BEGIN:VCALENDAR VERSION:2.0 PRODID:-//linuxsoftware.nz//NONSGML Joyous v1.4//EN BEGIN:VEVENT SUMMARY:Equipartition and Entanglement - Relation between ergodicity measu res DTSTART:20231206T143000Z DTEND:20231206T160000Z DTSTAMP:20260703T062936Z UID:ae1d2975-62ea-4a79-875d-76bf456da7cc SEQUENCE:1 CREATED:20231205T142543Z DESCRIPTION:Similarly to the ergodicity hypothesis in classical chaotic sy stems\, in the quantum setting there is asimilar concept\, related to quan tum thermalization and equipartition over degrees of freedom anddubbed as the eigenstate thermalization hypothesis. This concept is very useful as i t provides a linkbetween classical and quantum chaos. The concept of multi fractality of quantum wave-functions is away to break the above ergodicity in terms of chaotization and equipartitioning over degrees offreedom in q uantum systems. On the other hand\, in quantum information theory it is th e entanglemententropy which represents the main measure of ergodicity and thermalization. On the third side\, in theeigenstate thermalization hypoth esis the fluctuations of local observables and their scaling with thesyste m size play the central role. In this talk I will represent an exact relat ion between the above threemeasures\, namely multifractal dimensions\, sca ling of fluctuations of local observables and the (Renyi)entanglement entr opy. I will show that the fractal dimension of the non-ergodic wave functi on puts anupper bound on its entanglement entropy [1]. I will also provide a couple of explicit examplesdemonstrating that the entanglement entropy may reach its ergodic (Page) value when the wavefunction is still highly n on-ergodic and occupies a zero fraction of the total Hilbert space. If tim e permitsI will briefly discuss some other possible deviations from ergodi city relevant for the chaotic many-body. LAST-MODIFIED:20231205T142543Z LOCATION:Sala de Seminários do DF\, Pavilhão de Física\, 2º piso URL:http://df.vps.tecnico.ulisboa.pt/pt/eventos/equipartition-and-entangle ment-relation-between-ergodicity-measures/ X-ALT-DESC;FMTTYPE=text/html:

Similarly to the er godicity hypothesis in classical chaotic systems\, in the quantum setting there is asimilar concept\, related to quantum thermalization and equipart ition over degrees of freedom anddubbed as the eigenstate thermalization h ypothesis. This concept is very useful as it provides a linkbetween classi cal and quantum chaos. The concept of multifractality of quantum wave-func tions is away to break the above ergodicity in terms of chaotization and e quipartitioning over degrees offreedom in quantum systems. On the other ha nd\, in quantum information theory it is the entanglemententropy which rep resents the main measure of ergodicity and thermalization. On the third si de\, in theeigenstate thermalization hypothesis the fluctuations of local observables and their scaling with thesystem size play the central role. I n this talk I will represent an exact relation between the above threemeas ures\, namely multifractal dimensions\, scaling of fluctuations of local o bservables and the (Renyi)entanglement entropy. I will show that the fract al dimension of the non-ergodic wave function puts anupper bound on its en tanglement entropy [1]. I will also provide a couple of explicit examplesd emonstrating that the entanglement entropy may reach its ergodic (Page) va lue when the wavefunction is still highly non-ergodic and occupies a zero fraction of the total Hilbert space. If time permitsI will briefly discuss some other possible deviations from ergodicity relevant for the chaotic m any-body.

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