We provide a detailed examination of a thermal out-of-time-order correlator (OTOC) growing exponentially in time in systems without chaos. The system is a one-dimensional quantum mechanics with a potential whose part is an inverted harmonic oscillator. We numerically observe the exponential growth of the OTOC when the temperature is higher than a certain threshold. The Lyapunov exponent is found to be of the order of the classical Lyapunov exponent generated at the hilltop, and it remains non-vanishing even at high temperature. We adopt various shape of the potential and find these features universal. The study confirms that the exponential growth of the thermal OTOC does not necessarily mean chaos when the potential includes a local maximum. We also provide a bound for the Lyapunov exponent of the thermal OTOC in generic quantum mechanics in one dimension, which is of the same form as the chaos bound obtained by Maldacena, Shenker and Stanford.

Exponential growth of thermal out-of-time-order correlator (OTOC) is an indicator of a possible gravity dual, and a simple toy quantum model showing the growth is being looked for. We consider a system of two harmonic oscillators coupled nonlinearly with each other, and numerically observe that the thermal OTOC grows exponentially in time. The system is well-known to be classically chaotic, and is a reduction of Yang-Mills-Higgs theory. The exponential growth is certified because the growth exponent (quantum Lyapunov exponent) of the thermal OTOC is well matched with the classical Lyapunov exponent, including their energy/temperature dependence. Even in the presence of the exponential growth in the OTOC, the energy level spacings are not sufficient to judge a Wigner distribution, hence the OTOC is a better indicator of quantum chaos.

Malignant melanoma favors spreading to bone, resulting in a weakened bone with a high fracture risk. Here, we revealed the disorganized alignment of apatite crystals in the bone matrix associated with the homing of cancer cells by developing an artificially controlled ex vivo melanoma bone metastasis model. The ex vivo metastasis model reflects the progressive melanoma cell activation in vivo, resulting in decreased bone mineral density and expression of MMP1-positive cells. Moreover, less organized intercellular connections were observed in the neighboring osteoblasts in metastasized bone, indicating the abnormal and randomized organization of bone matrix secreted by disconnected osteoblasts. Our study revealed that the deteriorated microstructure associated with disorganized osteoblast arrangement was a determinant of malignant melanoma-related bone dysfunction.

We provide a formula to reconstruct bulk spacetime metrics inside black holes by the time dependence of complexity in the dual quantum field theory, based on the complexity=volume (CV) conjecture in the holographic duality.