English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We consider a set of macroscopic (classical) degrees of freedom coupled to anarbitrary many-particle Hamiltonian system, quantum or classical. These degreesof freedom can represent positions of objects in space, their angles, shapedistortions, magnetization, currents and so on. Expanding their dynamics nearthe adiabatic limit we find the emergent Newton's second law (force is equal tothe mass times acceleration) with an extra dissipative term. In systems withbroken time reversal symmetry there is an additional Coriolis type forceproportional to the Berry curvature. We give the microscopic definition of themass tensor relating it to the non-equal time correlation functions inequilibrium or alternatively expressing it through dressing by virtualexcitations in the system. In the classical (high-temperature) limit the masstensor is given by the product of the inverse temperature and the Fubini-Studymetric tensor determining the natural distance between the eigenstates of theHamiltonian. For free particles this result reduces to the conventionaldefinition of mass. This finding shows that any mass, at least in the classicallimit, emerges from the distortions of the Hilbert space highlighting deepconnections between any motion (not necessarily in space) and geometry. Weillustrate our findings with four simple examples.

Emergent Newtonian dynamics and the geometric origin of mass