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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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01:20Mechanisms of Heat Transfer II
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01:14Mechanisms of Heat Transfer I
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01:14Mechanisms of Heat Transfer
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Locality and heating in periodically driven, power-law-interacting systems.
Minh C Tran1,2,3, Adam Ehrenberg1,2, Andrew Y Guo1,2
1Joint Center for Quantum Information and Computer Science, National Institute of Standards and Technology, University of Maryland, College Park, Maryland 20742, USA.
Physical Review. A
|January 10, 2022
Summary
Heating time in driven quantum systems with power-law interactions is exponentially long for specific interaction decay rates. This is shown using linear-response theory and Magnus-like expansions, with implications for quantum dynamics.
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Area of Science:
- Quantum physics
- Condensed matter physics
- Statistical mechanics
Background:
- Periodically driven quantum systems exhibit complex dynamics.
- Interactions decaying as power laws are relevant in many-body systems.
- Understanding heating time is crucial for predicting system evolution.
Purpose of the Study:
- Investigate heating time in D-dimensional systems with power-law interactions.
- Analyze the role of interaction decay exponent (alpha) and dimensionality (D).
- Extend existing theoretical frameworks like linear-response theory and Lieb-Robinson bounds.
Main Methods:
- Application of linear-response theory.
- Utilization of a generalized Magnus-like expansion.
- Generalization of Lieb-Robinson bounds for k-body interactions.
Main Results:
- Exponentially long heating time for alpha > D using linear-response theory.
- Exponentially long heating time for alpha > 2D via quasiconserved observables.
- Extended Lieb-Robinson bounds yield longer heating times than prior work.
Conclusions:
- Heating time is robustly long for power-law interactions under specific conditions.
- The observed gap between theories is attributed to limitations in current bounds.
- Hypothetical tight bounds would reconcile theoretical predictions.