  An explicit microscopic realization of the phenomenon of holography is
provided by a class of simple quantum theories of a bosonic field inhabiting a
d-dimensional space and experiencing a momentum dependent attractive
interaction. An exact mode counting reveals a family of holographic states. In
each a set of gapless modes emerges with their number equal to the area of a
(d-1)-dimensional sphere. These modes store an exponentially large number of
patterns within a microscopic energy gap. The resulting micro-state entropy
obeys the area-law reminiscent of a black hole entropy. We study the
time-evolution of the stored patterns and observe the following phenomenon:
Among the degenerate micro-states the ones with heavier loaded memories survive
longer than those that store emptier patterns. Thus, a state gets stabilized by
the burden of its own memory. From time to time the information pattern gets
off-loaded from one holographic state into another but cannot escape the
system. During this process the pattern becomes highly entangled and scrambled.
We suggest that this phenomenon is universal in systems with enhanced memory
storage capacity, such as black holes or critical neural networks. This
universality sheds an interesting light on the puzzle of why, despite the
evaporation, is a black hole forced to maintain information internally for a
very long time.
