318 papers
The paper demonstrates that for open quantum systems coupled to Gaussian environments, the evolution can be described by a Markovian quantum master equation with an error that decreases exponentially with the inverse system-bath coupling strength, achieved through a generalized Born-Markov approximation that can be iterated to arbitrarily high orders.
This paper proves that max-LINSAT is tightly inapproximable within any constant factor beyond the random-assignment ratio under , a hardness threshold that coincides with the asymptotic performance limit of decoded quantum interferometry, thereby delineating the boundary between classical worst-case hardness and potential quantum advantage.
This paper derives characteristic identities for the split Casimir operator of the Lie algebra in spinor representations to construct invariant projectors, calculate colour factors for ladder Feynman diagrams in gauge theories, and obtain a new -invariant solution to the Yang-Baxter equation.
This monograph explores the mathematical foundations of Special Relativity in flat spacetime, with a specific focus on the Lorentz group and its applications to mechanics and electrodynamics.
This paper utilizes the method of resurgent continuation of transseries to establish a novel correspondence between the -series counting quarter-BPS black hole degeneracies and invariants of Chern-Simons theory on specific orientation-reversed 3-manifolds.
This paper establishes the Drinfeld correspondence between Poisson Lie groups and Lie bialgebras in the infinite-dimensional setting, specifically extending the theory to regular Lie groups modeled on convenient vector spaces such as nuclear Fréchet and Silva spaces, with applications to loop groups and diffeomorphism groups.
This paper proves that the coordinate change formula for the Liouville quantum gravity distance function holds almost surely for all conformal maps simultaneously, thereby rigorously establishing the definition of a quantum surface as a random equivalence class of domains equipped with both LQG area and distance measures.
This paper introduces a general quantum weight reduction procedure for arbitrary CSS codes that utilizes surface code patches to form a "Layer Code," achieving lower check weights and qubit degrees than existing methods while being well-suited for modular architectures with long-range interconnects.
This paper compares causal fermion systems, non-commutative geometry, and generalized trace dynamics, highlighting their shared recovery of fiber bundle structures in the continuum limit and identifying the encoding of spacetime relations via a generalized two-point correlator—replacing Synge's world function—as the key innovation that can be unified across all three frameworks.
This paper introduces a method to construct an ancilla system of size for measuring arbitrary logical Pauli operators of weight in general qLDPC stabilizer codes, thereby significantly reducing the asymptotic overhead of various quantum code surgery schemes.
This paper constructs a path integral measure invariant under the Lorentz group and quasi-invariant under diffeomorphisms by drawing an analogy with the rotationally invariant Wiener measure on the Euclidean plane, thereby establishing a correspondence between paths in the future light cone of Minkowski space and paths on the coverings of the Euclidean plane.
This paper provides a rigorous construction of Dyson Brownian motion on a rectifiable Jordan curve and analyzes its fundamental properties, including the associated Fokker-Planck-Kolmogorov equation, convergence to the stationary Coulomb gas distribution, low-temperature large deviations, and the limiting McKean-Vlasov equation in the many-particle regime.
This paper establishes the nonlinear stability of multi-dimensional rarefaction waves for the compressible Euler equations by introducing a novel Geometric Weighted Energy Method that overcomes derivative loss issues through the identification of a hidden vanishing structure in the top-order derivatives of the characteristic speed.
This paper establishes the well-posedness of the heat equation with homogeneous Dirichlet boundary conditions in time-evolving domains undergoing topological transitions by introducing anisotropic space-time function spaces and applying the Babuška-Banach theorem to prove existence, uniqueness, and a priori estimates for weak solutions.
This paper investigates the Gibbs phenomenon in the Fourier approximation of the sign function using Krawtchouk polynomials, demonstrating that unlike classical orthogonal polynomials, it exhibits a distinct Gibbs constant and a bounded steepness that converges to as the degree increases.
This paper introduces convex optimization, specifically Linear Programming, as a tool to solve the inverse micromechanics problem for isotropic composites with spherical inclusions by determining component volume fractions from known dielectric constants and effective properties using the Eshelby-Mori-Tanaka model.
This paper employs Lie Symmetry Analysis and Noether Point Symmetry methods to derive the symmetry generators and conserved quantities of the Einstein vacuum field equations, thereby offering a novel reformulation of Birkhoff's Theorem.
This paper utilizes the isomorphism between the six-dimensional nilpotence variety and within the pure spinor superfield formalism to classify and explicitly construct various six-dimensional supermultiplets, including vector, hyper, and supergravity multiplets, by associating them with line bundles and higher-rank equivariant vector bundles on projective spaces.
This paper establishes a relative Poincaré–Verdier duality for supermanifolds via Berezin fiber integration to rigorously define picture changing operators and prove the equivalence of component, superspace, and geometric formulations of 3d supergravity.
This paper investigates a discrete model of a heterogeneous elastic line with random springs, demonstrating that when the spring constant distribution follows a power law with exponent , the system exhibits anomalous scaling driven by sample-to-sample fluctuations and abrupt shape jumps, a finding that challenges previous theoretical predictions and is validated by numerical simulations.