Zhanyuan Yan

When a time-dependent harmonic system is further driven by an external source, it presents significant challenges to obtaining analytical solutions for the system. This paper applies the Lewis-Riesenfeld invariant method to a mesoscopic time-dependent dissipative inductor-capacitor (RLC) circuit with an external source. By constructing quantum invariant Hermitian operators and introducing auxiliary equations that can describe the effects of external sources and resistance, we analytically solve the Schrödinger equation of the system. Taking an alternating current (AC) voltage source as an example, we derive the generalized coherent states of a mesoscopic time-dependent RLC circuit with an external source, calculate the quantum fluctuations of charge and current, and obtain their corresponding uncertainty relations. The results indicate that the time-dependent inductance and resistance disrupt the minimum uncertainty relation of the Glauble coherent states in driven time-dependent mesoscopic RLC circuits. This research contributes to the establishment of a quantum theory for mesoscopic circuits.

We propose a quantum Otto heat engine using a finite-size Dicke-Stark model as the working substance. In the extended coherent state space, the complete energy spectrum and eigenstates are obtained through numerical calculations. Within the infinite-time and finite-time thermodynamics frameworks, we find that the output work, efficiency, and power can be optimized by adjusting the Stark field strength, the qubit-boson coupling strength, stroke times, and number of atoms. Our results reveal that output work and efficiency are maximized near the coupling strength at the superradiant phase transition (SPT). Tuning the Stark field strength modifies the energy level structure and SPT, effectively suppressing entropy generation and quantum friction during nonequilibrium evolution. We also show that asymmetric heat engines-where the two isochoric strokes operate with different Stark field strengths and durations-further improve engine performance. These results may guide future implementations of efficient quantum heat engines.

The nonlinear Schrödinger equation (NLSE) underpins nonlinear wave phenomena in optics, Bose–Einstein condensates, and plasma physics, but computing its excited states remains challenging due to nonlinearity-induced non-orthonormality. Traditional methods, such as imaginary time evolution, work for ground states but fail for excited states. We propose a neural network quantum state (NNQS) approach, parameterizing wavefunctions with neural networks to directly minimize the energy functional, enabling computation of both ground and excited states. By designing compact, interpretable network architectures, we obtain analytical approximation of solutions. We apply the solutions to a case of spatiotemporal chaos in the NLSE, demonstrating its capability to study complex chaotic dynamics. This work establishes NNQS as a tool for bridging machine learning and theoretical studies of chaotic wave systems.

We report a method of improving the precision and resolution of sensing systems based on position sensitive detectors (PSDs). In the method, we improved the precision and resolution by reducing the gain of the condition circuit and conducting spatial filtering on the measured spot position. To demonstrate the method, we experimentally built a PSD-based displacement sensing system. With the system, a precision of 0.3 μm and a resolution of 0.5 μm were obtained. The precision is two orders of magnitude better than that obtained with the use of a commercial condition circuit (SPC02, SiTek, Partille, Sweden) and without using any filter. Moreover, we tested the radiation-resistance performance of the system using a ⁶⁰Co radiation source. The system kept the precision and resolution after exposure to radiation with a dose set to 100 krad. Our study is very useful to realize high-precision PSD-based sensing in space.

We propose a quantum Otto heat engine that employs a finite-size Dicke-Stark model as the working substance. In the extended coherent state space, the complete energy spectrum and eigenstates of this model are obtained through numerical calculations. Within the infinite-time and finite-time thermodynamics frameworks, we investigate the effects of the Stark field strength, coupling strength, adiabatic stroke time, isochoric stroke time, and number of atoms in the DS model on the heat engine's output work, efficiency, and power. The results show that the maximum values of the output work and efficiency appear near the coupling strength corresponding to the superradiant phase transition point. Regulating the Stark field strength can tune the energy level structure of the system and the superradiant phase transition, effectively reducing entropy generation and quantum friction during nonequilibrium evolution of the system's states and thereby significantly increasing the engine's output work, efficiency, and power. Asymmetric heat engines, where the two isochoric strokes have different Stark field strengths and stroke times, are more conducive to optimizing the heat engine's performance. Additionally, in the DS model, an increase in the number of atoms is also beneficial for increasing the heat engine's output work and efficiency. The results of this paper facilitate the design of high-performance quantum heat engines.

The nonlinear Schrödinger equation (NLSE) underpins nonlinear wave phenomena in optics, Bose-Einstein condensates, and plasma physics, but computing its excited states remains challenging due to nonlinearity-induced non-orthonormality. Traditional methods like imaginary time evolution work for ground states but fail for excited states. We propose a neural network quantum state (NNQS) approach, parameterizing wavefunctions with neural networks to directly minimize the energy functional, enabling computation of both ground and excited states. By designing compact, interpretable network architectures, we obtain analytical approximation of solutions. We apply the solutions to a case of spatiotemporal chaos in the NLSE, demonstrating its capability to study complex chaotic dynamics. This work establishes NNQS as a tool for bridging machine learning and theoretical studies of chaotic wave systems.

A quantum theory of mesoscopic circuits, based on the discreteness of electric charges, was recently proposed. However, it is not applied widely, mainly because of the difficulty of the mathematical solution to the finite-difference Schrödinger equation. In this paper, we propose an improved perturbation method to calculate Schrödinger equations of the inductance and capacity coupling mesoscopic circuit. With a unitary transformation, the finite differential Schrödinger equation of the system is divided into two equations in generalized momentum representation. The concrete value of the parameter in circuits is important to solving the equation. Both the perturbation method suitable case and the improved perturbation method suitable case, the wave functions, and energy level of the system are achieved. As an application, the current fluctuations are calculated and discussed. The improved mathematical method would be helpful for the popularization of the quantum circuits theory.

To conquer the challenges of charge accumulation and surface flashover in epoxy resin under direct current (DC) electric fields, numerous efforts have been made to research dielectric barrier discharge (DBD) plasma treatments using CF₄/Ar as the medium gas, which has proven effective in improving surface flashover voltage. However, despite being an efficient plasma etching medium, SF₆/Ar has remained largely unexplored. In this work, we constructed a DBD plasma device with an SF₆/Ar gas medium and explored the influence of processing times and gas flow rates on the morphology and surface flashover voltage of epoxy resin. The surface morphology observed by SEM indicates that the degree of plasma etching intensifies with processing time and gas flow rate, and the quantitative characterization of AFM indicates a maximum roughness of 144 nm after 3 min of treatment. Flashover test results show that at 2 min of processing time, the surface flashover voltage reached a maximum of 19.02 kV/mm, which is 25.49% higher than that of the untreated sample and previously reported works. In addition to the effect of surface roughness, charge trap distribution shows that fluorinated groups help to deepen the trap energy levels and density. The optimal modification was achieved at a gas flow rate of 3.5 slm coupled with 2 min of processing time. Furthermore, density functional theory (DFT) calculations reveal that fluorination introduces additional electron traps (0.29 eV) and hole traps (0.38 eV), enhancing the capture of charge carriers and suppressing surface flashover.