Using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for nonreciprocal non-Hermitian systems such as the Hatano-Nelson model. Here, we propose a one-parameter scaling function using the participation ratio as the scaling variable. Employing a highly accurate numerical procedure based on exact diagonalization, we demonstrate that this one-parameter scaling function can describe Anderson localization transitions of nonreciprocal non-Hermitian systems in one and two dimensions of symmetry classes AI and A. The critical exponents of correlation lengths depend on symmetries and dimensionality only, a typical feature of universality. Then, we derive a complex-gap equation based on the self-consistent Born approximation to determine the critical disorder at which the point gap closes. The obtained critical disorders perfectly match those given by the one-parameter scaling function. Moreover, we propose a one-parameter β function that can describe the critical properties of such Anderson localization transitions. Finally, we show that the one-parameter scaling function is also valid for Anderson localization transitions in reciprocal non-Hermitian systems such as the two-dimensional class AII^{†} and can, thus, serve as a unified scaling function for disordered non-Hermitian systems.

Highly integrated energy systems are on the rise due to increasing global demand. To capture the underlying physics of such interdisciplinary systems, we need a modern framework that unifies all forms of energy. Here, we apply modified Lagrangian mechanics to the description of multi-energy systems. Based on the minimum entropy production principle, we revisit fluid mechanics in the presence of both mechanical and thermal dissipations and propose using exergy flow as the unifying Lagrangian across different forms of energy. We illustrate our theoretical framework by modeling a one-dimensional system with coupled electricity and heat. We map the exergy loss rate in real space and obtain the total exergy changes. Under steady-state conditions, our theory agrees with the traditional formula but incorporates more physical considerations such as viscous dissipation. The integral form of our theory also allows us to go beyond steady-state calculations and visualize the local, time-dependent exergy flow density everywhere in the system. Expandable to a wide range of applications, our theoretical framework provides the basis for developing versatile models in integrated energy systems.

In this paper, we introduce a mathematical framework for analyzing and optimizing district heating networks by leveraging the Green’s function method. Traditional numerical methods for simulating district heating networks often face computational challenges and lack transparency in revealing cause-and-effect relationships in heat propagation. By treating temperature as a scalar field, we employ Green’s function methods to derive analytical solutions that provide a more transparent and intuitive understanding of how heat propagates through the network in response to various inputs. We demonstrate the application of this framework through two numerical examples involving heating networks. Comparative results show that, under identical hardware conditions, the Green’s function method requires only about one-fifth of the computational time compared to the finite element method for the same case. This approach offers distinct advantages in terms of computational efficiency, accuracy, and interpretability, enabling more effective design, optimization, and control of sustainable district heating systems.

Understanding the physical and chemical processes at the interfaces of metals and topological insulators is crucial for the development of the next generation of topological quantum devices. Here, we report the discovery of robust superconductivity in Pd/Bi₂Se₃ bilayers fabricated by sputtering Pd on the surface of Bi₂Se₃. Through transmission electron microscopy measurements, we identify that the observed interfacial superconductivity originates from the diffusion of Pd into Bi₂Se₃. In the diffusion region, Pd chemically reacts with Bi₂Se₃ and forms a layer of PdBiSe, a known superconductor with a bulk transition temperature of 1.5 K. Our work provides a method for the introduction of superconductivity into Bi₂Se₃, laying the foundation for the development of sophisticated Bi₂Se₃-based topological devices.