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In this paper, we study random features manifested in components of energy eigenfunctions of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on semiclassical analysis, particularly on Berry's conjecture, it is shown that the components in classically allowed regions can be regarded as Gaussian random numbers in certain sense, when appropriately rescaled with respect to the average shape of the eigenfunctions. This suggests that, when a perturbed system changes from integrable to chaotic, deviation of the distribution of rescaled components in classically allowed regions from the Gaussian distribution may be employed as a measure for the ``distance'' to quantum chaos. Numerical simulations performed in the LMG model and the Dicke model show that this deviation coincides with the deviation of the nearest-level-spacing distribution from the prediction of random-matrix theory. Similar numerical results are also obtained in two models without classical counterpart., Comment: 11 pages, 13 figures

Diamond is a solid-state platform to develop quantum technologies, but it has been a long-standing problem that the current understanding of quantum states in diamond is mostly limited to single-electron pictures. Here, we combine the full configuration interaction quantum Monte Carlo method and the density-matrix functional embedding theory, to achieve unprecedented accuracy in describing the many-body quantum states of nitrogen vacancy (NV) centers in diamond. More than 30 electrons and 130 molecular orbitals are correlated, which reveals the multi-configurational wavefunction of the many-body quantum states in diamond. The multi-configurational description explains puzzling experimental measurements in intersystem crossing and charge state transition in NV centers in diamond. The calculations not only reproduce the available experimental measurements of the energy gaps between quantum states but also provide new benchmarks for states that are still subject to considerable uncertainty. This study highlights the importance of multi-configurational wavefunction in the many-body quantum states in solids.

The so-called eigenstate thermalization hypothesis (ETH), which has been tested in various models by numerical simulations, supplies a way of understanding eventual thermalization and is believed to be important for understanding processes of thermalization. However, an analytical proof of ETH is still lacking. In this Letter, the ETH ansatz is demonstrated for an arbitrary observable of an arbitrary subsystem in a generic many-body quantum chaotic system, to which the so-called Berry's conjecture is applicable. In particular, semiclassical expressions are derived for two unknown functions in the ETH ansatz., Comment: 4 pages

Natural materials usually consist of isotopic mixtures, for which different isotopic ratios can lead to distinct material properties such as thermal conductivity and nucleation process. However, the knowledge of isotopic interface remains largely unexplored mainly due to the challenges in isotopic identification and property measurement at an atomic scale. Here, by using monochromated electron energy-loss spectroscopy in a scanning transmission electron microscope, we reveal momentum-transfer-dependent lattice vibration behavior at an artificial h-10BN/h-11BN heterostructure with sub-unit-cell resolution. We find the vibrational energy changes across the isotopic interface gradually, featuring a wide transition regime, which suggests strong delocalization of the out-of-plane optical phonons at the interface. In addition, we identify phonons near the Brillouin zone center have a transition regime ~3.34 nm (10 atomic layers), whereas phonons at the Brillouin zone boundary transition in ~1.66 nm (5 atomic layers). We propose that the isotope-induced charge effect at the interface accounts for the distinct delocalization behavior. Moreover, intra-atomic layer variation of vibration energy is also sensitive to the momentum transfer, thus at the interface it depends on both of momentum transfer and mass change. The revealed lattice vibration behavior at an isotopic interface provides new insights to understand the isotopic effects on properties in natural materials.

A unified framework, which is directly established on the quantum ground, is proposed for elementary physical entities, called \emph{modes} in this paper. The framework is mainly built upon five basic assumptions, which loosely speaking have the following contents. (i) The state space of each mode is given by the direct product of a momentum-state space and a spinor-state space, the latter of which is certain representation space of the $SL(2,C)$ group (a covering group of the Lorentz group); (ii) spinor states of modes have a layer-type structure and modes are either fermionic or bosonic, depending on their helicity properties; (iii) there are three fundamental processes -- free evolution, vacuum fluctuation (emergence or vanishing of a pair of fermionic modes that possess exactly opposite physical properties), and two fundamental interaction processes (change of two fermionic modes into one bosonic mode and the reverse); (iv) vacuum fluctuation happens instantly; and (v) the time evolution operator is constructed from operators, which map state spaces of incoming modes of fundamental processes to those of outgoing modes. The time evolution operator turns out to be a function of quantum fields that are constructed from creation and annihilation operators for free-mode states, whose interaction part has a local feature. As an example, a simple model of modes is studied and is compared with the first-generation part of the standard model (SM). Concerning electroweak interactions, the studied model has a time evolution operator, whose main body is formally similar to that of the SM. Besides, it predicts $\frac 13$ and $\frac 23$ electronic changes for quark-type modes, gives an interpretation to the color degree of freedom, and contains certain modes that behave like dark matters., Comment: 42 pages, no figure

We study the long-time average of the reduced density matrix (RDM) of an $m$-level central system, which is locally coupled to a large environment, under an overall Schr\"{o}dinger evolution of the total system. We consider a class of interaction Hamiltonian, whose environmental part satisfies the so-called eigenstate thermalization hypothesis (ETH) ansatz with a constant diagonal part in the energy region concerned. On the eigenbasis of the central system's Hamiltonian, $\frac{1}{2}(m-1)(m+2)$ relations among elements of the averaged RDM are derived. When steady states exist, these relations imply the existence of a preferred basis, given by a renormalized Hamiltonian that includes certain averaged impact of the system-environment interaction. Numerical simulations performed for a qubit coupled to a defect Ising chain conform the analytical predictions.

We propose a non-perturbative $ab$ $initio$ approach to calculate the electrical conductivity of a liquid metal. Our approach is based on the Kubo formula and the theory of electron-phonon coupling (EPC), and unlike the conventional empirical approach based on the Kubo-Greenwood formula, fully takes into account the effect of coupling between electrons and moving ions. We show that the electrical conductivity at high temperature is determined by an EPC parameter $\lambda_{\mathrm{tr}}$, which can be inferred, non-perturbatively, from the correlation of electron scattering matrices induced by ions. The latter can be evaluated in a molecular dynamics simulation. Based on the density-functional theory and pseudopotential methods, we implement the approach in an $ab$ $initio$ manner. We apply it to liquid sodium and obtain results in good agreement with experiments. This approach is efficient and based on a rigorous theory, suitable for applying to general metallic liquid systems., Comment: 9 pages, 5 figures

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos., Comment: 7 pages. 9 figures

Enhanced light-matter interaction at the nanoscale is pivotal in the foundation of nonlinear optics, quantum optics, and nanophotonics, which are essential for a vast range of applications including single-photon sources, nanolasers, and nanosensors. In this context, the combination of strongly confined polaritons and low-loss nanocavities provides a promising way to enhance light-matter interaction, thus giving rise to a high density of optical states, as quantified by the so-called Purcell factor - the ratio of the decay rate of an optical quantum emitter to its value in free space. Here, we exploit whispering-gallery hyperbolic-phonon-polariton (WG-HPhP) modes in hBN nanotubes (BNNTs) to demonstrate record-high Purcell factors (~10^12) driven by the deep-subwavelength confinement of phonon polaritons and the low intrinsic losses in these atomically smooth nanocavities. Furthermore, the measured Purcell factor increases with decreasing BNNT radius down to 5 nm, a result that extrapolates to ~10^14 in a single-walled BNNT. Our study supports WG-HPhP modes in one-dimensional nanotubes as a powerful platform for investigating ultrastrong light-matter interactions, which open exciting perspectives for applications in single-molecular sensors and nanolasers., Comment: 21 pages, 4 figures

Exciton-phonon coupling (ExPC) is crucial for energy relaxation in semiconductors, yet the first-principles calculation of such coupling remains challenging, especially for low-dimensional systems. Here, an accurate algorithm for calculating ExPC is developed and applied in exciton relaxation problems in monolayer WSe2. Considering the interplay between the exciton wave functions and electron-phonon coupling (EPC) matrix elements, we find that ExPC shows distinct selection rules from the ones of EPC. By employing the Wannier exciton model, we generalize these selection rules, which state that the angular quantum numbers of the exciton must match the winding numbers of the EPC matrix elements for the ExPC to be allowed. To verify our theory and algorithm, we calculate inter-valley exciton relaxation pathways, which agrees well with a recent experiment., Comment: 6 pages, 4 figures