A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Quantum field theory connects Riemannian geometry to quantum fluctuations.
Quantum connections replace metrics with operator inner products.
The paper calculates fractional quantum numbers on complex orbifolds with strong magnetic fields.
Optimal transport theory applied to quantum states on Grassmannians.
Quantum transport maps network clusters on a circle, revealing complex community structures.
Program connects quantum computing and topological field theories.
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is governed via (a kind of) a parallel transport in this bundle. Some problems concernin…
We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum s…
Paper explores Monge-Ampère in deep learning and quantum geometry.
We explain how the kind of ``parallel transport'' of a wavefunction used in discussing the Berry or Geometrical phase induces the conventional parallel transport of certain real vectors. These real vectors are associated with operators whose commutators yield diagonal operators; or in Lie algebras those operators whose…
Quantum SU(n) representations are asymptotically faithful with norm estimates.
FEAT estimates free energy using adaptive transports.
The quantum navigation problem of finding the time-optimal control Hamiltonian that transports a given initial state to a target state through quantum wind, that is, under the influence of external fields or potentials, is analysed. By lifting the problem from the state space to the space of unitary gates realising the…
We generalize the notion of parallel transport along paths for abelian bundles to parallel transport along surfaces for abelian gerbes using an embedded Topological Quantum Field Theory (TQFT) approach. We show both for bundles and gerbes with connection that there is a one-to-one correspondence between their local des…
Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first order transversally elliptic operator with the (classical) evolution of it…
New approach uses neural networks to predict quantum advantage on graphs.
Geometric arbitrage theory uses quantum mechanics to model market dynamics and arbitrage opportunities.
New smooth 2-group extensions from bundle gerbes on manifolds.
We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree of the positive Hermitian …
Develops optimal transport in Lorentzian spaces with synthetic curvature bounds.
Simulated Bifurcation outperforms quantum machines in community detection.
Paper studies non-associativity in quantum systems with magnetic fields.
Study geometric quantization of Hamiltonian flows using Berezin-Toeplitz operators.
Optimal transport simplifies machine learning by comparing probability measures.
Generalizes differentiation under integral sign to submanifolds with corners.
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structu…
A new geometric framework resolves singularities in anomalous transport.
New method for modeling densities on Riemannian manifolds with symmetries.
We consider the Dirichlet Laplacian in tubular neighbourhoods of complete non-compact Riemannian manifolds immersed in the Euclidean space. We show that the essential spectrum coincides with the spectrum of a planar tube provided that the second fundamental form of the manifold vanishes at infinity and the transport of…
We study the differential geometry of principal G-bundles whose base space is the space of free paths (loops) on a manifold M. In particular we consider connections defined in terms of pairs (A,B), where A is a connection for a fixed principal bundle P(M,G) and B is a 2-form on M. The relevant curvatures, parallel tran…
New diagrammatic approach connects knot Floer homology with quantum group representations.
A new training method for normalizing flows without samples.
In this paper, we will provide a review of the geometric construction, proposed by Witten, of the SU(n) quantum representations of the mapping class groups which are part of the Reshetikhin-Turaev TQFT for the quantum group U_q(sl(n, C)). In particular, we recall the differential geometric construction of Hitchin's pro…
Quantum algorithm improves portfolio optimization quality measured by Wasserstein distance.
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…
This is a review of explicit computations of Connes distance in noncommutative geometry, covering finite dimensional spectral triples, almost-commutative geometries, and spectral triples on the algebra of compact operators. Several applications to physics are covered, like the metric interpretation of the Higgs field, …
The relativistic quantum mechanic approach is used to develop a stock market dynamics. The relativistic is conceptional here as the meaning of big external volatility or volatility shock on a financial market. We used a differential geometry approach with the parallel transport of the prices to obtain a direct shift of…
Geometric quantization for symplectic maps via Toeplitz operators.
New Hermite approximations accelerate convergence with adaptive coordinate transformations.
Artificial neural networks reduce computational costs for predicting excitation energy transfer properties in light-harvesting systems.
Paper addresses optimization on Hadamard manifolds, generalizing gradient flow.
We give a brief introduction to the Gauge Theory of Arbitrage. Treating a calculation of Net Present Values (NPV) and currencies exchanges as a parallel transport in some fibre bundle, we give geometrical interpretation of the interest rate, exchange rates and prices of securities as a proper connection components. Thi…
Paper uses second-order differential geometry to study stochastic mechanics.
Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family of Hilbert spaces, and the question arises if the spaces are canonically isomorphic. [ADW] and [Hi] suggest to view as fibers of a Hilbert bundle , introduce a connec…
Stability proved for martingale and weak transport problems.
New methods estimate transport-growth pairs in unbalanced optimal transport.
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The …
Novel approach learns optimal transport using convex neural networks.