In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use…
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48 results for “Quantum Hall effect”
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodi…
Study on quantum Hall effect using Riemann surfaces and Quillen metric.
problem Quantum Hall effect and its adiabatic transport coefficients.
method Analyzing generating functional, adiabatic curvature, and Quillen metric.
result Identified Quillen metric as non-local part of generating functional expansion.
Geometrically proves Zabrodin-Wiegmann conjecture for integer QH states.
problem Proving a geometric version of Zabrodin-Wiegmann conjecture for integer Quantum Hall states.
method Using Riemann surfaces, canonical sections, and asymptotic expansions, the authors construct a canonical element in cohomology and relate its norm to the partition function.
result The constant term of the asymptotic expansion of the partition function matches a geometric version of Zabrodin-Wiegmann's prediction.
This paper is the continuation of Part I, expanding previous results of math.DG/9803051. This paper uses techniques in noncommutative geometry as developed by Alain Connes in order to study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant u…
The twisted Connes-Moscovici higher index theorem is generalized to the case of good orbifolds. The higher index is shown to be a rational number, and in fact non-integer in specific examples of 2-orbifolds. This results in a non-commutative geometry model that predicts the occurrence of fractional quantum numbers in t…
Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…
Analyzes the asymptotic expansion of analytic torsion for line bundles and orbifolds.
problem Analyzing the asymptotic expansion of Ray-Singer analytic torsion.
method Proves and calculates coefficients of the asymptotic expansion for specific cases.
result Calculates coefficients for the terms in the Kahler case.
Topological Quantum Computationquant-ph
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liqu…
Braiding Majorana Fermionscond-mat.str-el
This paper explores Majorana fermions and their braiding representations.
problem Understanding the structure and behavior of Majorana fermions.
method Study of Clifford algebra and braid group representations related to Majorana fermions.
result Clifford Braiding Theorem showing robust representation of braid group phases.
Uncertainty quantification of a multi-component Hall thruster model at varying facility pressuresstat.AP
Bayesian inference calibrates Hall thruster model uncertainty at varying pressures.
problem Quantifying uncertainty in a multi-component Hall thruster model at different facility pressures.
method Bayesian inference applied to calibrate and quantify prediction uncertainty in a coupled multi-component Hall thruster model.
result Model reduces predictive errors in thrust and discharge current by more than 50% compared to a previous model.
In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain an information about classes of t…
Hodge Topology of Semiclassical Transport: A Coordinate-Free Geometric Framework for the Anomalous Hall Effect and Non-Linear Berry Dipolecond-mat.mes-hall
A new geometric framework resolves singularities in anomalous transport.
problem Mathematical singularities in quantum Berry connections.
method Hodge-de Rham decomposition of the Brillouin zone.
result A smooth geometric proxy potential for anomalous transport.
The elliptic Hall algebra governs torus link homology.
problem Proving the elliptic Hall algebra's role in torus link homology.
method Developed a rational Shareshian-Wachs involution to prove the symmetry of generating functions.
result Resolved a conjecture by establishing the elliptic Hall algebra's role in torus link homology.
Gluing two manifolds M_1 and M_2 with a common boundary S yields a closed manifold M. Extending to formal linear combinations x=Sum_i(a_i M_i) yields a sesquilinear pairing p=<,> with values in (formal linear combinations of) closed manifolds. Topological quantum field theory (TQFT) represents this universal pairing p …
Town hall discusses AI's impact on statistics, culture, and training.
problem Adapting statistics to AI advancements and infrastructure.
method Open panel discussion and audience Q&A.
result Candid perspectives on evolving statistical practices.
A natural one-parameter family of Kähler quantizations of the cotangent bundle of a compact Lie group , taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the associated Blattner-Kostant-Sternberg (BKS) pairing map is unitary and coincides with the…
Neural-Network Quantum States connect to Tensor-Network states, enhancing quantum state representation.
problem Describing complex quantum wave functions efficiently.
method Introducing Neural-Network Quantum States and showing their connections to Tensor-Network states.
result Neural-Network Quantum States and String-Bond States can approximate chiral topological states with better accuracy.
This paper constructs cohomological Hall algebras for 3-Calabi-Yau categories.
problem Mathematical definition of the algebra of BPS states.
method Construction of cohomological Hall algebras for 3-Calabi-Yau categories.
result Construction of cohomological Hall algebras and proof of Joyce's conjecture.
The paper studies partition functions of point processes on Kähler manifolds, generalizing geometric functionals and relating to QHE.
problem Analyzing partition functions of determinantal point processes on Kähler manifolds.
method Using geometric functionals and TYZ expansion coefficients of the Bergman kernel.
result The coefficients of the partition function expansion are geometric functionals on Kähler metrics.
A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two propertie…
The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.
problem Decomposing the cohomology of smooth symmetric stacks into invariant parts.
method Using cohomological Hall induction and intersection cohomology of moduli spaces.
result Establishes the BPS decomposition theorem for various symplectic stacks.
The trace of the affine Hecke category is compared with the elliptic Hall algebra.
problem Comparing the trace of the affine Hecke category with the elliptic Hall algebra.
method Using Wakimoto objects and Rouquier complexes, the trace is generated by objects .
result The trace of the affine Hecke category yields an integral form of the elliptic Hall algebra.
In the paper we consider the following conjecture: if a finite group possesses a solvable -Hall subgroup , then there exist elements such that the identity holds. The minimal counter example is shown to be an almost simple group of Lie type.
We classify all unitary modular tensor categories (UMTCs) of rank . There are a total of 70 UMTCs of rank (Note that some authors would have counted as 35 MTCs.) In our convention there are two trivial unitary MTCs distinguished by the modular matrix . Each such UMTC can be obtained from …
Paper analyzes origami slope gaps and their distribution, finding a unique pattern.
problem Analyzing slope gaps in origami surfaces.
method Derived slope gap distribution of a specific origami by considering return times under the horocycle flow.
result Found a unique distribution of origami slope gaps, not a sum of scaled Hall distributions.
Extends Borsuk-Ulam theorem with applications in sphere coverings and colorings.
problem Complexity bounds and structural insights for triangulated sphere mappings.
method Combinatorial labeling and order type analysis of finite point sets.
result New topological Hall theorem and generalizations of hypergraph Hall theorems.
Study on Lin-Lu-Yau curvature and diameter of amply regular graphs.
problem Lower bounds of Lin-Lu-Yau curvature in amply regular graphs.
method Application of Hall's marriage theorem and geometric proof.
result Conference graphs have positive Lin-Lu-Yau curvature.
Proves a pentagon relation in skein theory.
problem Developed a skein-theoretic version of cluster theory and conjectured a pentagon relation.
method Topological proof using skein algebra and elliptic Hall algebra.
result Proves the pentagon relation for the skein dilogarithm.
Given a finitely-generated group G, and a finite group Γ, Philip Hall defined δ_Γto be the number of factor groups of G that are isomorphic to Γ. We show how to compute the Hall invariants by cohomological and combinatorial methods, when G is finitely-presented, and Γbelongs to a certain class of metabelian groups. Key…
Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big e…
Symmetric function lifts torus link homology.
problem Computing the triply-graded Khovanov-Rozansky homology of torus links.
method Defined a symmetric function and showed it satisfies a recursion for torus link homology.
result Triply-graded Khovanov-Rozansky homology of torus links is a specialization of .
SNRA combines power-efficient probabilistic and deterministic computing for deep belief networks.
problem Efficiently training and evaluating deep belief networks with low power consumption.
method Developed a spintronic neuromorphic reconfigurable array (SNRA) for in-circuit training and evaluation of deep belief networks (DBNs). Used probabilistic spin logic devices and a four-state finite state machine for unsupervised training.
result SNRA achieves more than 80% reduction in combined dynamic and static power dissipation compared to SRAM-based configurable fabrics.
On the effects of biased quantum random numbers on the initialization of artificial neural networksquant-ph
Study finds no significant difference in neural network weights with quantum random numbers.
problem Effects of biased quantum random numbers on neural network initialization.
method Empirical study using quantum hardware and classical pseudo-random numbers.
result No statistically significant difference found between quantum random numbers and other types.
Quantum model investigates financial derivative price dynamics with quantum interference effects.
problem Investigate quantum drift in financial derivatives using Heisenberg Equation of Motion.
method Apply geometric techniques to integrate Heisenberg Equation of Motion, model financial market as quantum observable.
result Quantum interference effects can act as drag or boost on financial returns.
This paper applies quantum probability theory to model asset returns, avoiding assumptions about quantum effects.
problem Modeling asset returns with classical probability theory.
method Derives a Schrödinger-like trading equation using quantum probability, linking it to traders' decisions and market behaviors.
result Quantum probability can describe multimodal distributions of asset returns without assuming quantum effects.
Hybrid quantum algorithm tackles binary optimization problems with multiple constraints.
problem Efficiently solving binary optimization problems with multiple constraints using quantum algorithms.
method Combines QAOA with penalty dephasing and Zeno effect for non-Ising constraints.
result Significant improvement in solving practical aircraft loading problems.
Applications of Quantum Tunneling effect have long gone beyond the traditional physical meaning. Initially created by Gamow to explain α-decay of nuclear particles, along the time, quantum tunneling found fertile domain of research in chemistry and recently in biology, where the new discipline of Quantum Biology emerge…
New quantum kernels avoid overfitting by combining local and global components.
problem Exponential concentration in quantum kernels leads to overfitting.
method Local-global quantum kernels combining small subsystem and full-system measurements.
result Demonstrated benign overfitting in local-global quantum kernels.
Finsler Spinopticsmath-ph
The objective of this article is to build up a general theory of geometrical optics for spinning light rays in an inhomogeneous and anisotropic medium modeled on a Finsler manifold. The prerequisites of local Finsler geometry are reviewed together with the main properties of the Cartan connection used in this work. The…
Study evaluates capacity and trainability of parametrized quantum circuits.
problem Finding the best type of circuits for hybrid quantum-classical algorithms.
method Geometric structure of parameter space, effective quantum dimension, and circuit expressiveness.
result Identifies a transition in quantum geometry leading to decay of quantum natural gradient for deep circuits.
Iterative Quantum Feature Mapsquant-ph
A new hybrid framework reduces quantum runtime and noise effects.
problem Challenges in deploying deep QFMs on real quantum hardware.
method Iterative Quantum Feature Maps (IQFMs) combining shallow QFMs and classical augmentation weights.
result Numerical experiments show IQFMs outperforming quantum convolutional neural networks.
The study finds quasi-Einstein metrics on sphere bundles.
problem Finding quasi-Einstein metrics on specific types of manifolds.
method Adapting Hall's work, the study explores quasi-Einstein metrics on sphere bundles over Fano Kaehler-Einstein manifolds and their blow-downs.
result The discovery of quasi-Einstein metrics on sphere bundles.
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that contain information of the cluster structure in high-dimensional space. Based on this …
We suggest to use the Hall-Littlewood version of Rosso-Jones formula to define the germs of -adic HOMFLY-PT polynomials for torus knots , which possess at least the topological invariance. This calls for generalizations to other knot families and is a challenge for several br…
BCIQT model improves ML prediction effectiveness using quantum theory.
problem Improving prediction effectiveness in machine learning models.
method Proposes Binary Classifier Inspired by Quantum Theory (BCIQT) model.
result BCIQT model outperforms state-of-the-art models in recall.
Refined scattering diagrams and theta functions from asymptotic analysis of Maurer-Cartan equationsmath.AG
New geometric proofs and interpretations of scattering diagrams and theta functions.
problem Analyzing the asymptotic behavior of Maurer-Cartan elements for differential graded Lie algebras.
method Asymptotic analytic approach and differential geometric proofs.
result Alternative proofs of consistent completion of scattering diagrams and geometric interpretations of theta functions.