Time Evolution of Correlation Functions in Quantum Many-Body Systems
- Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
- McMaster Univ., Hamilton, ON (Canada)
- Univ. of Massachusetts, Boston, MA (United States); Univ. of Maryland, College Park, MD (United States); National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States). Joint Center for Quantum Information and Computer Science (QuICS)
We give rigorous analytical results on the temporal behavior of two-point correlation functions—also known as dynamical response functions or Green’s functions—in closed many-body quantum systems. We show that in a large class of translation-invariant models the correlation functions factorize at late times $$\langle$$A ( t ) B$$\rangle$$β → $$\langle$$ A$$\rangle$$ β $$\langle$$ B$$\rangle$$β, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that for systems with a generic spectrum the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For autocorrelation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values and does not increase with system size. We give numerical examples that show that this bound is a good estimate in nonintegrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.
- Research Organization:
- Univ. of Maryland, College Park, MD (United States). Joint Quantum Inst. (JQI) and Joint Center for Quantum Information and Computer Science (QuICS)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Advanced Research Projects Agency - Energy (ARPA-E)
- Grant/Contract Number:
- SC0019515; SC0019040; SC0019449
- OSTI ID:
- 1606355
- Alternate ID(s):
- OSTI ID: 1605507
- Journal Information:
- Physical Review Letters, Vol. 124, Issue 11; ISSN 0031-9007
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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