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Related Concept Videos

Laws of Logarithms I01:30

Laws of Logarithms I

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Logarithms are fundamental mathematical operations that serve as the inverse of exponentiation. They provide a means to express how many times a base must be raised to yield a given number. For base 10, often referred to as the common logarithm, the notation is written simply as log. Thus, if 10n = x, then log⁡(x) = n. This relationship makes logarithms especially valuable in simplifying complex calculations involving multiplication, division, and exponentiation.Logarithmic expressions...
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Logarithmic functions are powerful tools for simplifying the mathematical representation of phenomena involving exponential changes. Their ability to convert multiplicative relationships into additive ones is especially valuable in various scientific and engineering contexts. One notable application of logarithms is measuring sound intensity, specifically through the decibel (dB) scale used in acoustics.Sound intensity levels vary over an extensive range, from the faintest audible whisper to...
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Logarithmic laws provide essential tools for simplifying and evaluating exponential expressions, particularly in mathematical and applied settings where powers and repeated multiplication play a central role. Two important rules are the power law and the change-of-base formula, both allowing for transforming expressions into more manageable forms.The power law of logarithms states that the logarithm of a number raised to an exponent equals the exponent multiplied by the logarithm of the base...
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When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...
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Logarithmically Slow Relaxation in Quasiperiodically Driven Random Spin Chains.

Philipp T Dumitrescu1, Romain Vasseur2,3,4, Andrew C Potter1

  • 1Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA.

Physical Review Letters
|March 16, 2018
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Summary
This summary is machine-generated.

We simulate disordered spin chains with Fibonacci drives, revealing a long-lived glassy phase before thermalization. Metastable dynamics, like time quasicrystals, emerge, challenging standard high-frequency approximations.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Disordered Systems

Background:

  • Understanding the dynamics of disordered quantum systems under time-dependent drives is crucial.
  • Quasiperiodic driving sequences offer unique pathways to explore non-equilibrium phenomena.
  • The behavior of interacting spin chains in such regimes remains an active area of research.

Purpose of the Study:

  • To simulate and analyze the non-equilibrium dynamics of a disordered interacting spin chain.
  • To investigate the effects of a quasiperiodic time-dependent drive (Fibonacci sequence).
  • To explore the emergence of metastable dynamical phases and thermalization.

Main Methods:

  • Efficient numerical simulation exploiting the recursive structure of the Fibonacci drive.
  • Analysis of entanglement growth and correlation decay to characterize system dynamics.
  • Comparison with high-frequency expansion methods for Floquet systems.

Main Results:

  • Observation of a long-lived glassy regime with logarithmic entanglement growth and correlation decay.
  • Emergence of metastable dynamical phases, including a 'time quasicrystal' with persistent oscillations.
  • Demonstration of eventual thermalization to infinite temperature at long timescales.
  • Breakdown of standard high-frequency expansions beyond fourth order for this system.

Conclusions:

  • Quasiperiodic driving can lead to novel, long-lived non-equilibrium phases in disordered spin chains.
  • The system exhibits prethermal glassy relaxation distinct from typical Floquet dynamics.
  • Standard theoretical approximations fail to capture the observed complex dynamics at higher orders.