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SUMMARY:Low-Rank Split-Operator Propagation for Structured Open Quantum Sy
 stems
DTSTART;VALUE=DATE-TIME:20260924T112000Z
DTEND;VALUE=DATE-TIME:20260924T114000Z
DTSTAMP;VALUE=DATE-TIME:20260914T040747Z
UID:indico-contribution-547@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Roman Ovsiannikov (NSC «Kharkov Institute of Physic
 s and Technology»)\nDirect numerical simulation of open quantum systems i
 s limited by the quadratic memory cost of storing the density matrix. We p
 resent a deterministic low-rank propagation method for time-local Markovia
 n dynamics. The method applies to Hamiltonians composed of a time-dependen
 t diagonal part and terms that become tridiagonal after suitable permutati
 ons of the basis\, as well as to collapse operators with diagonal or narro
 w-banded representations. The density matrix is represented by a low-rank 
 ensemble of state vectors. Coherent evolution is advanced using a symmetri
 c Suzuki–Trotter decomposition: diagonal factors are applied exactly\, w
 hile tridiagonal factors are evaluated using Cayley transforms that requir
 e only solving tridiagonal linear systems. Dissipation is incorporated thr
 ough infinitesimal Kraus branches\, after which the enlarged ensemble is c
 ompressed to a prescribed rank using a small Gram matrix. For a fixed reta
 ined rank and number of collapse channels\, the memory requirement and the
  dominant computational operations scale linearly with the Hilbert-space d
 imension.\n\nThe method is benchmarked on a driven finite-spin model of an
  NV-center ensemble coupled to a microwave cavity. The interaction terms b
 ecome tridiagonal in different basis orderings\, while the cavity and coll
 ective-spin collapse operators retain a banded structure. Comparison with 
 full-density-matrix simulations in QuTiP shows close agreement for the cav
 ity quadrature variance in the tested regime\, while the integrated errors
  of the monitored observables decrease systematically as the retained rank
  is increased from 2 to 16. Pure-propagation timing benchmarks exhibit nea
 r-linear scaling\, with fitted exponents between 1.09 and 1.23. The method
  is therefore most effective when the density matrix remains approximately
  low rank\; strongly mixed states and continuously pumped lasing regimes m
 ay require larger ranks and reduce the computational advantage.\n\nhttps:/
 /indico.bitp.kiev.ua/event/18/contributions/547/
LOCATION:Bogolyubov Institute for Theoretical Physics Conference Hall
URL:https://indico.bitp.kiev.ua/event/18/contributions/547/
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