114 entries matching the current filters. Sorted by recently added.
Given a finite-dimensional memoryless quantum channel mathcal N through an explicit rational/algebraic Choi matrix and a rational varepsilon 0 , does a single algorithm always terminate and output q satisfying |q-Q(…
For specified one-dimensional translation-invariant nearest-neighbour Hamiltonian families and product-state inputs, determine when a local-observable long-time-average threshold problem is decidable. Specify a finite…
For finitely specified one-parameter local-Hamiltonian families, identify restrictions giving terminating algorithms for phase-boundary locations to rational accuracy varepsilon 0 , or for specified local order…
Classify decidability for specified small-local-dimension and frustration-free one-dimensional chains. A concrete promise problem takes a finite rational/algebraic nearest-neighbour interaction 0 le h le I and rational…
For scalar Schrödinger operators - Delta+V on L^2( mathbb R^3) , is the optimal constant in operatorname Tr (- Delta+V) - le L 1,3 int mathbb R^3 V -(x)^ 5/2 ,dx equal to its semiclassical value L 1,3 ^ mathrm cl ?
For H lambda=- Delta+ lambda V omega on ell^2( mathbb Z^2) with independent potentials uniform on [-1,1] , prove that for every lambda 0 the almost-sure spectrum is pure point with exponentially localized eigenfunctions…
For a specified Anosov quantum system, bound the mass that a semiclassical measure of exact eigenstates can assign to an unstable periodic orbit, and determine whether the bounds are attainable by exceptional…
Establish random-matrix local spectral statistics for an explicitly specified class of quantized chaotic Hamiltonians. A first target is unfolded two-point GOE statistics for a stated class of time-reversal-invariant,…
For every compact connected smooth surface without boundary and with strictly negative curvature, does every sequence of normalized Laplace eigenfunctions with eigenvalues tending to infinity have Liouville…
For a stated two-dimensional PEPS tensor class, give verifiable sufficient tensor or boundary-state conditions implying a system-size-independent bulk gap of its parent Hamiltonian, with an explicit lower bound.
Extend verifiable bulk-gap stability criteria to a specified interacting lattice family outside current theorems. Fix the unperturbed gap, ground-space assumptions and interaction-decay norm, and prove a…
For the spin-1 antiferromagnetic Heisenberg chain H L= sum j=1 ^L vec S j cdot vec S j+1 with periodic boundary conditions and coupling one, prove liminf L to infty (E 1(L)-E 0(L)) 0 , where E 1 is the first energy…
For a specified ensemble of interacting disordered spin chains, establish or exclude thermodynamic many-body localization with a stated energy window, probability bound and quasilocal-integral-of-motion criterion.…
For H lambda=- Delta+ lambda V omega on ell^2( mathbb Z^3) , with independent potentials uniform on [-1,1] , prove that all sufficiently small lambda 0 admit a nonempty interval in the free band with almost-sure nonzero…
For the nonrelativistic Coulomb Hamiltonian of fermionic spin-1/2 electrons and a fixed point nucleus of charge Z , prove that the maximal number of bound electrons satisfies N c(Z) le Z+C , with C independent of Z .
Given a local algebraic instrument and a compact spacetime coupling region, characterize whether localized coupling to an admissibly prepared probe field can implement or approximate the instrument while respecting…
For a specified interacting field model and class of globally hyperbolic curved spacetimes, construct local observables and admissible states beyond formal perturbation theory; state any extra boundary, symmetry or…
For specified gauge-invariant operations and boundary access, characterize distillable resources of spatial subsystems and prove when their continuum predictions are regulator independent; compare different access…
For specified local algebras, spacetime separation and energy/work budgets, bound entanglement distillation and catalytic embezzlement yields and errors under physically implementable local operations, including mixed…
For a specified charged model, construct infrared-finite scattering predictions for stated inclusive observables and asymptotic charge sectors, prove the applicable completeness statement, and control collinear…
For a specified massive, local, interacting relativistic QFT in 3+1 dimensions, prove that the vacuum and scattering states of stable particles span the chosen physical sector; formulate separate completeness criteria…
Construct nonperturbative regulators for non-Abelian chiral gauge theories with all local and global anomalies cancelled, proving locality, global gauge consistency, removal of unwanted mirror modes and the required…
Either construct nontrivial four-dimensional continuum QED satisfying specified relativistic QFT axioms, or prove that removing the ultraviolet cutoff forces its renormalized interaction to vanish; control the charge…
In zero-temperature continuum pure SU(N) Yang–Mills theory, prove a positive asymptotic string tension for external sources with nonzero N -ality, using a renormalized Wilson-loop or static-potential criterion.
For every compact simple gauge group G , construct a nontrivial quantum Yang–Mills theory on mathbb R ^4 satisfying suitable axioms and prove its Hamiltonian has a mass gap Delta 0 .