Tag: Mathematical Physics
Spectral localizer matches local Chern and winding markers
What the study found The study explicitly demonstrates that the spectral localizer is equivalent to local Chern and winding markers. The authors show that Chern and winding markers appear as leading-order terms in a perturbative expansion in the spectral localizer parameter κ. Why the authors say this matters The authors say this matters because the…
Log-Sobolev inequality holds for some Gibbs measures
What the study found The authors show that the Gibbs measures for the focusing Schrödinger equation satisfy a log-Sobolev inequality when 2 ≤ p ≤ 4. For p > 4, they establish a lower bound for the Hessian of the effective potential. Why the authors say this matters The study suggests that the log-Sobolev inequality…
Heterotic supergravity deformations are constructed with vector methods
What the study found The authors constructed bi- and uni-vector deformations of 10d heterotic supergravity solutions. They also generalized the "open/closed" map for this setting and examined examples of the resulting deformed solutions, especially for the F1 string solution. Why the authors say this matters The abstract does not state a broader significance or application…
Global regularity and blow-up criteria are established for a non-local equation
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in MathematicsWhat the study found The study found that higher-order Sobolev solutions for a non-local integrable evolution equation can exist globally under a natural assumption on the initial momentum. It also identified a criterion for the existence of blow-up solutions. Why the authors say this matters The authors say the equation is related to pseudospherical surfaces…
Non-Abelian Dirac oscillator shows isospin splitting
What the study found The study finds that a covariant Dirac oscillator can be extended to an SU(2) non-Abelian gauge background, where the commutator term produces matrix-valued spin-isospin couplings and, for an aligned planar background, a closed-form isospin splitting. Why the authors say this matters The authors conclude that the framework separates commutator-driven effects from…
Upper bound estimated for Weyl points from multifold degeneracies
What the study found The study finds an upper bound on the number of Weyl points, meaning generic twofold energy-degeneracy points, that can arise when a multifold degeneracy point in a quantum system is perturbed. Why the authors say this matters The authors say their work helps connect physics and mathematics by using singularity theory…
