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Exact Universal Bounds on Quantum Dynamics and Fast Scrambling.
Amit Vikram1, Victor Galitski1
1Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Physical Review Letters
|February 9, 2024
Summary
The spectral form factor provides a universal bound on quantum dynamics, surpassing existing speed limits for both short and long times. This finding impacts understanding quantum chaos and information scrambling in many-body systems.
Area of Science:
- Quantum physics
- Quantum chaos
- Condensed matter theory
Background:
- Quantum speed limits, like Mandelstam-Tamm and Margolus-Levitin bounds, constrain quantum dynamics over short timescales.
- These limits are formulations of the energy-time uncertainty principle.
Purpose of the Study:
- To establish a universal, state-independent bound on quantum dynamics applicable over arbitrarily long times.
- To generalize this bound to time-dependent or dissipative systems.
- To constrain the speed of information scrambling in interacting many-body systems.
Main Methods:
- Utilizing the spectral form factor, a key quantity in quantum chaos.
- Analyzing the real-time dynamics of quantum systems, including time-dependent and dissipative ones.
- Investigating the mathematical properties of the density of states for Hamiltonian systems.
Main Results:
- The spectral form factor sets a tighter, universal bound on quantum dynamics than previously known speed limits.
- This bound applies to complete sets of initial states over extended durations.
- For Hamiltonian systems, the fastest scrambling time is linked to the non-negativity of Fourier transforms of the density of states.
- In the Sachdev-Ye-Kitaev model, sustained scrambling in large fermion subsystems requires exponentially long times.
Conclusions:
- The spectral form factor offers a powerful, general tool for bounding quantum dynamics and information scrambling.
- The study reveals fundamental limits on the speed of quantum information scrambling, even in highly chaotic systems.
- Understanding these bounds is crucial for developing quantum technologies and comprehending complex quantum phenomena.
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