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1. Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics

   https://doi.org/10.1039/D0CP05527A  

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

   null (Ed.)

   The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer. A simple theoretical analysis establishes bounds and limiting behaviors. The contributions to purity from a purely incoherent term obtained from the diagonal elements of the reduced density matrix, a term associated with the difference of the two eigenstate populations, and a third term related to the square of the time derivative of a site population, are discussed in various regimes. In the case of tunneling dynamics from a localized initial condition, the complex interplay among these contributions leads to the recovery of purity under low-temperature, weakly dissipative conditions. Memory effects from the bath are found to play a critical role to the dynamics of purity. It is shown that the strictly quantum mechanical decoherence process associated with spontaneous phonon emission is responsible for the long-time recovery of purity. These analytical and numerical results show clearly that the loss of quantum coherence during the evolution toward equilibrium does not necessarily imply the decay of purity, and that the time scales relevant to these two processes may be entirely different. 

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2. B800-to-B850 relaxation of excitation energy in bacterial light harvesting: All-state, all-mode path integral simulations

   https://doi.org/10.1063/5.0093828  

   Kundu, Sohang ; Dani, Reshmi ; Makri, Nancy ( July 2022 , The Journal of Chemical Physics)

   We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton–vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang–Rhys factors and to a weakly dissipative bath that models the biomolecular environment. Simulations of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component that transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has an anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton–vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/ e time of 0.5 ps, which is in good agreement with experimental results.

    

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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. Nonlinear, dissipative phenomena in whole blood clot mechanics

   https://doi.org/10.1039/D0SM01317J  

   Sugerman, Gabriella P. ; Parekh, Sapun H. ; Rausch, Manuel K. ( November 2020 , Soft Matter)

   When a thrombus breaks off and embolizes it can occlude vital vessels such as those of the heart, lung, or brain. These thromboembolic conditions are responsible for 1 in 4 deaths worldwide. Thrombus resistance to embolization is driven by its intrinsic fracture toughness as well as other, non-surface-creating dissipative mechanisms. In our current work, we identify and quantify these latter mechanisms toward future studies that aim to delineate fracture from other forms of dissipation. To this end, we use an in vitro thrombus mimic system to produce whole blood clots and explore their dissipative mechanics under simple uniaxial extension, cyclic loading, and stress-relaxation. We found that whole blood clots exhibit Mullins-like effect, hysteresis, permanent set, strain-rate dependence, and nonlinear stress-relaxation. Interestingly, we found that performing these tests under dry or submerged conditions did not change our results. However, performing these tests under room temperature or body temperature conditions yielded differences. Importantly, because we use venous blood our work is most closely related to venous in vivo blood clots. Overall, we have demonstrated that whole blood clots show several dissipative phenomena – similarly to hydrogels – that will be critical to our understanding of thrombus embolization. 

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5. Collisionless Relaxation from Near-equilibrium Configurations: Linear Theory and Application to Tidal Stripping

   https://doi.org/10.3847/1538-4357/ad4c6e  

   Rozier, Simon ; Errani, Raphaël ( August 2024 , The Astrophysical Journal)

   Placed slightly out of dynamical equilibrium, an isolated stellar system quickly returns toward a steady virialized state. We study this process of collisionless relaxation using the matrix method of linear response theory. We show that the full phase-space distribution of the final virialized state can be recovered directly from the disequilibrium initial conditions, without the need to compute the time evolution of the system. This shortcut allows us to determine the final virialized configuration with minimal computational effort. Complementing this result, we develop tools to model the system's full time evolution in the linear approximation. In particular, we show that moments of the velocity distribution can be efficiently computed using a generalized moment matrix. We apply our linear methods to study the relaxation of energy-truncated Hernquist spheres, mimicking the tidal stripping of a cuspy dark matter subhalo. Comparison of our linear predictions against controlled, isolatedN-body simulations shows agreement at percent level for the parts of the system where a linear response to the perturbation is expected. We find that relaxation generates a tangential velocity anisotropy in the intermediate regions, despite the initial disequilibrium state having isotropic kinematics. Our results also strengthen the case for relaxation depleting the amplitude of the density cusp, without affecting its asymptotic slope. Finally, we compare the linear theory against anN-body simulation of tidal stripping on a radial orbit, confirming that the theory still accurately predicts density and velocity dispersion profiles for most of the system.

    

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