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1. Long-time properties of generic Floquet systems are approximately periodic with the driving period

   https://doi.org/10.1088/1367-2630/ad5eb1  

   Huang_黄溢辰, Yichen (July 2024, New Journal of Physics)

   Abstract A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time. 

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2. Partial thermalisation of a two-state system coupled to a finite quantum bath

   https://doi.org/10.21468/SciPostPhys.12.3.103  

   Crowley, Philip; Chandran, Anushya (January 2022, SciPost Physics)

   The eigenstate thermalisation hypothesis (ETH) is a statisticalcharacterisation of eigen-energies, eigenstates and matrix elements oflocal operators in thermalising quantum systems. We develop an ETH-likeansatz of a partially thermalising system composed of aspin- \tfrac{1}{2} 1 2 coupled to a finite quantum bath. The spin-bath coupling is sufficientlyweak that ETH does not apply, but sufficiently strong that perturbationtheory fails. We calculate (i) the distribution of fidelitysusceptibilities, which takes a broadly distributed form, (ii) thedistribution of spin eigenstate entropies, which takes a bi-modal form,(iii) infinite time memory of spin observables, (iv) the distribution ofmatrix elements of local operators on the bath, which is non-Gaussian,and (v) the intermediate entropic enhancement of the bath, whichinterpolates smoothly between S = 0 S = 0 and the ETH value of S = \log 2 S = log 2 .The enhancement is a consequence of rare many-body resonances, and isasymptotically larger than the typical eigenstate entanglement entropy.We verify these results numerically and discuss their connections to themany-body localisation transition. 

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3. Bridging two quantum quench problems — local joining quantum quench and Möbius quench — and their holographic dual descriptions

   https://doi.org/10.1007/JHEP08(2024)213  

   Kudler-Flam, Jonah; Nozaki, Masahiro; Numasawa, Tokiro; Ryu, Shinsei; Tan, Mao Tian (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We establish an equivalence between two different quantum quench problems, the joining local quantum quench and the Möbius quench, in the context of (1 + 1)-dimensional conformal field theory (CFT). Here, in the former, two initially decoupled systems (CFTs) on finite intervals are joined att= 0. In the latter, we consider the system that is initially prepared in the ground state of the regular homogeneous Hamiltonian on a finite interval and, aftert= 0, let it time-evolve by the so-called Möbius Hamiltonian that is spatially inhomogeneous. The equivalence allows us to relate the time-dependent physical observables in one of these problems to those in the other. As an application of the equivalence, we construct a holographic dual of the Möbius quench from that of the local quantum quench. The holographic geometry involves an end-of-the-world brane whose profile exhibits non-trivial dynamics. 

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4. Functional Equivariance and Conservation Laws in Numerical Integration

   https://doi.org/10.1007/s10208-022-09590-8  

   McLachlan, Robert I.; Stern, Ari (September 2022, Foundations of Computational Mathematics)

   Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important properties of the system. For example, a time-evolution PDE may have an observable that satisfies a local conservation law, such as the multisymplectic conservation law for Hamiltonian PDEs. We introduce the concept of functional equivariance, a natural sense in which a numerical integrator may preserve the dynamics satisfied by certain classes of observables, whether or not they are invariant. After developing the general framework, we use it to obtain results on methods preserving local conservation laws in PDEs. In particular, integrators preserving quadratic invariants also preserve local conservation laws for quadratic observables, and symplectic integrators are multisymplectic. 

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5. Matsubara dynamics approximation for generalized multi-time correlation functions

   https://doi.org/10.1063/5.0146654  

   Videla, Pablo E.; Batista, Victor S. (May 2023, The Journal of Chemical Physics)

   We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems. 

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