Correlation Functions In Open Systems Research Articles

Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach

Recent theoretical and experimental studies have shown the significance of quantum information scrambling (i.e., the spread of quantum information over a system's degrees of freedom) for problems encountered in high-energy physics, quantum information, and condensed matter. Due to the complexity of quantum many-body systems it is plausible that new developments in this field will be achieved by experimental explorations. Since noise effects are inevitably present in experimental implementations, a better theoretical understanding is needed of quantum information scrambling in systems affected by noise. To address this problem we study indicators of quantum scrambling---out-of-time-ordered correlation functions (OTOCs) in open quantum systems. As most experimental protocols for measuring OTOCs are based on backward time evolution, we consider two possible scenarios of joint system-environment dynamics reversal: In the first one the evolution of the environment is reversed, whereas in the second it is not. We derive general formulas for OTOCs in those cases and study in detail the model of a spin chain coupled to the environment of harmonic oscillators. In the latter case we derive expressions for open-system OTOCs in terms of the Feynman-Vernon influence functional. Subsequently, assuming that dephasing dominates over dissipation, we provide bounds on open-system OTOCs and illustrate them for a spectral density known from the spin-boson problem. In addition to being significant for quantum information scrambling, the results also advance the understanding of decoherence in processes involving backward time evolution.

Extension of the Nakajima-Zwanzig approach to multitime correlation functions of open systems

We extend the Nakajima-Zwanzig projection operator technique to the determination of multitime correlation functions of open quantum systems. The correlation functions are expressed in terms of certain multitime homogeneous and inhomogeneous memory kernels for which suitable equations of motion are derived. We show that under the condition of finite memory times these equations can be used to determine the memory kernels by employing an exact stochastic unraveling of the full system-environment dynamics. The approach thus allows to combine exact stochastic methods, feasible for short times, with long-time master equation simulations. The applicability of the method is demonstrated by numerical simulations of 2D-spectra for a donor-acceptor model, and by comparison of the results with those obtained from the reduced hierarchy equations of motion. We further show that the formalism is also applicable to the time evolution of a periodically driven two-level system initially in equilibrium with its environment.

Entropy and Molecular Correlation Functions in Open Systems. I. Derivation

A method is presented for obtaining an expression for the entropy in terms of molecular correlation functions defined in the grand canonical ensemble. The procedure is for a system of a single molecular species whose dynamics are determined by classical equations of motion. The entropy is obtained as a sum of two different classes of functions each involving the correlations between n-tuples of molecules. One class contains logarithmic terms similar to those obtained for the closed system; the other class involves isothermal activity derivatives of potentials of mean force. The latter terms, which are moments of the correlations between disjoint sets of molecules, can make appreciable contributions to the entropy. The method leads to results similar to those obtained from a different procedure by Nettleton and Green. The expression for the entropy is obtained and properties of the results are discussed for a simple fluid system.

Entropy and Molecular Correlation Functions in Open Systems. II Two- and Three-Body Correlations

We consider the contributions from the correlation of pairs and triples of molecules to the configurational entropy per molecule of a simple fluid system. Using numerical values of the pair function and only certain moments of the triplet function, we have computed the first few terms in an expression for the entropy in terms of the correlation functions. The results, which compare favorably with experimental values over a range of densities including that of the liquid, indicate that contributions from the correlations of triples of molecules can be appreciable. The computations are done for a fluid of hard spheres and liquid neon and the results are discussed in terms of the molecular correlations in a simple fluid.