We introduce fractal liquids by generalizing classical liquids of integer dimensions d=1,2,3 to a noninteger dimension dl. The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid droplets confined ...

What is the dimension of a smooth family of complex Hadamard matrices including the Fourier matrix? We address this problem with a power series expansion. Studying all dimensions up to 100 we find that the first order result is misleading unless the dimension is 6, or a power of a prime. In general the answer depends critically on the prime number decomposition of the dimension. Our results sug...

Abstract By modifying constructions of Bĕıdar and Small we prove that for countably generated prime F -algebras of finite GK dimension there exists an affinization having finite GK dimension. Using this result we show: for any field there exists a prime affine algebra of GK dimension two that is neither primitive nor PI; for any countable field F there exists a prime affine F -algebra of GK dim...

We construct a discrete subset of Narain CFTs from quantum stabilizer codes with qudit (including qubit) systems whose dimension is prime number. Our construction exploits three important relations. The first relation between and classical codes. second Lorentzian lattices. third lattices CFTs. In particular, we study Calderbank-Shor-Steane (CSS) as special class the ensembles code constructed ...