[PDF] Top 20 Numerical Methods for Many-Body Quantum Dynamics

... the dynamics are constrained to the same subspace of the Hilbert ...the dynamics is limited by the finite bond dimension χ, as the evolution explores this subspace, both methods reach the same ... See full document

... 2.3 Beyond TDHF approaches The TDHF approach gives only classical trajectories for the time-evolution and expectation values of one-body ob- servables. In particular, it does not include tunnelling of the ... See full document

... Figure 2A demonstrate the strength of the Bohmian approach in modeling quantum systems with strong interactions and nonlinear ion dynamics. For static and thermodynamic properties, we obtain results in very ... See full document

... values can thus provide a measure of the breakup time-scale. The concepts outlined above can be put on firmer ground by making calculations of the most likely range of relative energies for the di ff erent breakup ... See full document

... of many-body localization in d > 1 Recent works on many-body localization [120, 71, 70] have started to re-examine the case for the existence and stability of the MBL state, going beyond ... See full document

... the dynamics of highly correlated systems, after a quantum quench [14, 15, ...of many-body physics, and requires sophisticated techniques for its ... See full document

... “The Dynamics of Quantum Information”, where part of this work was completed. S.C. acknowledges sup- ports from the Miller Institute for Basic Research in Sci- ence. H.P. is supported by the NSF through a ... See full document

... observe dynamics in a quantum many-body system dominated by second- and third-order tunneling and identify resonant fourth- and fifth-order tunneling ...long-range many-body ... See full document

... open quantum systems - microscopic systems exhibiting quantum coherence that are coupled to their environment - has become increasingly important in the past years, as the ability to control quantum ... See full document

... of quantum chaos in all three representations of the quantum ...identifying quantum chaotic dynamics more generally, whereas RMT is limited in small and large systems or rapidly becomes ... See full document

... interacting many-body states, ranging from paired states of fermions to topological ...with many open questions, ranging from specific questions such as the effect of spontaneous emissions on dynamical ... See full document

... Chapter 2 discusses the main numerical methods used in this thesis for the study of MBL. I provide both theoretical background as well as discuss some more practical matters, such as their advantages and ... See full document

... of quantum spin models Systems of interacting spins are used since many years to model magnetic phe- ...since many different physical phenomena can be mapped, exactly or approximately, onto spin ... See full document

... showed numerical evidence that ergodic systems generically heat-up to infinite temperature with periodic driving, whereas many-body localized systems can remain stable as an extensive set of ... See full document

... quench dynamics evolves in a subspace whose size, contrary to those of low-excitation subspaces (the subject of our previous work [23]), grows exponentially with ... See full document

... open quantum many-body systems? We first study slow scrambling in many-body localized systems via calculating various correlators, two-point retarded correlators and ...thermalizing ... See full document

... We also obtain an explicit expression for the LR velocity v , see (38) in [48]. Appropriately, v is a decreasing function of α . Let us discuss α + u from a quantitative viewpoint. Since Theorem 2 holds for arbitrary ... See full document

... general quantum many-body system, we have generated random density matrices and studied a relationship between both sides of Equation ...this numerical test over a random mixed ... See full document

... their dynamics - and hence effect on the logical state - is unlikely to be efficiently classically calculable in general (particularly if the anyon dynamics is BQP ... See full document

... of numerical imper- fections by considering the given problem in related, simpler ...of many such methods is to search for more conclusive numerical evidence in the proximity of a the regime ... See full document