraction in an external time- dependent magnetic field. We apply the approach to the case of hyperfine interaction with axial symmetry, which can be solved exactly in a constant, appropriately oriented magnetic field. In order to t reat t he n onstationary d ynamical p roblem, we modify the time-dependent Schrödinger equation through a change of representation that, by exploiting an instantaneous (adiabatic) basis makes the time-dependent Hamiltonian diagonal at any time instant. The solution of the transformed time-dependent Schrödinger FRVBUJPO in the form of chronologically ordered exponents with transpar…

Quantum ComputationPhysicsQuantum PhysicsGeometric PhaseSpinsQuantum Physics; Quantum PhysicsFOS: Physical sciencesSchrödinger equationMagnetic fieldsymbols.namesakeExact solutions in general relativityQuantum mechanicssymbolsHamiltonian (quantum mechanics)Adiabatic processAxial symmetryQuantum Physics (quant-ph)QubitsHyperfine structure
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Thermodynamic, dynamic and transport properties of quantum spin liquid in herbertsmithite from experimental and theoretical point of view

2019

In our review we focus on the quantum spin liquid, defining the thermodynamic, transport and relaxation properties of geometrically frustrated magnets (insulators) represented by herbertsmithite $\rm ZnCu_{3}(OH)_6Cl_2$.

Quantum phase transitionGeometrical frustrationFOS: Physical sciences02 engineering and technologyengineering.material01 natural sciencesCondensed Matter - Strongly Correlated ElectronsQuantum state0103 physical sciences010306 general physicsQuantum computerPhysicsQuantum PhysicsCondensed matter physicsStrongly Correlated Electrons (cond-mat.str-el)quantum spin liquidsherbertsmithitetopological quantum phase transitions021001 nanoscience & nanotechnologyCondensed Matter Physicslcsh:QC1-999Electronic Optical and Magnetic Materialsflat bandsengineeringQuasiparticleState of matterHerbertsmithiteCondensed Matter::Strongly Correlated ElectronsQuantum spin liquidfermion condensation0210 nano-technologyQuantum Physics (quant-ph)lcsh:Physics
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Uhlmann curvature in dissipative phase transitions

2018

We study the mean Uhlmann curvature in fermionic systems undergoing a dissipative driven phase transition. We consider a paradigmatic class of lattice fermion systems in non-equilibrium steady-state of an open system with local reservoirs, which are characterised by a Gaussian fermionic steady state. In the thermodynamical limit, in systems with translational invariance we show that a singular behaviour of the Uhlmann curvature represents a sufficient criterion for criticalities, in the sense of diverging correlation length, and it is not otherwise sensitive to the closure of the Liouvillian dissipative gap. In finite size systems, we show that the scaling behaviour of the mean Uhlmann curv…

Quantum phase transitionPhase transitionSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciCritical phenomenaGaussianlcsh:MedicineFOS: Physical sciencesQuantum phase transitionCurvature01 natural sciencesArticle010305 fluids & plasmassymbols.namesake0103 physical sciencesUhlmann curvatureStatistical physics010306 general physicslcsh:ScienceQuantumCondensed Matter - Statistical MechanicsPhysicsQuantum PhysicsMultidisciplinaryStatistical Mechanics (cond-mat.stat-mech)lcsh:RUhlmann geometric phaseFermionDissipative systemsymbolslcsh:QQuantum Physics (quant-ph)
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Geometric-phase backaction in a mesoscopic qubit-oscillator system

2012

We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro- and nanomechanical devices coupled to an effective two-level system. © 2012 American Physical Society.

Quantum phase transitionPhysicsNANOMECHANICAL RESONATOR; BACK-ACTION; QUANTUM; OPTOMECHANICS; MECHANICS; EVOLUTION; MODEAtomic and Molecular Physics and OpticsSettore FIS/03 - Fisica Della MateriaPhase qubitOptical phase spaceClassical mechanicsGeometric phaseQuantum harmonic oscillatorPhase spaceQubitQuantum mechanicsGeometric phases atomic physics quantum interferometryHarmonic oscillator
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