{"product_id":"stilla-anderson-localization-physics-t-shirt","title":"Stilla – Anderson Localization Physics T-Shirt","description":"\u003cp\u003eStilla was walking. Then the pillars got random, her own echoes pinned her in place, and she stopped spreading.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eIn a lattice with random site energies, waves scattered along many paths interfere and can stop diffusing altogether. With enough disorder the wave is trapped in an envelope that falls off exponentially, |ψ(x)| ~ e^(−|x|\/ξ), where ξ is the localization length. In 1-D all states localise; in 2-D there is no true metal (for non-interacting electrons without spin-orbit coupling); in 3-D there is a mobility edge.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eH = Σᵢ εᵢ cᵢ† cᵢ − t Σ⟨ij⟩ cᵢ† cⱼ,   εᵢ random in [−W\/2, W\/2]\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eH: Hamiltonian, energy (J)\u003c\/li\u003e\n\u003cli\u003eεᵢ: random energy of site i (J)\u003c\/li\u003e\n\u003cli\u003ecᵢ†, cᵢ: create \/ remove a particle at site i (dimensionless operators)\u003c\/li\u003e\n\u003cli\u003et: hopping energy between neighbouring sites (J)\u003c\/li\u003e\n\u003cli\u003eW: width of the disorder (J)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eP. W. Anderson proposed it in 1958; in 2008 it was seen in matter waves, a Bose-Einstein condensate (Billy et al.; Roati et al.).\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e Localization stops diffusion, not all motion, and the 2-D \"no metal\" result needs the conditions above.\u003c\/p\u003e\u003ch3\u003eOn the shirt\u003c\/h3\u003e\u003cp\u003eFront: Stilla, the pixel-art character, with the title. Back: the Anderson Hamiltonian, the exponential envelope, the 1-D\/2-D\/3-D summary and four sources from 1958 to 2008. Printed on a unisex tee.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"S \/ White","offer_id":50936583356519,"sku":"30781765432919331627","price":29.99,"currency_code":"USD","in_stock":true},{"title":"S \/ Black","offer_id":50936583389287,"sku":"89829253120957105109","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ White","offer_id":50936583422055,"sku":"33244784884606609131","price":29.99,"currency_code":"USD","in_stock":true},{"title":"M \/ Black","offer_id":50936583454823,"sku":"14262517444384156913","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ White","offer_id":50936583487591,"sku":"81370720904951521769","price":29.99,"currency_code":"USD","in_stock":true},{"title":"L \/ Black","offer_id":50936583520359,"sku":"29094579203915531613","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ White","offer_id":50936583553127,"sku":"70416376715800114677","price":29.99,"currency_code":"USD","in_stock":true},{"title":"XL \/ Black","offer_id":50936583585895,"sku":"15804844961621409981","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ White","offer_id":50936583618663,"sku":"29369519257978775309","price":29.99,"currency_code":"USD","in_stock":true},{"title":"2XL \/ Black","offer_id":50936583651431,"sku":"32083662352818387419","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ White","offer_id":50936583684199,"sku":"15871526386275280396","price":29.99,"currency_code":"USD","in_stock":true},{"title":"3XL \/ Black","offer_id":50936583716967,"sku":"27352240688762274784","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ White","offer_id":50936583749735,"sku":"78450301915221275236","price":29.99,"currency_code":"USD","in_stock":true},{"title":"4XL \/ Black","offer_id":50936583782503,"sku":"30741898633480551454","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ White","offer_id":50936583815271,"sku":"85533233349873361926","price":29.99,"currency_code":"USD","in_stock":true},{"title":"5XL \/ Black","offer_id":50936583848039,"sku":"15162211975820351851","price":29.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/anderson-localization_front_02_white.png?v=1793595583","url":"https:\/\/pixelatedphysics.com\/zh-hant\/products\/stilla-anderson-localization-physics-t-shirt","provider":"Pixelated Physics","version":"1.0","type":"link"}