{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0f89268a904fb668ad15c8bd292589a6fd209c35a3da4431b72c936269d24c93","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"20e3ea21a2246b7ff7a0f8505684b8d2626083b804e51358a7efd069709c00f4","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.mbl.quasiperiodic-2d","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"A non-random but irregular potential, built from waves whose wavelengths have an irrational ratio to the lattice spacing (quasiperiodic), has no rare weak spots, so the rare-region argument may not apply. Whether such systems localize in two dimensions is open.","posed_since":"","precise":"Interacting bosons or fermions on a square lattice in the quasiperiodic potential $V_i = V [\\operatorname{cos}(2 \\pi \\beta x_i + \\phi_x) + \\operatorname{cos}(2 \\pi \\beta y_i + \\phi_y)]$ with irrational $\\beta$: is there $V_c$ such that local memory persists at infinite time as $L \\to \\infty$? Answer yes or no.","problem_ref":null,"references":"","settled_by":"A size-independent localization crossover over a wide range of L in experiment, together with a theory excluding resonant instabilities in the quasiperiodic case.","status_note":"Agrawal, Vasseur, Gopalakrishnan (PRB 106, 094206, 2022) argue it is stable in $d=2$ at strong modulation, and a 2025 optical-lattice experiment up to 24 x 24 sites saw no clear size drift of the quasiperiodic crossover.","title":"Is quasiperiodic localization stable in two dimensions","topic_ref":"7f4724a8f5124a8d3b0876fec78a4f3f0f7b467672032acb318713bcededaa82"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b2c96948618b9bdf65ac085b2effb75c317753d7761e602cdb458f8db86d9bd2","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"8af72900dcc6650f71837646e2ca69ab4ca762a3c2f18e73e218dba9cbd2fdbb","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"blMZPxrz1CYspFt_svdZGj-59n6sxra4Gd0mTzn3wNJz-dt518gI09Cduy42hyh4umGOqBh1k-axSnQqWhW3Ag"},"schema":"pubphys.envelope/1"},"record_hash":"b2c96948618b9bdf65ac085b2effb75c317753d7761e602cdb458f8db86d9bd2","leaf_index":1088}