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Register a new userNon-Markovian finite-temperature two-time correlation functions of system operators of a pure-dephasing model
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We evaluate the non-Markovian finite-temperature two-time correlation functions (CFs) of system operators of a pure-dephasing spin-boson model in two different ways, one by the direct exact operator technique and the other by the recently derived evolution equations, valid to second order in the system-environment interaction Hamiltonian. This pure-dephasing spin-boson model that is exactly solvable has been extensively studied as a simple decoherence model. However, its exact non-Markovian finite-temperature two-time system operator CFs, to our knowledge, have not been presented in the literature. This may be mainly due to the fact, illustrated in this article, that in contrast to the Markovian case, the time evolution of the reduced density matrix of the system (or the reduced quantum master equation) alone is not sufficient to calculate the two-time system operator CFs of non-Markovian open systems. The two-time CFs obtained using the recently derived evolution equations in the weak system-environment coupling case for this non-Markovian pure-dephasing model happen to be the same as those obtained from the exact evaluation. However, these results significantly differ from the non-Markovian two-time CFs obtained by wrongly directly applying the quantum regression theorem (QRT), a useful procedure to calculate the two-time CFs for weak-coupling Markovian open systems. This demonstrates clearly that the recently derived evolution equations generalize correctly the QRT to non-Markovian finite-temperature cases. It is believed that these evolution equations will have applications in many different branches of physics.
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An extremely useful evolution equation that allows systematically calculating the two-time correlation functions (CFs) of system operators for non-Markovian open (dissipative) quantum systems is derived. The derivation is based on perturbative quantum master equation approach, so non-Markovian open quantum system models that are not exactly solvable can use our derived evolution equation to easily obtain their two-time CFs of system operators, valid to second order in the system-environment interaction. Since the form and nature of the Hamiltonian are not specified in our derived evolution equation, our evolution equation is applicable for bosonic and/or fermionic environments and can be applied to a wide range of system-environment models with any factorized (separable) system-environment initial states (pure or mixed). When applied to a general model of a system coupled to a finite-temperature bosonic environment with a system coupling operator L in the system-environment interaction Hamiltonian, the resultant evolution equation is valid for both L = L^+ and L eq L^+ cases, in contrast to those evolution equations valid only for L = L^+ case in the literature. The derived equation that generalizes the quantum regression theorem (QRT) to the non-Markovian case will have broad applications in many different branches of physics. We then give conditions on which the QRT holds in the weak system-environment coupling case, and apply the derived evolution equation to a problem of a two-level system (atom) coupled to a finite-temperature bosonic environment (electromagnetic fields) with L eq L^+.
We introduce a formalism for time-dependent correlation functions for systems whose evolutions are governed by non-Hermitian Hamiltonians of general type. It turns out that one can define two different types of time correlation functions. Both these definitions seem to be physically consistent while becoming equivalent only in certain cases. Moreover, when autocorrelation functions are considered, one can introduce another function defined as the relative difference between the two definitions. We conjecture that such a function can be used to assess the positive semi-definiteness of the density operator without computing its eigenvalues. We illustrate these points by studying analytically a number of models with two energy levels.
This work concerns the dynamical two-point spin correlation functions of the transverse Ising quantum chain at finite (non-zero) temperature, in the universal region near the quantum critical point. They are correlation functions of twist fields in the massive Majorana fermion quantum field theory. At finite temperature, these are known to satisfy a set of integrable partial differential equations, including the sinh-Gordon equation. We apply the classical inverse scattering method to study them, finding that the ``initial scattering data corresponding to the correlation functions are simply related to the one-particle finite-temperature form factors calculated recently by one of the authors. The set of linear integral equations (Gelfand-Levitan-Marchenko equations) associated to the inverse scattering problem then gives, in principle, the two-point functions at all space and time separations, and all temperatures. From them, we evaluate the large-time asymptotic expansion ``near the light cone, in the region where the difference between the space and time separations is of the order of the correlation length.
We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of their out-of-time-ordered nature, OTOCs are difficult to measure experimentally. In this Letter we propose an OTOC measurement protocol that does not rely on the reversal of time evolution and is easy to implement in a range of experimental settings. We demonstrate application of our protocol by the characterization of quantum chaos in a periodically driven spin.
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