286 papers
This paper introduces a geometric framework based on the -logarithm linearization principle that unifies the density profiles of 1D quantum fluids across interaction regimes—from the ideal Bose gas to the Tonks-Girardeau gas—within a discrete hierarchy and derives a universal sound velocity scaling law linking static geometry to dynamical excitations.
This paper initiates the study of "twisted holography" for BFSS and IKKT matrix models by identifying their admissible twists, computing their BV-BRST cohomology, and demonstrating that these correspond to twisted IIA and IIB string theories in the planar limit, thereby revealing infinite-dimensional symmetry algebras and connections to specific BPS truncations of eleven-dimensional supergravity.
This paper demonstrates that the Transient Time Correlation Function (TTCF) method is a computationally efficient and precise alternative to traditional time-averaging approaches for calculating nonequilibrium transport coefficients in both linear and nonlinear regimes, as validated through case studies of the Lorentz gas and anharmonic oscillator chains.
This paper establishes a rigorous two-way equivalence between the incompressible Navier-Stokes equations and the principle of minimum pressure gradient (PMPG), demonstrating that the former is mathematically identical to the instantaneous minimization of the pressure force required to enforce incompressibility, thereby offering a variational framework that generalizes classical Galerkin projections and provides new insights into flow stability and the vanishing-viscosity limit.
This paper extends a geometric approach to light rings from spherically symmetric to general axially symmetric spacetimes by utilizing Randers-Finsler optical geometry to determine circular photon orbits via vanishing geodesic curvature and classify their stability through intrinsic flag curvature, while rigorously demonstrating its equivalence to the conventional effective potential method.
This paper proves that the semimetallic phase of incommensurate twisted bilayer graphene remains stable against large-momentum Umklapp scattering for a large set of twist angles satisfying specific Diophantine conditions, thereby providing a rigorous justification for neglecting these terms in effective continuum descriptions.
This paper establishes the uniqueness of singular radial potentials in Schrödinger operators by proving that infinitely many Dirichlet spectra satisfying a Müntz-type condition determine the potential globally, while two spectra from specific distinct angular momenta ensure local uniqueness near the zero potential, thereby refining previous results and confirming a conjecture by Rundell and Sacks.
This paper establishes strong convergence rates for semi-discrete and fully discrete finite element approximations of a fourth-order stochastic pseudo-parabolic equation driven by additive noise, supported by numerical experiments.
This paper analytically demonstrates that the formation of finite-time singularities in axisymmetric 3D incompressible Euler flows within a cylinder is determined exclusively by the local geometric flatness of the initial vortex stretching rate near its global minimum, with specific power-law thresholds distinguishing between regular solutions and blowup scenarios depending on the singularity's location.
This paper presents a proof of the reverse isoperimetric inequality for black holes in Einstein gravity with using a geometric-analytic approach, demonstrating that the reversal of the usual inequality stems from the curved background structure dictated by Einstein's equations.
This paper extends the authors' formalism of elliptic virtual structure constants to encompass hypersurfaces and complete intersections within weighted projective spaces that possess a single Kähler class.
This paper solves a novel nonlocal discrete isoperimetric problem by characterizing the minimizers of a generalized "bi-axial" perimeter that accounts for all internal and external components of a polyomino, thereby establishing a rigorous link to the metastable behavior of a long-range bi-axial Ising model.
This paper establishes global well-posedness, scattering results, and polynomial stability for wave-type equations with singular potentials and data on by employing Yamazaki-type estimates on Lorentz spaces, fixed point arguments, and dispersive estimates within a weak- framework.
This paper revisits the generalized Segal-Bargmann transform associated with a specific Poisson-type distribution on a scaled lattice, presenting new results on its unitary mapping properties and demonstrating how its study naturally connects to the normal ordering problem in the Weyl algebra.
This paper constructs a non-trivial, renormalized Hamiltonian for supercritical spin-boson models, including the Weisskopf-Wigner spontaneous emission, by employing a non-unitary dressing transformation within the Hamiltonian formalism of constructive quantum field theory to resolve the issue of triviality found in unitarily-renormalized versions.
This paper demonstrates that decomposing second variations of the causal action enables an approximate decoupling of linearized field equations, leading to a canonical construction of an extended Hilbert space for solutions of the dynamical wave equation that admits a positive definite, time-evolution-invariant inner product.
This paper systematically characterizes categorical duality operators on spin and anyon chains with internal fusion category symmetry by parameterizing them via quantum cellular automata and associated bimodule categories, demonstrating that such operators form a simplex whose extreme points correspond to simple objects, and proving that these structures inevitably flow to weakly integral fusion categories in the infrared limit when defined on tensor product Hilbert spaces.
This paper constructs Patterson-Sullivan distributions on finite regular graphs via eigenfunction boundary values and establishes their connections to both Wigner distributions and invariant Ruelle distributions, thereby providing discrete analogues of key results from the study of quantum chaos on compact hyperbolic surfaces.
This paper constructs modular families of quantum-integrable elliptic long-range spin chains with q-deformed interactions by freezing spin-Ruijsenaars systems at classical equilibrium configurations, thereby providing a unified framework that interpolates between nearest-neighbour and long-range models while encompassing various known integrable chains and their deformations.
This paper establishes that solitons on non-compact metric graphs satisfying a specific topological assumption remain confined to their initial half-line and reflect off the graph's core, while proving the orbital stability of the unique ground state that exists only on the exceptional "bubble-tower" graph.