322 papers
This paper provides a comprehensive, self-contained derivation of the 8/33 separability probability for two-qubit states under the Hilbert-Schmidt measure by establishing a framework that connects Hilbert-Schmidt volumes of quantum state spaces and flag manifolds to symplectic volumes via the Duistermaat-Heckman measure.
This paper proposes a background-independent quantum framework that describes the evolution of a system relative to a quantum reference frame (such as a quantum clock) via the Ricci-flat Kähler-Einstein equation, recovering standard non-relativistic quantum mechanics in the linear limit while naturally incorporating inertial forces and offering a geometric fiber bundle interpretation of entangled states.
This paper demonstrates that the spectrum of the sector in Jordanian-deformed string theory remains integrable and solvable via the Baxter framework despite the breaking of highest-weight symmetry by a non-abelian Drinfel'd twist, yielding analytic results that match the deformed string spectrum at the one-loop level.
This paper introduces a novel operator-based framework for laser-plasma wakefield acceleration that utilizes specific mathematical operators to systematically describe coupled laser-plasma dynamics, establishes a formal connection to Hilbert-space theory for analyzing energy transfer, and integrates neural operators to enable efficient reduced-order modeling and predictive control.
This paper proposes an analytic approach to determine integrable boundary conditions in two-dimensional sigma-models by analyzing the divisor structure of the Lax connection, which is applied to open strings on with mixed flux to identify two distinct branches of integrable boundaries that generalize known conformal D-branes.
This paper proposes a quantum-coherent thermodynamic framework that extends eigenstate thermalization beyond equilibrium by foliating state space into "minimum-variance leaves" defined via quantum Fisher information, where a "leaf typicality" hypothesis asserts that local observables under unitary evolution are determined solely by the leaf and energy.
This paper establishes rigorous integrability conditions for one-dimensional quantum systems to be classified as free or interacting fermions by defining free fermions through the simultaneous satisfaction of the Yang-Baxter equation and Shastry's decorated star-triangle relation, and provides a procedure to construct integrable interacting models, such as the Hubbard and XY models, via deformations of these free fermionic -matrices.
This paper uses numerical certification to construct a counterexample proving that two-dimensional discrete periodic Schrödinger operators are not Fermi isospectrally rigid, thereby disproving a long-standing conjecture regarding the irreducibility of Fermi varieties for nontrivial real-valued potentials.
This paper investigates the admissibility of pre-Lie structures for semisimple Lie algebras over by analyzing anti-flexible algebras and proving that -associative algebras serve as universal pre-Lie structures for any Lie algebra, including semisimple ones.
This paper provides physics motivations and expositions on tangential structures and invertible field theories to support the construction of fully local 3-dimensional Chern-Simons theories using the cobordism hypothesis, as detailed in a recent collaboration with Claudia Scheimbauer.
This paper establishes a cut and project scheme based on cocompact Fuchsian groups acting on the Poincaré disc, demonstrating that specific fundamental domains generate chaotic Delone sets with countably infinite tile lengths, thereby addressing the potential for improved graded metamaterials and extending previous work on hyperbolic aperiodic structures.
This paper demonstrates that autoparallel curves associated with torsion-free, non-metric-compatible affine connections can be derived from a variational principle by explicitly constructing an action functional through the systematic solution of the inverse problem of the calculus of variations and the associated Helmholtz conditions.
This paper investigates the structure and large genus asymptotics of certain Hurwitz numbers by utilizing the value of the central character on transpositions.
This paper generalizes the large genus asymptotics of Hurwitz numbers from the Riemann sphere to arbitrary compact Riemann surfaces, specifically for cases involving a fixed number of general profiles and some profiles.
This paper classifies systems of nonlinear Camassa-Holm-type partial differential equations that describe surfaces of constant curvature by utilizing the flatness condition of connection 1-forms, leading to new examples and the construction of nonlocal symmetries and solutions for specific two-component systems.
This paper establishes the global existence, uniform boundedness, and scattering of solutions for an energy-subcritical defocusing nonlinear Schrödinger equation in with inhomogeneous nonlinear damping and trapping potential by introducing a novel virial-modified energy to overcome the loss of energy monotonicity caused by spatially dependent damping.
The paper demonstrates that quantum irreducible flag manifolds satisfy an analogue of the Einstein condition, characterized by the proportionality between the Ricci tensor and the metric, within a small open interval surrounding the classical quantization parameter.
This paper provides a concise mathematical introduction to open quantum systems, using the dissipative Jaynes-Cummings model to derive master equations and subsequently establishing the foundational theory of completely positive trace-preserving maps and the GKSL theorem through proofs and exercises.
This paper introduces a reduced-order model based on periodic capacitance matrices and shape optimization to design metascreens that achieve efficient broadband absorption of low-frequency acoustic waves through superabsorption mechanisms.
This paper demonstrates that formulating a well-posed minimum work transition problem in finite-time stochastic thermodynamics requires imposing speed limits on control protocols, a constraint that distinguishes optimal equilibration from minimum work processes and reveals that only generalized Schrödinger bridges remain physically consistent when such limits are removed.