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1. Density matrix and purity evolution in dissipative two-level systems: II. Relaxation

   https://doi.org/10.1039/D0CP05528J  

   Chatterjee, Sambarta ; Makri, Nancy ( March 2021 , Physical Chemistry Chemical Physics)

   null (Ed.)

   We investigate the time evolution of the reduced density matrix (RDM) and its purity in the dynamics of a two-level system coupled to a dissipative harmonic bath, when the system is initially placed in one of its eigenstates. We point out that the symmetry of the initial condition confines the motion of the RDM elements to a one-dimensional subspace and show that the purity always goes through its maximally mixed value at some time during relaxation, but subsequently recovers and (under low-temperature, weakly dissipative conditions) can rise to values that approach unity. These behaviors are quantified through accurate path integral calculations. Under low-temperature, weakly dissipative conditions, we observe unusual, nonmonotonic population dynamics when the two-level system is initially placed in its ground state. We also analyze the origin of the system-bath interactions responsible for the nonmonotonic behavior of purity during relaxation. Our results show that classical dephasing processes arising from site level fluctuations lead to a monotonic decay of purity, and that the quantum mechanical decoherence events associated with spontaneous phonon emission are responsible for the subsequent recovery of purity. Last, we show that coupling with a low-temperature bath can purify a mixed two-level system. In the case of the maximally mixed initial RDM, the purity increases monotonically even during short time. 

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2. PathSum : A C++ and Fortran suite of fully quantum mechanical real-time path integral methods for (multi-)system + bath dynamics

   https://doi.org/10.1063/5.0151748  

   Kundu, Sohang ; Makri, Nancy ( June 2023 , The Journal of Chemical Physics)

   This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system–bath problems and extended systems comprising many coupled system–bath units, and is offered in C++ and Fortran implementations. The system–bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum–classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples. 

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3. Electronic frustration, Berry’s phase interference and slow dynamics in some tight-binding systems coupled to harmonic baths

   https://doi.org/10.1088/1751-8121/acbff2  

   Makri, Nancy ( March 2023 , Journal of Physics A: Mathematical and Theoretical)

   Conical intersections in two-state systems require a coordinate-dependent coupling. This paper identifies and investigates conical intersections in cyclic tight-binding system-bath Hamiltonians with an odd number of sites and a constant site-to-site coupling. In the absence of bath degrees of freedom, such tight-binding systems with a positive coupling parameter exhibit electronic frustration and a doubly-degenerate ground state. When these systems interact with a harmonic bath, the degeneracy becomes a conical intersection between the adiabatic ground and first excited states. Under weak system-bath coupling, overlapping wavefunctions associated with different sites give rise to distinct pathways with interfering geometric phases, which lead to considerably slower transfer dynamics. The effect is most pronounced in the presence of low-temperature dissipative baths characterized by a continuous spectral density. It is found that the transfer dynamics and equilibration time of a cyclic dissipative three-site system with a positive coupling exceeds that of a similar three-site system with a negative coupling, as well as that of cyclic four-site systems, by an order of magnitude.

    

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4. Matrix product operator approach to nonequilibrium Floquet steady states

   https://doi.org/10.1103/PhysRevB.106.L220307  

   Cheng, Zihan ; Potter, Andrew C. ( December 2022 , Physical Review B)

   We present a numerical method to simulate nonequilibrium Floquet steady states of one-dimensional periodically driven many-body systems coupled to a dissipative bath, based on a matrix product operator ansatz for the Floquet density matrix in frequency space. This method enables access to large systems beyond the reach of exact simulations, while retaining the periodic micromotion information. An excited-state extension of this technique allows computation of the dynamical approach to the steady state. We benchmark our method with a driven-dissipative Ising model and apply it to study the possibility of stabilizing prethermal discrete time-crystalline order by coupling to a cold bath. 

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5. BROTOCs and Quantum Information Scrambling at Finite Temperature

   https://doi.org/10.22331/q-2022-06-27-746  

   Anand, Namit ; Zanardi, Paolo ( June 2022 , Quantum)

   Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature OTOC. We introduce analytical results for the bipartite regularized OTOC (BROTOC): the regularized OTOC averaged over random unitaries supported over a bipartition. We show that the BROTOC has several interesting properties, for example, it quantifies the purity of the associated thermofield double state and the operator purity of the analytically continued time-evolution operator. At infinite-temperature, it reduces to one minus the operator entanglement of the time-evolution operator. In the zero-temperature limit and for nondegenerate Hamiltonians, the BROTOC probes the groundstate entanglement. By computing long-time averages, we show that the equilibration value of the BROTOC is intimately related to eigenstate entanglement. Finally, we numerically study the equilibration value of the BROTOC for various physically relevant Hamiltonian models and comment on its ability to distinguish integrable and chaotic dynamics. 

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