Hasil untuk "Electric apparatus and materials. Electric circuits. Electric networks"

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arXiv Open Access 2026
Ultrafast electrically controlled magnetism in charge-order-induced ferroelectric altermagnet

Yuhao Gu, Yu-Hui Song, Yihao Wang et al.

The altermagnetism with antiparallel spin alignment exhibits anisotropic spin splitting and may possess an insulating state with a high Neel temperature, while the charge-order-induced ferroelectricity has ultrafast electric polarization switching. Considering that altermagnetism requires breaking space inversion,, the physical foundation for exploring ultrafast electrically controlled magnetism in altermagnetic ferroelectric materials is thus established. In this Letter, based on symmetry analysis and first-principles electronic structure calculations, we predict that LiV$_2$F$_6$ is a material that simultaneously hosts altermagnetism and charge-order-induced ferroelectricity. Since both the altermagnetism and ferroelectricity originate from charge order, LiV$_2$F$_6$ should exhibit strong magnetoelectric coupling. Our calculations indeed demonstrate that electric polarization reversal can induce band spin-polarization switching in LiV$_2$F$_6$. Moreover, time-dependent density functional theory calculations show that the electric polarization reversal in LiV$_2$F$_6$ occurs in 15 femtoseconds. Consequently, ultrafast electrically controlled magnetism can be realized in LiV$_2$F$_6$. Given that LiV$_2$F$_6$ has already been experimentally synthesized, our work provides a promising material platform for achieving ultrafast electrically controlled magnetism, which might have significant implications for the design of future electronic devices.

en cond-mat.mtrl-sci, physics.comp-ph
DOAJ Open Access 2025
Influence of Highly Charged Ion Irradiation on the Electrical and Memory Properties of Black Phosphorus Field‐Effect Transistors

Stephan Sleziona, Osamah Kharsah, Lucia Skopinski et al.

Abstract Black phosphorus (bP) is one of the more recently discovered layered materials. Utilizing the hysteresis in the transfer characteristics of bP field‐effect transistors (FETs), several approaches to realize non‐volatile memory devices are successfully demonstrated. This hysteresis is commonly attributed to charge trapping and detrapping in impurities and defects whose nature and location in the device are however unclear. In this work, defects are deliberately introduced into bP FETs by irradiating the devices with highly charged Xe30 + at a kinetic energy of 180 and 20 keV to manipulate their electrical and memory properties. The results show for the ion with higher energy an increase of conductance and an increase of p‐doping of up to 1.2 · 1012 cm−2 with increasing fluence, while the charge carrier mobility degrades for the higher ion fluences. Most notably, an increase in the hysteresis' width and of the memory window are observed due to the irradiation. By controlling the kinetic energy of the ions, it can be demonstrated, that the modifications of electronic properties arise from defects in bP and the underlying SiO2 substrate. However, changes in hysteretic properties are attributed exclusively to irradiation‐induced defects in the substrate, so ion irradiation can significantly improve the properties of bP based memory devices.

Electric apparatus and materials. Electric circuits. Electric networks, Physics
DOAJ Open Access 2025
Stress control in trench field-plate power MOSFETs and its impact on on-resistance reduction

Hiroaki Kato, Shin-ichi Nishizawa, Wataru Saito

The limitations regarding lateral cell pitch narrowing and on-resistance reduction were investigated. Trench field plate MOSFETs feature deep trenches with thick oxide films. This disrupts the stress balance, leading to significant wafer warpage, which poses a critical challenge in device integration. Stress control has become essential for enabling cell pitch narrowing, achieving high breakdown voltage device designs, and implementing innovative device pattern layouts such as dot pattern cell structures. In this study, stress and wafer warpage associated with lateral cell pitch narrowing were estimated using 3D simulations. Based on these results, the on-resistance reduction limit was also estimated through analytical models. For stripe pattern cell structures, pitch narrowing was constrained by both increased wafer warpage and on-resistance saturation. Notably, the X-direction wafer warpage was identified as the limiting factor for pitch narrowing in high breakdown voltage device designs. In contrast, the dot pattern cell structure significantly reduced wafer warpage and allowed narrower pitches compared to the stripe pattern, despite a weakened mobility enhancement effect.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2025
Advanced Microfluidic‐Based Wearable Electrochemical Sensors for Continuous Biochemical Monitoring

Sehyun Park, Seongyeop Kim, Soojin Lee et al.

Abstract Microfluidic‐based wearable electrochemical sensors represent a transformative approach to non‐invasive, real‐time health monitoring through continuous biochemical analysis of body fluids such as sweat, saliva, and interstitial fluid. These systems offer significant potential for personalized healthcare and disease management by enabling real‐time detection of key biomarkers. However, challenges remain in optimizing microfluidic channel design, ensuring consistent biofluid collection, balancing high‐resolution fabrication with scalability, integrating flexible biocompatible materials, and establishing standardized validation protocols. This review explores advancements in microfluidic design, fabrication techniques, and integrated electrochemical sensors that have improved sensitivity, selectivity, and durability. Conventional photolithography, 3D printing, and laser‐based fabrication methods are compared, highlighting their mechanisms, advantages, and trade‐offs in microfluidic channel production. The application section summarizes strategies to overcome variability in biofluid composition, sensor drift, and user adaptability through innovative solutions such as hybrid material integration, self‐powered systems, and AI‐assisted data analysis. By analyzing recent breakthroughs, this paper outlines critical pathways for expanding wearable sensor technologies and achieving seamless operation in diverse real‐world settings, paving the way for a new era of digital health.

Electric apparatus and materials. Electric circuits. Electric networks, Physics
DOAJ Open Access 2025
Damage tolerance performance of high strength and toughness titanium alloys formed by additive manufacturing in aerospace: A review

Guozheng Liu, Qinyang Zhao, Weiju Jia et al.

In aerospace, high strength and toughness titanium alloys (HSTTAs) formed by additive manufacturing (AM) are mostly utilized to create complex shaped structural components. It can fulfill the bespoke design specifications of components, enhance material consumption and production efficiency, and decrease costs and time. As the requirement for safety and stability in structural components rises, damage tolerance performance (DTP) has emerged as the design benchmark for titanium alloys in aviation. This review initially presents the historical evolution of HSTTAs and subsequently discusses related research on the HSTTAs formed by AM. This review covers recent research advancements on the DTP of HSTTAs formed by AM, detailing the deformation behavior, fracture toughness, and fatigue crack propagation characteristics of the alloy. The primary approaches for enhancing the DTP of HSTTAs formed by AM, including process parameter optimization and heat treatment, are examined. Finally, the existing problems on current research and prospective research directions are identified. Investigating the DTP of HSTTAs formed by AM can enhance the overall performance of materials and guarantee structural integrity, while also fostering innovation in AM and propelling technological advancement. And it provides certain reference significance for upgrading AM processes and post-treatment processes, optimizing properties, and developing new high damage tolerant titanium alloys.

Materials of engineering and construction. Mechanics of materials, Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2025
A Review of Glass Substrate Technologies

Pratik Nimbalkar, Pragna Bhaskar, Lakshmi Narasimha Vijay Kumar et al.

Artificial intelligence is redefining the computing landscape. Chiplets and heterogeneous integration have become the key strategies for current and next-generation processors. In the wake of Moore’s law slowing down, system integration through advanced packaging has emerged as the leading approach to achieve the highest performance per cost. Overall, the system is converging around substrate which is the main component of packaging. Glass stands out as the superior integration platform for chiplet-based systems. Glass substrates provide unmatched electrical and mechanical properties leading to unprecedented design and integration flexibility at a lower cost than competitive technologies. Three key advantages make glass the platform of choice: the ability to tune material properties, the ability to structure glass, and the feasibility of processing on a large panel scale. This review details the fundamentals of glass processing and manufacturing, innovative integration techniques, and cutting-edge research that collectively position glass substrate as a superior option for the next-generation systems for AI and beyond. Finally, we outline how technology must be shaped in the coming years to drive system scaling.

Electronic computers. Computer science, Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2025
Surface Ion Trap for Fast Microwave Gates

Ilya Gerasin, Ilya Semerikov, Wei Zhang

Microwave-driven quantum logic gates in trapped-ion systems offer a scalable and laser-free alternative to optical control, with the potential for robust integration into surface-electrode trap architectures. In this work, we present a systematic design guideline for planar ion traps optimized for fast two-qubit microwave gates using chip-integrated conductors. We investigate two electrode configurations, one employing a single microwave line for driving <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula> transitions, and another with two symmetric lines for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>π</mi></semantics></math></inline-formula> transitions. Through finite-element simulations, we analyze ion height, magnetic field gradients, heating effects, and gate durations under realistic cryogenic conditions. Our results show that both configurations can achieve two-qubit gate times in the order of 10 μs for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mmultiscripts><mi>Be</mi><none></none><mn>+</mn><mprescripts></mprescripts><none></none><mn>9</mn></mmultiscripts></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mmultiscripts><mi>Ca</mi><none></none><mn>+</mn><mprescripts></mprescripts><none></none><mn>40</mn></mmultiscripts></semantics></math></inline-formula> ions.

Electronic computers. Computer science, Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2025
High-Accuracy Bandgap Reference of <20 ppm/°C: A Review

Haoyu Zhuang, Xudong Chen, Enzhe Zhang et al.

This review discusses the principle of typical bandgap reference circuits and analyzes their sources of errors. In order to provide readers with a clear perspective, we categorize the error sources into four types: (a) amplifier offset; (b) high-order nonlinearity of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>V</mi><mrow><mi>B</mi><mi>E</mi></mrow></msub></semantics></math></inline-formula>; (c) current mirror mismatch; and (d) other error sources. For these error sources, the most commonly used methods to reduce or minimize them to achieve high accuracy are summarized. Furthermore, this review explores sub-1V bandgap reference design techniques, addressing the increasing demand for low-power and low-voltage applications. Finally, we provide some suggestions for a future high-accuracy reference design.

Electronic computers. Computer science, Electric apparatus and materials. Electric circuits. Electric networks
arXiv Open Access 2025
Electric Field Induced Superconductivity in Bilayer Octagraphene

Yitong Yao, Jun Li, Jiacheng Ye et al.

We investigate the energy bands, magnetism, and superconductivity of bilayer octagraphene with A-A stacking under a perpendicular electric field. A tight-binding model is used to analyze the band structure of the system. The doubling of the unit cell results in each band of the single layer splitting into two. We find that applying a perpendicular electric field increases the band splitting. As the electric field strength increases, the nesting of the Fermi Surface(FS) weakens, eventually disrupting the antiferromagnetic order and bilayer octagraphene exhibits superconductivity. Spin fluctuations can induce unconventional superconductivity with s+--wave pairing. Applying a perpendicular electric field to bilayer octagraphene parent weakens the nesting of the FS, ultimately killing the spin-density-wave (SDW) ordered state and transitioning it into the superconducting state, whichworks as a doping effect. We use the random-phase approximation approach to obtain the pairing eigenvalues and pairing symmetries of the perpendicular electric field-tuned bilayer octagraphene in the weak coupling limit. By tuning the strength of the perpendicular electric field, the critical interaction strength for SDW order can be modified, which in turn may promote the emergence of unconventional superconductivity.

en cond-mat.supr-con
arXiv Open Access 2025
Orbital Longitudinal Magneto-electric Coupling in Multilayer Graphene

Jin-Xin Hu, Justin C. W. Song

Magneto-electric coupling enables the manipulation of magnetization by electric fields and vice versa. While typically found in heavy element materials with large spin-orbit coupling, recent experiments on rhombohedral-stacked pentalayer graphene (RPG) have demonstrated a {\it longitudinal magneto-electric coupling} (LMC) without spin-orbit coupling. Here we present a microscopic theory of LMC in multilayer graphene and identify how it is controlled by a ``layer-space'' quantum geometry and interaction-driven valley polarization. Strikingly, we find that the interplay between valley-polarized order and LMC produces a butterfly shaped magnetic hysteresis controlled by out-of-plane electric field: a signature of LMC and a multiferroic valley order. Furthermore, we identify a nonlinear LMC in multilayer graphene under time-reversal symmetry, while the absence of centrosymmetry enables the generation of a second-order nonlinear electric dipole moment in response to an out-of-plane magnetic field. Our theoretical framework provides a quantitative understanding of LMC, as well as the emergent magneto-electric properties of multilayer graphene.

en cond-mat.mes-hall
DOAJ Open Access 2024
Understanding the Inherent Properties of Vapor Phase Poly (3,4 – Ethylenedioxythiophene) Deposited Stretchable Conducting Films

Vithyasaahar Sethumadhavan, Eliza Switalska, Mahboobeh Shahbazi et al.

Abstract Stretchable conducting films are a prime necessity for future stretchable and wearable electronics. In this work, highly conducting poly(3,4 ethylenedioxythiophene):Tosylate (PEDOT:Tos) films are deposited on extremely stretchable styrene‐ethylene‐butylene‐styrene (SEBS) substrates via vapor phase polymerization (VPP) and their inherent properties are systematically studied. The charge transport and electrical properties of VPP PEDOT:Tos stretchable films are measured from room temperature down to the low temperature of 5 K. Interestingly, the mechanical properties of the stretchable substrate lead to buckling of the PEDOT:Tos that affect the electrical conductivity but not the charge carrier mobility, optical, and structural properties. The VPP PEDOT:Tos on the stretchable SEBS substrate show a semiconducting behavior as electrical resistance is enhanced upon cooling from room temperature to 5 K. Such kind of stretchable conducting films can be used for stretchable transistors, wearable sensing, energy storage, and electrochromic applications.

Electric apparatus and materials. Electric circuits. Electric networks, Physics
DOAJ Open Access 2024
Design and development of an EMG controlled transfemoral prosthesis

R. Dhanush Babu, S. Siva Adithya, M. Dhanalakshmi

Electromyography (EMG) signals are biomedical signals that measure electrical currents generated by the activity of muscles when they contract. EMG is essential for optimizing the control of various prosthetic devices, particularly for transfemoral amputees, where the complexity of muscle signal integration presents significant challenges. The proposed study aims to develop a prosthetic knee that actuates in real-time using the EMG signals from the amputee’s residual limb. Pre-processing techniques are employed to obtain EMG signals from the femoris and vastus muscle targets in the transfemoral region. Moving average filters and Butterworth bandpass filters are implemented to process the raw signals. Sliding windows of various widths were applied for feature extraction. The window size of 200 ms is determined for our study based on the outcomes of the t-SNE plots and the corresponding silhouette scores. After the extraction of the pertinent features, several supervised classifier algorithms are put into practice to classify the knee flexion and extension motion. The k-nearest Neighbor (KNN) algorithm, with an accuracy rating of 80 %, proved to be suitable for motor control. Real-time control is implemented using the Raspberry Pi board to power the prosthesis allowing above-the-knee amputees to voluntarily move the leg back and forth. The EMG signals are then extracted and used to drive the DC motor. The prosthesis would therefore be able to move more precisely since the EMG readings are being gathered in real-time. Thus, this work can enhance the patient’s comfort with the ease of carrying out knee movements.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2024
Analysis and development of smart production and distribution line system in smart grid based on optimization techniques involving digital twin

Thangaraja Arumugam, Nitin Kundlik Kamble, Venkataramana Guntreddi et al.

The term Digital Twin (DT) is defined as the virtual demonstration of an object that is represented through real-time datasets. DT is done through artificial intelligence to enhance decision-making techniques. DT includes the process of simulation, amalgamation, observation, analysis, and conservation. The DT is simply the exact reproduction of the physical structures. DT is used in the identification and evaluation of problems through real-time analysis. It is important to have prior analysis and evaluation of the object before existing in the real world. These digital twins help in the manufacturing and implementation of the production line system. DT includes the production line with the station division and the hours needed for the operating conditions for the assembly process. The systems are integrated to reduce the overall cost parameter. The physical simulation model is employed to obtain higher performance with reduced cost. An artificial neural network with a genetic algorithm is used for the optimization process to achieve a production line system using digital twins.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2024
PCA based feature extraction and MPSO based feature selection for gene expression microarray medical data classification

Abdul Razzaque, Dr Abhishek Badholia

In this paper, a novel Multi Class based Feature Extraction (MC-FE) method has been proposed for medical data classification. Genomic datasets, or gene expression-based microarray medical datasets, are categorised for cancer diagnosis. The first stage involves applying a feature extraction technique. The Principal Component Analysis (PCA) is used to extract the features for medical data classification to detect leukemia, colon tumors, and prostate cancer. The MPSO (modified particle swarm optimization) technique is used at the second stage to pick features from high-dimensional microarray medical datasets like prostate cancer, leukemia, and colon tumors. Finally, SVM, KNN, and Naive Bayes classifiers are used to classify medical data. Then, the classified data are stored in the cloud IOT sensors. When compared to the existing methods, the proposed method gives better optimized results for SVM, KNN, and Naive Bayes of 0.88, 0.86, and 0.73, respectively. The results of cancer data extraction and feature selection are also contrasted and assessed using certain performance measure factors.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2024
A Wireless Power Conversion Chain With Fully On-Chip Automatic Resonance Tuning System for Biomedical Implants

Mohammad Javad Karimi, Menghe Jin, Catherine Dehollain et al.

This paper presents a wireless power conversion system designed for biomedical implants, with integrated automatic resonance tuning. The automatic tuning mechanism improves power transfer efficiency (PTE) by finely tuning the resonant frequency of the power link and maximizing the rectified voltage. This adjustment ensures robust and reliable remote powering, even in the face of environmental changes and process variations, while also minimizing tissue exposure to power. On-chip switched array capacitors are connected in parallel with the resonant capacitor, and the system identifies the optimal switched capacitor combination for the highest rectified voltage by iterating over each of them. The proposed system is implemented and fabricated in standard 180nm CMOS technology, with a total area of 0.339 mm2, and its operation is verified. The measurement results demonstrate that this system provides tolerance up to mismatches equivalent to 75 pF capacitance variation in LC tank, &#x00B1;15&#x0025; LC variation in this design. The system offers a PTE enhancement from 9.1&#x0025; to 30.2&#x0025; in case of high LC variation, and the tuning control consumes 154.7<inline-formula> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> of power during resonance tuning. Moreover, the power conversion chain delivers an optimized rectified voltage along with a regulated voltage of 1.8 V.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2024
Simulink and real-time implementation of the E-cycle for measuring the reliability of the model using sensors

T. Viveka, NVS. Sree Rathna Lakshmi, S. Amosedinakaran et al.

Utilization of rechargeable battery based bicycles has been significantly increased in India. In this study, battery powered electric vehicles have been implemented in MATLAB 2013a Simulink and real-time hardware systems. In order to design and integrate a working model of electric cycle, one needs to know about the different components involved in a system, such as lithium-ion batteries, Brushless DC motor (BLDC), and controller systems. The detailed study about the component selection has been described in this study. The drive testing has been implemented in both Simulink and real time respectively. Within a single charging system, the proposed model of electric cycle has been derived up to 25 kilo-meter up to speed of 30 kilo-meter per second respectively. The characteristics of electric vehicles such as torque (N-m) versus time (s), speed (km/h) versus time (s) and distance (km) versus time (s) have been discussed in this study. Based on characteristics study, reliability of the electric vehicle model has been enhanced in electric bicycle system by physical model confirmation.

Electric apparatus and materials. Electric circuits. Electric networks
DOAJ Open Access 2024
Omega‐Gate Silicon Nanowire Geometric Diodes with Reconfigurable Self‐Switching Operation and THz Rectification

Kelly L. White, Gordon V. Rogelberg, James P. Custer Jr. et al.

Abstract Geometric diodes (GDs) represent a relatively unconventional class of diode that produces an asymmetric current response through carrier transport in an asymmetric geometry. Synthesized from the bottom up, Si nanowire‐based GDs are three‐dimensional, cylindrically symmetric nanoscale versions capable of room‐temperature rectification at GHz‐THz frequencies with near zero‐bias turn‐on voltages. Here, by fabricating three‐terminal n‐type Si nanowire GDs with axial contacts and an omega‐gate electrode, a distinct class of reconfigurable self‐switching geometric diodes (SSGDs) is reported. Single‐nanowire SSGD device measurements demonstrate a significant dependence of diode current and polarity on gate potential, where the diode polarity reverses at a gate potential of ≈−1 V under specific grounding conditions. Finite‐element modeling reproduces the experimental results and reveals that the gate potential—in combination with the morphology and dopant profile—produces an asymmetric potential along the nanowire axis that changes asymmetrically with axial bias, altering the effective conductive channel within the nanowire to yield diode behavior. The self‐switching effect is retained in two‐terminal SSGD devices, and modeling demonstrates that both three‐terminal and two‐terminal devices support rectification through THz frequencies. The results reveal a new mechanism of operation for nanowire‐based GDs and characterize a new type of self‐switching diode with reconfigurable polarity.

Electric apparatus and materials. Electric circuits. Electric networks, Physics
arXiv Open Access 2024
Non-intrusive data-driven model order reduction for circuits based on Hammerstein architectures

Joshua Hanson, Paul Kuberry, Biliana Paskaleva et al.

We demonstrate that system identification techniques can provide a basis for effective, non-intrusive model order reduction (MOR) for common circuits that are key building blocks in microelectronics. Our approach is motivated by the practical operation of these circuits and utilizes a canonical Hammerstein architecture. To demonstrate the approach we develop parsimonious Hammerstein models for a nonlinear CMOS differential amplifier and an operational amplifier circuit. We train these models on a combination of direct current (DC) and transient Spice circuit simulation data using a novel sequential strategy to identify their static nonlinear and linear dynamical parts. Simulation results show that the Hammerstein model is an effective surrogate for for these types of circuits that accurately and efficiently reproduces their behavior over a wide range of operating points and input frequencies.

en eess.SY, cs.LG
arXiv Open Access 2024
Electric Space-time Translation and Floquet-Bloch Wavefunction

Chenhang Ke, Kun Yang, Congjun Wu

As for the study of Landau level wavefunctions for the quantum Hall effect, the magnetic Bloch wavefunctions based on the magnetic translation symmetry have been extensively investigated in the past few decades. In this article, the electric Floquet-Bloch wavefunctions based on the electric translation symmetry are studied as well as the momentum-frequency Brillouin zone, which is applied to the problem of one dimensional tight-binding model under an external electric field. The spectrum of electric Floquet-Bloch states can be generated by the projective representation of electric translation group, and the topological properties of these states are investigated.

en cond-mat.mes-hall, cond-mat.str-el
arXiv Open Access 2024
Quantum Synchronization in Nonconservative Electrical Circuits with Kirchhoff-Heisenberg Equations

Matteo Mariantoni, Noah Gorgichuk

We investigate quantum synchronization phenomena in electrical circuits that incorporate specifically designed nonconservative elements. A dissipative theory of classical and quantized electrical circuits is developed based on the Rayleigh dissipation function. The introduction of this framework enables the formulation of a generalized version of classical Poisson brackets, which are termed Poisson-Rayleigh brackets. By using these brackets, we are able to derive the equations of motion for a given circuit. Remarkably, these equations are found to correspond to Kirchhoff's current laws when Kirchhoff's voltage laws are employed to impose topological constraints, and vice versa. In the quantum setting, the equations of motion are referred to as the Kirchhoff-Heisenberg equations, as they represent Kirchhoff's laws within the Heisenberg picture. These Kirchhoff-Heisenberg equations, serving as the native equations for an electrical circuit, can be used in place of the more abstract master equations in Lindblad form. To validate our theoretical framework, we examine three distinct circuits. The first circuit consists of two resonators coupled via a nonconservative element. The second circuit extends the first to incorporate weakly nonlinear resonators, such as transmons. Lastly, we investigate a circuit involving two resonators connected through an inductor in series with a resistor. This last circuit, which incidentally represents a realistic implementation, allows for the study of a singular system, where the absence of a coordinate leads to an ill-defined system of Hamilton's equations. To analyze such a pathological circuit, we introduce the concept of auxiliary circuit element. After resolving the singularity, we demonstrate that this element can be effectively eliminated at the conclusion of the analysis, recuperating the original circuit.

en quant-ph, cond-mat.other

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