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Register a new userOut-of-time-order correlators in finite open systems
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We study out-of-time order correlators (OTOCs) of the form $langlehat A(t)hat B(0)hat C(t)hat D(0)rangle$ for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially $propto sum a_i e^{-t/tau_i}+const$ to a constant value at $trightarrowinfty$, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times $tau_i$ and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.
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We present a method to probe the Out-of-Time-Order Correlators (OTOCs) of a general system by coupling it to a harmonic oscillator probe. When the systems degrees of freedom are traced out, the OTOCs imprint themselves on the generalized influence functional of the oscillator. This generalized influence functional leads to a local effective action for the probe whose couplings encode OTOCs of the system. We study the structural features of this effective action and the constraints on the couplings from microscopic unitarity. We comment on how the OTOCs of the system appear in the OTOCs of the probe.
The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time.
We study non-Hermitian higher-order Weyl semimetals (NHHOWSMs) possessing real spectra and having inversion $mathcal{I}$ ($mathcal{I}$-NHHOWSM) or time-reversal symmetry $mathcal{T}$ ($mathcal{T}$-NHHOWSM). When the reality of bulk spectra is lost, the NHHOWSMs exhibit various configurations of surface Fermi Arcs (FAs) and Exceptional Fermi Rings (EFRs), providing a setup to investigate them on an equal footing. The EFRs only appear in the region between 2nd-order WNs. We also discover Weyl nodes originating from non-Hermicity, called non-Hermitian Weyl nodes (NHWNs). Remarkably, we find T-NHHOWSMs which host only 2nd-order NHWNs, having both surface and hinge FAs protected by the quantized biorthogonal Chern number and quadrupole moment, respectively. We call this intrinsically non-Hermitian phase exceptional HOWSM. In contrast to ordinary WNs, the NHWNs can instantly deform to line nodes, forming a monopole comet. The NHWNs also show exceptional tilt-rigidity, which is a strong resistance towards titling due to attachment to exceptional structures. This phenomenon can be a promising experimental knob. Finally, we reveal the exceptional stability of FAs called exceptional helicity. Surface FAs having opposite chirality can live on the same surface without gapping out each other due to the complex nature of the spectrum. Our work motivates an immediate experimental realization of NHHOWSMs.
Out-of-time-order correlators (OTOC) are considered to be a promising tool to characterize chaos in quantum systems. In this paper we study OTOC in XY model. With the presence of anisotropic parameter $gamma$ and external magnetic field $lambda$ in the Hamiltonian, we mainly focus on their influences on OTOC in thermodynamical limit. We find that the butterfly speed $v_B$ is dependent of these two parameters, and the recent conjectured universal form which characterizes the wavefront of chaos spreading are proved to be positive with varying $v_B$ in different phases of XY model. Moreover, we also study the behaviors of OTOC with fixed location, and we find that the early-time part fully agrees with the results derived from Hausdorff-Baker-Campbell expansion. The long-time part is studied either, while in the local case $C(t)$ decay as power law $t^{-1}$, $|F(t)|$ with nonlocal operators show quite interesting and nontrivial power law decay corresponding to different choices of operators and models. At last, we observe temperature dependence for OTOC with local operators at ($gamma=0, lambda=1$), and divergent behavior with low temperature for nonlocal operator case at late time.
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to zero with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to zero and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.
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