Survival Probability, Particle Imbalance, and Their Relationship in Quadratic Models.

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Many-Body Systems

Background:

• Understanding the relationship between single-particle and many-body dynamics is crucial in quantum physics.
• Particle imbalance and survival probabilities are key observables in characterizing quantum systems.

Purpose of the Study:

• To establish a connection between particle imbalance dynamics in many-body systems and single-particle survival probabilities.
• To generalize this connection to density correlation functions and transition probabilities.
• To investigate the possibility of measuring single-particle properties via many-body observables.

Main Methods:

• Theoretical analysis of quadratic fermionic models.
• Generalization to density correlation functions and transition probabilities.
• Numerical simulations using the 3D Anderson and 1D Aubry-André models.

Main Results:

• Particle imbalance dynamics in many-body systems are largely indistinguishable from single-particle survival probabilities for most initial states.
• Density correlation functions in many-body states show analogies with single-particle transition probabilities.
• Numerical tests confirm these findings in paradigmatic localization models.

Conclusions:

• A direct link exists between many-body particle imbalance dynamics and single-particle survival probabilities.
• This link provides a method to probe single-particle physics using many-body system measurements.
• The study confirms the possibility of measuring single-particle survival and transition probabilities through many-body observables.