期刊
ANNALS OF PHYSICS
卷 345, 期 -, 页码 141-165出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2014.03.009
关键词
Emergent property; Driven open quantum system; Adiabatic perturbation theory; Berry curvature
资金
- BSF [2010318]
- NSF [DMR-0907039]
- AFOSR [FA9550-10-1-0110]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1206410] Funding Source: National Science Foundation
We consider a set of macroscopic (classical) degrees of freedom coupled to an arbitrary many-particle Hamiltonian system, quantum or classical. These degrees of freedom can represent positions of objects in space, their angles, shape distortions, magnetization, currents and so on. Expanding their dynamics near the adiabatic limit we find the emergent Newton's second law (force is equal to the mass times acceleration) with an extra dissipative term. In systems with broken time reversal symmetry there is an additional Coriolis type force proportional to the Berry curvature. We give the. microscopic definition of the mass tensor. The mass tensor is related to the non-equal time correlation functions in equilibrium and describes the dressing of the slow degree of freedom by virtual excitations in the system. In the classical (high-temperature) limit the mass tensor is given by the product of the inverse temperature and the Fubini Study metric tensor determining the natural distance between the eigenstates of the Hamiltonian. For free particles this result reduces to the conventional definition of mass. This finding shows that any mass, at least in the classical limit, emerges from the distortions of the Hilbert space highlighting deep connections between any motion (not necessarily in space) and geometry. We illustrate our findings with four simple examples. (C) 2014 Elsevier Inc. All rights reserved.
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