318 papers
This paper establishes the continuum limit of a discrete Hodge-Dirac operator on -dimensional square lattices by introducing a novel higher-dimensional discrete differential calculus framework that generalizes standard simplicial complex methods and proves the operator's convergence to its continuous counterpart as the lattice spacing vanishes.
This paper investigates the Rumin differentials within irreducible unitary representations of the (2,3,5) nilpotent Lie group, computing their spectra and zeta-regularized determinants for Schrödinger representations while evaluating the analytic torsion for generic representations.
This paper presents an unbiased method for mapping particles to distribution functions that unifies Boltzmann's and Gibbs' paradigms to derive the principle of maximum entropy, enabling a rigorous statistical mechanical treatment of self-gravitating systems through the decoupling of time and ensemble averages.
This paper introduces the concept of strongly interlocked modules for vertex operator algebras to establish the well-definedness and key properties of graded pseudo-traces, subsequently applying this framework to fully characterize such modules for rank one Heisenberg and universal Virasoro algebras.
This paper classifies low-order local Hamiltonian operators for two-component evolutionary differential-difference equations, including degenerate cases beyond previous scalar results, and computes the Poisson cohomology of a specific degenerate operator to elucidate its deformation theory and bi-Hamiltonian structure in integrable systems like the Toda lattice.
This paper establishes a rigorous framework demonstrating that quantum contextuality is an intrinsic and necessary feature of universal fault-tolerant quantum computation, providing a new classification criterion for identifying which subsystem stabilizer codes and protocols can support universal gate sets.
This paper introduces new "vertical" intertwining operators that change the particle number in the quantum Calogero model for integer coupling, complementing existing "horizontal" operators to form a grid structure that enables the derivation of Liouville charges and a new basis of non-symmetric integrals through iterated intertwining.
This paper presents an exact frequency-domain formulation of pendulum-like systems that unifies oscillatory, separatrix, and rotational regimes under a single universal spectral kernel, revealing that regime transitions are symmetry-driven reorganizations in frequency space rather than changes in the underlying spectral structure.
This paper derives a novel, local, and crossing-symmetric dispersion relation for 2-2 scattering amplitudes motivated by string theory, demonstrating its utility in bounding Wilson coefficients for gravitational effective field theories and providing convergent series representations for Veneziano, Virasoro-Shapiro, and multi-variable generalizations.
This paper establishes a unified framework based on homological algebra that guarantees the preservation of logical qubit isomorphism when embedding Calderbank-Shor-Steane (CSS) codes into modified structures with additional physical qubits and parity checks, while demonstrating how previous constructions fit within this general theory.
This paper develops a unified algebraic framework using moments to derive equilibrium equations for weighted point configurations with vanishing first moments, extending classical central configuration theory to arbitrary dimensions and mutual distances without relying on variational principles or isometric reductions.
This paper proposes and rigorously establishes a symmetrization relation between 4d BPS quivers and 3d symmetric quivers, demonstrating that the wall-crossing structure of 4d Argyres-Douglas theories is isomorphic to the unlinking of their 3d counterparts and that these symmetric quivers successfully capture the Schur indices of the original 4d theories.
This paper constructs -symmetric conformal boundary states in the Wess-Zumino-Witten conformal field theory by embedding , identifies them as ground states of Affleck-Kennedy-Lieb-Tasaki spin chains within the integrable Uimin-Lai-Sutherland model, and analytically computes their boundary entropy using exact overlap formulas.
This paper demonstrates that Gaussian operations are sufficient to embezzlement arbitrary Gaussian entangled states from ground states of non-interacting critical fermions, establishing embezzlement as a generic property of fermionic Gaussian states and bridging finite-size systems with abstract von Neumann algebra classifications through novel distance bounds.
This paper employs combinatorial methods based on the tree-level effective action to provide an explicit proof of the covariance of on-shell connected functions and derive a closed formula for tree-level scattering amplitudes with any number of external legs, without relying on specific Lagrangian formulations.
This review paper demonstrates that six specific two-dimensional quantum superintegrable systems in flat space are exactly solvable and share a common hidden Lie algebraic structure, characterized by polynomial eigenfunctions, infinite flags of invariant subspaces, and finite-order polynomial algebras of integrals.
This paper introduces a novel Geometric Structure-Preserving Interpolation (-SPIN) method that utilizes geodesic elements and a projection-based relaxation of rotation-deformation coupling to achieve stable, locking-free finite-strain Cosserat micropolar elasticity simulations, particularly in the asymptotic couple-stress limit.
This paper introduces and validates two new structure-preserving discontinuous Galerkin methods, SWIPD-L and SIPGD-L, for the Cahn-Hilliard-Navier-Stokes equations with degenerate mobility, demonstrating that they achieve optimal convergence, preserve key physical properties like mass conservation and energy dissipation, and offer significant computational savings on adaptive meshes compared to existing approaches.
This paper establishes that the real image of a G-invariant variety is metrically rare within its quotient space, a geometric property that explains the prevalence of symmetry in optimization problems by showing that critical points and global minima are statistically driven toward high-symmetry boundary strata.
This paper introduces a new class of smooth conditional entropies based on measured Rényi divergences to establish a tightened one-shot bound for quantum privacy amplification that significantly improves existing results, recovers optimal asymptotic error exponents, and proves optimality up to logarithmic terms.