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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
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Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
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Bistability and time crystals in long-ranged directed percolation.

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This study introduces a novel cellular automaton with long-range interactions, demonstrating a new type of matter called a discrete time crystal. This system exhibits unique behaviors under periodic modulation, influenced by initial conditions.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Stochastic processes are fundamental to many scientific systems.
  • Probabilistic cellular automata offer a minimal model for noisy many-particle systems.
  • Traditional models often use time-independent, short-ranged rules.

Purpose of the Study:

  • To propose a cellular automaton with power-law interactions.
  • To investigate its potential for novel phases of matter.
  • To explore the impact of periodic modulation on system dynamics.

Main Methods:

  • Development of a cellular automaton model with power-law interactions.
  • Analysis of system behavior under periodic modulation of update rules.
  • Investigation of long-range directed percolation and bistable phases.
  • Examination of discrete time translation symmetry breaking.

Main Results:

  • The proposed automaton exhibits a bistable phase of long-ranged directed percolation.
  • System behavior depends on both dynamics and initial conditions.
  • A discrete time crystal phase is observed under periodic modulation.
  • Long-range interactions enable a self-correcting mechanism against noise.

Conclusions:

  • The study provides a concrete example of a classical discrete time crystal.
  • The findings open avenues for exploring new non-equilibrium phases.
  • Driven probabilistic cellular automata represent an underexplored research area.