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Related Concept Videos

Fermi Level01:18

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The Fermi-Dirac function is represented by an S-shaped curve indicating the probability of an energy state being occupied by an electron at a given temperature. The Fermi level is the energy level at which there is a fifty percent chance of finding an electron, and it is positioned between the lower-energy valence band and the higher-energy conduction band.
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The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
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First Law: Particles in One-dimensional Equilibrium01:10

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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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Emergence of Fermi's Golden Rule.

Tobias Micklitz1, Alan Morningstar2, Alexander Altland3

  • 1Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil.

Physical Review Letters
|October 14, 2022
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Summary
This summary is machine-generated.

Fermi's golden rule describes quantum state decay into a continuum. This study explores decay into discrete states, revealing corrections to the rule and the emergence of the spectral form factor.

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Area of Science:

  • Quantum mechanics
  • Many-body systems
  • Statistical physics

Background:

  • Fermi's golden rule describes quantum state decay into a continuum of final states.
  • Investigating deviations from this rule is crucial for understanding complex quantum systems.

Purpose of the Study:

  • To explore quantum state decay beyond the continuum limit, focusing on discrete final states.
  • To analyze the universal crossovers in decay dynamics as level spacing varies.

Main Methods:

  • Analytical calculations for different symmetry classes.
  • Numerical simulations to study decay dynamics.
  • Investigation of the spectral form factor in the long-time regime.

Main Results:

  • Identified universal crossovers in the average decay of initial quantum states.
  • Demonstrated the emergence of Fermi's golden rule in the continuum limit.
  • Observed corrections to exponential decay, including the spectral form factor for small level spacing.

Conclusions:

  • The study extends the applicability of Fermi's golden rule to systems with discrete final states.
  • Non-exponential decay and spectral form factors are key features away from the continuum limit.
  • Findings are relevant for recently investigated many-body systems.