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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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Thermal strain is a concept that arises when we consider how temperature changes affect structures. Unlike the conventional assumption that structures remain constant under load, real-world scenarios often involve temperature fluctuations that can significantly impact these structures. Consider a homogeneous rod with a uniform cross-section resting freely on a flat horizontal surface. If the rod's temperature increases, the rod elongates. This elongation is proportional to the temperature...
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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Eigenstate thermalization hypothesis and eigenstate-to-eigenstate fluctuations.

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The eigenstate thermalization hypothesis (ETH) holds in non-integrable systems but is violated in integrable ones. This difference arises from persistent eigenstate fluctuations in integrable systems, impacting thermalization properties.

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Area of Science:

  • Quantum Many-Body Physics
  • Statistical Mechanics
  • Condensed Matter Theory

Background:

  • The Eigenstate Thermalization Hypothesis (ETH) posits that isolated quantum systems can thermalize.
  • Investigating ETH validity is crucial for understanding thermalization in quantum systems.
  • Spin-1/2 XXZ chains provide a key model for studying integrability and ETH.

Purpose of the Study:

  • To determine the validity and violation of ETH in integrable and non-integrable spin-1/2 XXZ chains.
  • To analyze the statistical properties of matrix elements in the energy eigenstate basis.
  • To elucidate the microscopic origins of thermalization breakdown in integrable systems.

Main Methods:

  • Energy-resolved analysis of observable matrix elements within energy shells.
  • Construction of block submatrices for eigenstates within constant-width energy shells.
  • Measurement of the second moment of off-diagonal elements and analysis of its variance.

Main Results:

  • In non-integrable systems, the variance of columnar second moments decreases with system size, indicating self-averaging and ETH consistency.
  • In integrable systems, variance persists, showing eigenstate-to-eigenstate fluctuations.
  • These fluctuations explain the breakdown of the fluctuation-dissipation theorem in integrable systems.

Conclusions:

  • ETH is supported in non-integrable spin-1/2 XXZ chains.
  • ETH is violated in integrable spin-1/2 XXZ chains due to persistent eigenstate fluctuations.
  • Eigenstate fluctuations offer new insights into the fundamental meaning and limitations of ETH.