Singular behavior of eigenstates in Anderson's model of localization

Utilisation willingness for institutional care by the disabled elderly and its influencing factors based on Andersen's model: a cross-sectional survey of Henan, China

OBJECTIVE

To explore the factors that influence institutional care for the disabled elderly in China and the key factors that influence individuals based on the Andersen model.

DESIGN

Cross-sectional survey.

SETTING

The research was conducted in 18 cities in Henan Province, China.

MAIN OUTCOME MEASURES

A multistage, stratified sampling design was employed. The χ² test was used to compare the differences in basic information of the disabled elderly. A binary Logit model was used to examine the factors influencing the willingness to institutionalise elderly people with disabilities. The determinants of willingness to care in an institution were also explored in a stratified study by gender, age and region to identify the key differences affecting institutionalisation. The Andersen model was used as the theoretical framework to infer the impact strength of each model.

RESULTS

Of the 2810 disabled elderly people in Henan, China, 7.4% of the elderly had a willingness for institutional care. In the binary logistic regression analysis, whether living alone (OR (95% CI)=0.596 (0.388 to 0.916)), medical payment method (basic medical insurance for urban employees: OR (95% CI)=2.185 (1.091 to 4.377)), having mental illness (OR (95% CI)=2.078 (1.044 to 4.137)) had a statistically significant difference (p<0.05) on the impact on the willingness of the disabled elderly to receive institutional care. Validation of the fitted coefficients of the model revealed that the needs factor had the most significant effect on the enabling variable, while the predisposing factor had more minerally effect.

CONCLUSIONS

Several factors influence the willingness of the disabled elderly to institutionalise. Therefore, it is recommended that relevant authorities take targeted measures to focus on the disabled elderly to identify more precise elderly care services to deal with the ageing crisis.

Many-body thermodynamics on quantum computers via partition function zeros

Partition functions are ubiquitous in physics: They are important in determining the thermodynamic properties of many-body systems and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtain its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here, we show how to find partition function zeros on noisy intermediate-scale trapped-ion quantum computers in a scalable manner, using the XXZ spin chain model as a prototype, and observe their transition from XY-like behavior to Ising-like behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the future calculation of critical phenomena for systems beyond classical computing limits.

Local integrals of motion in the two-site Anderson-Hubbard model

It has been proposed that the states of fully many-body localized systems can be described in terms of conserved local pseudospins. Due to the multitude of ways to define these, the explicit identification of the optimally local pseudospins in specific systems is non-trivial. Given continuing intense interest in the role of disorder in strongly correlated systems, we consider the disordered Hubbard model. By studying a small system we provide concrete examples of the form of local integrals of motion in the Anderson-Hubbard model. Moreover, we are able not only to identify the most local choice but also to explore the nature of the distribution of possible choices. We track the evolution of the optimally localized pseudospins as hopping and interactions are varied to move the system away from the trivially localized atomic limit.

Two-dimensional quantum percolation with binary nonzero hopping integrals

In a previous work [Dillon and Nakanishi, Eur. Phys. J. B 87, 286 (2014)EPJBFY1434-602810.1140/epjb/e2014-50397-4], we numerically calculated the transmission coefficient of the two-dimensional quantum percolation problem and mapped out in detail the three regimes of localization, i.e., exponentially localized, power-law localized, and delocalized, which had been proposed earlier [Islam and Nakanishi, Phys. Rev. E 77, 061109 (2008)PLEEE81539-375510.1103/PhysRevE.77.061109]. We now consider a variation on quantum percolation in which the hopping integral (w) associated with bonds that connect to at least one diluted site is not zero, but rather a fraction of the hopping integral (V=1) between nondiluted sites. We study the latter model by calculating quantities such as the transmission coefficient and the inverse participation ratio and find the original quantum percolation results to be stable for w>0 over a wide range of energy. In particular, except in the immediate neighborhood of the band center (where increasing w to just 0.02Vappears to eliminate localization effects), increasing w only shifts the boundaries between the three regimes but does not eliminate them until w reaches 10%-40% of V.

Persistence of energy-dependent localization in the Anderson-Hubbard model with increasing system size and doping

Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson-Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states.

Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.