arXiv subjects

Lutz Polley

Publications and source records attributed to Lutz Polley.

3 recordsLinked to original sources

arXiv2014

Toy observer in unitary evolution: Histories, consciousness, and state reduction

For a toy version of a quantum system with a conscious observer, it is demonstrated that the many-worlds problem is solved by retreating into the conscious subspace of an entire observer history. In every step of a discretised time, the observer tries to "see" records of his past and present in a coherent temporal sequence, by scanning through a temporal fine-graining cascade. The extreme most likely occurs at the end of some branch, thus determining observer's world line. The relevant neurons, each with two dimensions, are power-law distributed in number, so order statistics implies that conscious dimension is located almost entirely in the extremal branch.

quant-ph↗

arXiv2010

Extreme-value statistics of dimensions determining an observer's branch of the world?

In a many-worlds framework, combining decoherent histories and extreme-value statistics, it is conjectured that the (matrix) dimension of the Hamiltonian processing records and memories near the end of an observer's history is almost entirely located in a single branch of his/her wavefunction.

quant-ph↗

arXiv1998

Schroedinger equation as the universal continuum limit of nonrelativistic coherent hopping on a cubic spatial lattice

The Schroedinger equation with scalar and vector potentials is the continuum limit of any coherent hopping process (where position eigenstates superpose with neighbouring eigenstates after a time step) whose hopping amplitudes are homogeneous in quadratic order of the inverse lattice spacing, inhomogeneous in first order, and satisfying a summability condition with respect to higher-than-next neighbours.

quant-ph↗