Quantum chaos and the correspondence principle.

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically nonchaotic systems [E. B.

Identifying risk factors for chronic kidney disease stage 3 in adults with acquired solitary kidney from unilateral nephrectomy: a retrospective cohort study.

Background: We aimed to examine the risk factors for chronic kidney disease (CKD) stage 3 among adults with ASK from unilateral nephrectomy.

Methods: We retrospectively collected data from adult patients with ASK between January, 2009 and January, 2019, identified from a tertiary hospital in China. The clinical data were compared between patients who developed CKD stage 3 and those who did not develop CKD stage 3 during follow-up.

Closeness of the reduced density matrix of an interacting small system to the Gibbs state.

I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form and with a generic interaction strength, when the total system lies in an equilibrium state described by a microcanonical ensemble. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case and the RDM obtained in the uncoupled case. In the eigenbasis of the central system's Hamiltonian, it is shown that the difference between diagonal elements is mainly confined by the ratio of the maximum width of the eigenfunctions of the total system in the uncoupled basis to the width of the microcanonical energy shell; meanwhile, the difference between off-diagonal elements is given by the ratio of certain property of the interaction Hamiltonian to the related level spacing of the central system.

Characterization of random features of chaotic eigenfunctions in unperturbed basis.

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 a 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.

Fourier heat conduction as a strong kinetic effect in one-dimensional hard-core gases.

For a one-dimensional (1D) momentum conserving system, intensive studies have shown that generally its heat current autocorrelation function (HCAF) tends to decay in a power-law manner and results in the breakdown of the Fourier heat conduction law in the thermodynamic limit. This has been recognized to be a dominant hydrodynamic effect. Here we show that, instead, the kinetic effect can be dominant in some cases and leads to the Fourier law for finite-size systems.

Decoherence approach to energy transfer and work done by slowly driven systems.

A main problem, which is met when computing the energy transfer of or work done by a quantum system, comes from the fact that the system may lie in states with coherence in its energy eigenstates. As is well known, when the so-called environment-induced decoherence has happened with respect to a preferred basis given by the energy basis, no coherence exists among the energy basis and the energy change of the system can be computed in a definite way. I argue that one may make use of this property, in the search for an appropriate definition of quantum work for a total system that does not include any measuring apparatus.

Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices.

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation functions with respect to energy. The analytical results are tested in several models by numerical simulations.

Internal temperature of quantum chaotic systems at the nanoscale.

The extent to which a temperature can be appropriately assigned to a small quantum system, as an internal property but not as a property of any large environment, is still an open problem. In this paper, a method is proposed for solving this problem, by which a studied small system is coupled to a two-level system as a probe, the latter of which can be measured by measurement devices. A main difficulty in the determination of possible temperature of the studied system comes from the back-action of the probe-system coupling to the system.

[Correlation Study on Pathological Characteristics of Target Organs and Excess Evil Syndrome in IgA Nephropathy].

Objective: To explore the correlation between pathological characteristics of target organs and excess evil syndrome in IgA nephropathy.

Methods: Data were collected in multicenter cooperation. Totally 266 IgA nephropathy patients were typed into exogenous wind-heat affection syndrome (49 cases), lower energizer damp-heat syndrome (100 cases), damp-phlegm syndrome (43 cases), and blood stasis syndrome (74 cases).

Relative criterion for validity of a semiclassical approach to the dynamics near quantum critical points.

Based on an analysis of Feynman's path integral formulation of the propagator, a relative criterion is proposed for validity of a semiclassical approach to the dynamics near critical points in a class of systems undergoing quantum phase transitions. It is given by an effective Planck constant, in the relative sense that a smaller effective Planck constant implies better performance of the semiclassical approach. Numerical tests of this relative criterion are given in the XY model and in the Dicke model.

Statistically preferred basis of an open quantum system: its relation to the eigenbasis of a renormalized self-Hamiltonian.

We study the problem of the basis of an open quantum system, under a quantum chaotic environment, which is preferred in view of its stationary reduced density matrix (RDM), that is, the basis in which the stationary RDM is diagonal. It is shown that, under an initial condition composed of sufficiently many energy eigenstates of the total system, such a basis is given by the eigenbasis of a renormalized self-Hamiltonian of the system, in the limit of large Hilbert space of the environment. Here, the renormalized self-Hamiltonian is given by the unperturbed self-Hamiltonian plus a certain average of the interaction Hamiltonian over the environmental degrees of freedom.

Complexity and instability of quantum motion near a quantum phase transition.

We show that the number of harmonics of the Wigner function, recently proposed as a measure of quantum complexity, can also be used to characterize quantum phase transitions. The nonanalytic behavior of this quantity in the neighborhood of a quantum phase transition is illustrated by means of the Dicke model and is compared to two well-known measures of the (in)stability of quantum motion: the quantum Loschmidt echo and fidelity.

Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown.

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a one-dimensional Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, particularly for perturbation strength in the so-called Fermi-Golden-Rule regime.

Scaling behavior for a class of quantum phase transitions.

We show that for quantum phase transitions with a single bosonic zero mode at the critical point, like the Dicke model and the Lipkin-Meshkov-Glick model, metric quantities such as fidelity, that is, the overlap between two ground states corresponding to two values λ(1) and λ(2) of the controlling parameter λ, depend only on the ratio η = (λ(1) -λ(c))/(λ(2) -λ(c)), where λ = λ(c) at the critical point. This scaling property is valid also for time-dependent quantities such as the Loschmidt echo, provided time is measured in units of the inverse frequency of the critical mode.

Statistical description of small quantum systems beyond the weak-coupling limit.

An explicit expression is derived for the statistical description of small quantum systems, which are relatively weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is given by a renormalized self-Hamiltonian of the studied system, which appropriately takes into account the influence of the system-environment interaction. In the case that the system has a narrow spectrum and the environment is sufficiently large, the modification to the self-Hamiltonian usually has a mean-field feature, given by an environmental average of the interaction Hamiltonian.

Preferred states of decoherence under intermediate system-environment coupling.

The notion that decoherence rapidly reduces a superposition state to an incoherent mixture implicitly adopts a special representation, namely, the representation of preferred (pointer) states (PS). For weak or strong system-envrionment interaction, the behavior of PS is well known. Via a simple dynamical model that simulates a two-level system interacting with few other degrees of freedom as its environment, it is shown that even for intermediate system-environment coupling, approximate PS may still emerge from the coherent quantum dynamics of the whole system in the absence of any thermal averaging.

T-2 toxin induces degenerative articular changes in rodents: link to Kaschin-Beck disease.

Osteoarthritis (OA) is a degenerative joint disease that is characterized by joint pain and a progressive loss of articular cartilage. Kaschin-Beck Disease is a form of endemic OA in China whose etiology is unclear, but epidemiological data indicate a possible link to trichothecenes mycotoxin exposure. In vitro, T-2 toxin, a trichothecenes mycotoxin, has been demonstrated to inhibit aggrecan synthesis and promote aggrecanase and pro-inflammatory cytokine production in cultured chondrocytes.

Semiclassical approach to survival probability at quantum phase transitions.

We study the decay of survival probability at quantum phase transitions with infinitely degenerate ground levels at critical points. For relatively long times, the semiclassical theory predicts power-law decay of the survival probability in systems with d=1 and exponential decay in systems with sufficiently large d, where d is the degrees of freedom of the classical counterpart of the system. The predictions are checked numerically in four models.

Decay of Loschmidt echo in a Bose-Einstein condensate at a dynamical phase transition.

We study the quantum Loschmidt echo (LE) in a Bose-Einstein condensate (BEC) in a double-well potential. The BEC may undergo a dynamical phase transition between two phases: a tunneling phase and a self-trapping phase. For sufficiently weak perturbation, the LE has Gaussian decay in both phases.

Stability of Fock states in a two-component Bose-Einstein condensate with a regular classical counterpart.

We study the stability of a two-component Bose-Einstein condensate (BEC) in the parameter regime in which its classical counterpart has regular motion. The stability is characterized by the fidelity for both the same and different initial states. We study as initial states the Fock states with definite numbers of atoms in each component of the BEC.

Sensitivity of quantum motion to perturbation in a triangle map.

We study quantum Loschmidt echo, or fidelity, in the triangle map whose classical counterpart has linear instability and weak chaos. Numerically, three regimes of fidelity decay have been found with respect to the perturbation strength epsilon. In the regime of weak perturbation, the fidelity decays as exp(-c epsilon(2)t(gamma)) with gamma approximately 1.

Stability of quantum motion in regular systems: a uniform semiclassical approach.

We study the stability of quantum motion of classically regular systems in the presence of small perturbations. On the basis of a uniform semiclassical theory we derive the fidelity decay which displays a quite complex behavior, from Gaussian to power law decay t(-alpha), with 1 View Article and Find Full Text PDF

Uniform semiclassical approach to fidelity decay: from weak to strong perturbation.

We study fidelity decay by a uniform semiclassical approach, in the three perturbation regimes: namely, the perturbative regime, the Fermi golden rule (FGR) regime, and the Lyapunov regime. A semiclassical expression is derived for the fidelity of initial Gaussian wave packets with width of the order sqare root h (h being the effective Planck constant). The short-time decay of the fidelity of initial Gaussian wave packets is also studied with respect to two time scales introduced in the semiclassical approach.