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Quantum thermalization and average entropy of a subsystem 子系统的量子热化和平均熵
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-19 DOI: 10.1016/j.physleta.2025.131000
Smitarani Mishra, Shaon Sahoo
{"title":"Quantum thermalization and average entropy of a subsystem","authors":"Smitarani Mishra,&nbsp;Shaon Sahoo","doi":"10.1016/j.physleta.2025.131000","DOIUrl":"10.1016/j.physleta.2025.131000","url":null,"abstract":"<div><div>Page's seminal result on the average von Neumann (VN) entropy does not immediately apply to realistic many-body systems which are restricted to physically relevant smaller subspaces. We investigate here the VN entropy averaged over the pure states in the subspace <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>E</mi></mrow></msub></math></span> corresponding to a narrow energy shell centered at energy <em>E</em>. We find that the average entropy is <span><math><msub><mrow><mover><mrow><mi>S</mi></mrow><mo>‾</mo></mover></mrow><mrow><mn>1</mn></mrow></msub><mo>≃</mo><mi>ln</mi><mo>⁡</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>, where <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> represents first subsystem's effective number of states relevant to the energy scale <em>E</em>. If <span><math><msub><mrow><mi>d</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>=</mo><mi>dim</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>H</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo></math></span> and <em>D</em> (<span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>) is the Hilbert space dimension of the full system (first subsystem), we estimate that <span><math><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≃</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>γ</mi></mrow></msubsup></math></span>, where <span><math><mi>γ</mi><mo>=</mo><mi>ln</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>ln</mi><mo>⁡</mo><mo>(</mo><mi>D</mi><mo>)</mo></math></span> for nonintegrable (chaotic) systems and <span><math><mi>γ</mi><mo>&lt;</mo><mi>ln</mi><mo>⁡</mo><mo>(</mo><msub><mrow><mi>d</mi></mrow><mrow><mi>E</mi></mrow></msub><mo>)</mo><mo>/</mo><mi>ln</mi><mo>⁡</mo><mo>(</mo><mi>D</mi><mo>)</mo></math></span> for integrable systems. This result can be reinterpreted as a volume-law of entropy, where the volume-law coefficient depends on the density-of-states for nonintegrable systems, and remains below the maximal possible value for integrable systems. We numerically analyze a spin model to substantiate our main results.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 131000"},"PeriodicalIF":2.6,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Surpassing the phase noise in continuous-variable quantum key distribution via Gaussian filter 利用高斯滤波器克服连续变量量子密钥分配中的相位噪声
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-19 DOI: 10.1016/j.physleta.2025.130997
Wenqi Jiang , Yijun Wang , Zhengde Tan , Hang Zhang , Ying Guo
{"title":"Surpassing the phase noise in continuous-variable quantum key distribution via Gaussian filter","authors":"Wenqi Jiang ,&nbsp;Yijun Wang ,&nbsp;Zhengde Tan ,&nbsp;Hang Zhang ,&nbsp;Ying Guo","doi":"10.1016/j.physleta.2025.130997","DOIUrl":"10.1016/j.physleta.2025.130997","url":null,"abstract":"<div><div>Continuous-variable quantum key distribution (CV-QKD) protocol based on a local local oscillator (LLO) is able to defend against the attacks caused by transmitted local oscillator (TLO). However, the phase noise produced by measuring limits the transmission distance of the LLO protocol. For improving the performance of LLO protocol, we propose a method applying Gaussian filter for reference phases. In details, Bob applies Gaussian filter on reference phases for reducing phase noise, and then the processed phases are used to compensate the phases between LO pulses and signal pulses. Numerical analysis shows that the reference phase after Gaussian filtering is the closest to the true phase drift according to mean-square error, which are compared with Kalman filter and LSTM. In addition, the proposed scheme in this paper is capable of improving the transmission distance and the secret key rate in LLO CV-QKD system.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130997"},"PeriodicalIF":2.6,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Traveling wave solutions, numerical simulation and phase portraits for the conformable space-time fractional diffusive predator-prey system 适形时空分数扩散捕食-食饵系统的行波解、数值模拟和相位图
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-19 DOI: 10.1016/j.physleta.2025.130995
Zhao Li
{"title":"Traveling wave solutions, numerical simulation and phase portraits for the conformable space-time fractional diffusive predator-prey system","authors":"Zhao Li","doi":"10.1016/j.physleta.2025.130995","DOIUrl":"10.1016/j.physleta.2025.130995","url":null,"abstract":"<div><div>The main purpose of this article is to construct traveling wave solutions for the conformable space-time fractional diffusive predator-prey system by using the improved polynomial probing equation method with rank inhomogeneous. Firstly, the construction process of traveling wave solutions for general nonlinear partial differential equations is described based on the improved polynomial probing equation method with rank inhomogeneous. Secondly, the traveling wave solutions for the conformable space-time fractional diffusive predator-prey system are constructed. Finally, three-dimensional, two-dimensional, and the contour graphs of the traveling wave solutions are plotted using the improved polynomial probing equation method with rank inhomogeneous. Moreover, the planar dynamic behavior of the system is studied, and its planar phase portraits are drawn.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130995"},"PeriodicalIF":2.6,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spin-dependent charge injection induced spin filtering reversal in organic ferromagnet-based spin devices 有机铁磁基自旋器件中自旋相关电荷注入诱导自旋滤波反转
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-19 DOI: 10.1016/j.physleta.2025.130999
Hui Wang , Hongyan Shi , Runsheng Zhai , Zhen Wan , Wenhao Zhang , Wenkai Zhao , Guangping Zhang , Guichao Hu
{"title":"Spin-dependent charge injection induced spin filtering reversal in organic ferromagnet-based spin devices","authors":"Hui Wang ,&nbsp;Hongyan Shi ,&nbsp;Runsheng Zhai ,&nbsp;Zhen Wan ,&nbsp;Wenhao Zhang ,&nbsp;Wenkai Zhao ,&nbsp;Guangping Zhang ,&nbsp;Guichao Hu","doi":"10.1016/j.physleta.2025.130999","DOIUrl":"10.1016/j.physleta.2025.130999","url":null,"abstract":"<div><div>We conduct a detailed model study on the impact of injected spin-polarized charges on the spin polarized transport characteristics of organic ferromagnet-based spin valves. Our results indicate that when spin-down charges, which share the same spin orientation as radicals, are injected, the Hubbard electron-electron interaction significantly enhances the spin splitting of π-electron energy levels within organic ferromagnets. This enhancement leads to an increase in current spin polarization, thereby improving the spin-filtering performance of the device. Conversely, when spin-up charges are injected, the Hubbard electron-electron interaction first diminishes the spin splitting of π-electron energy levels, leading to a degradation in device performance. However, when a large number of spin-up charges are injected, the spin splitting of π-electron energy levels reverses, causing a reversal in the spin-filtering behavior of the device. These findings are anticipated to broaden the application of organic ferromagnets in the realm of spin logic devices.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130999"},"PeriodicalIF":2.6,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Electron and hole energy spectra in a non-concentric spherical core-shell quantum dot under a magnetic field 磁场作用下非同心球形核壳量子点的电子能谱和空穴能谱
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-18 DOI: 10.1016/j.physleta.2025.130996
R. Ya. Leshko , O.V. Leshko , I.V. Bilynskyi , M.V. Kvyk , Ya. Yu. Melnyk , A.O. Ocheretyanyi , M. Yu. Popov
{"title":"Electron and hole energy spectra in a non-concentric spherical core-shell quantum dot under a magnetic field","authors":"R. Ya. Leshko ,&nbsp;O.V. Leshko ,&nbsp;I.V. Bilynskyi ,&nbsp;M.V. Kvyk ,&nbsp;Ya. Yu. Melnyk ,&nbsp;A.O. Ocheretyanyi ,&nbsp;M. Yu. Popov","doi":"10.1016/j.physleta.2025.130996","DOIUrl":"10.1016/j.physleta.2025.130996","url":null,"abstract":"<div><div>This work investigates the influence of both the non-concentricity parameter and magnetic field on the electron and hole energy spectra in a spherical core–shell quantum dot. We analyze how the energies, wave functions, transition energies, and diamagnetic shifts depend on the magnetic field. The magnetic quantum number <em>m</em> degeneracy is lifted by the Zeeman effect and partially by non-concentricity, leading to a reordering of states with <em>m</em> = -1 and <em>m</em> = 0. We also determine the effective optical gap and the diamagnetic susceptibilities of electrons and holes as functions of magnetic field and non-concentricity. The electron susceptibility is found to be three orders of magnitude higher than that of the hole in a GaAs/Al<sub>x</sub>Ga<sub>1−x</sub>As/matrix heterostructure.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"562 ","pages":"Article 130996"},"PeriodicalIF":2.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the higher-dimensional Lax integrable models in shallow water waves 浅水波中的高维Lax可积模型
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-18 DOI: 10.1016/j.physleta.2025.130985
Jian-Gen Liu , Chun-Yan Ji , Yu-Feng Zhang
{"title":"On the higher-dimensional Lax integrable models in shallow water waves","authors":"Jian-Gen Liu ,&nbsp;Chun-Yan Ji ,&nbsp;Yu-Feng Zhang","doi":"10.1016/j.physleta.2025.130985","DOIUrl":"10.1016/j.physleta.2025.130985","url":null,"abstract":"<div><div>The higher-dimensional nonlinear models can theoretically describe more complex and diverse mechanisms of natural phenomena. However, constructing such higher-dimensional models remains a hot topic in nonlinear science. In this article, we derive two new higher-dimensional integrable shallow water waves models: a KdV-type equation and a Boussinesq-Burgers system. Moreover, we obtain the Lax pairs, Lie point symmetry, similarity reductions, optimal system and conservation laws of these models. Additionally, we derive a subsymmetry, a nonlinear transformation and exact solutions for the classical Boussinesq-Burgers system. The results presented in this work provide valuable insights into understanding complex natural phenomena.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130985"},"PeriodicalIF":2.6,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Enhancing sensitivity and selectivity of transformer oil dissolved gas sensor based on TM (Ni, Pd, Rh)-doped PtSe2 monolayer: A DFT study TM (Ni, Pd, Rh)掺杂PtSe2单层提高变压器油溶气传感器灵敏度和选择性的DFT研究
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-17 DOI: 10.1016/j.physleta.2025.130987
Tianyan Jiang, Sheng Xu, Yangxin You, Hao Chen, Maoqiang Bi, Zhipeng Ma
{"title":"Enhancing sensitivity and selectivity of transformer oil dissolved gas sensor based on TM (Ni, Pd, Rh)-doped PtSe2 monolayer: A DFT study","authors":"Tianyan Jiang,&nbsp;Sheng Xu,&nbsp;Yangxin You,&nbsp;Hao Chen,&nbsp;Maoqiang Bi,&nbsp;Zhipeng Ma","doi":"10.1016/j.physleta.2025.130987","DOIUrl":"10.1016/j.physleta.2025.130987","url":null,"abstract":"<div><div>This study employs density functional theory (DFT) to investigate Ni-, Pd-, and Rh-doped PtSe<sub>2</sub> monolayers for detecting transformer fault gases (C<sub>2</sub>H<sub>2</sub>, C<sub>2</sub>H<sub>4</sub>, CH<sub>4</sub>). Through analysis of adsorption energy, band structure, density of states, and charge transfer, we reveal the interaction mechanisms between gas molecules and doped substrates. While pristine PtSe<sub>2</sub> shows weak gas adsorption, transition metal doping significantly enhances both adsorption capacity and conductivity. Specifically, Pd-PtSe<sub>2</sub> demonstrates strong chemical adsorption for C<sub>2</sub>H<sub>2</sub>, while Ni- and Rh-doped systems effectively adsorb C<sub>2</sub>H<sub>4</sub>. The materials exhibit excellent selectivity and reversibility for C<sub>2</sub>H<sub>2</sub>/C<sub>2</sub>H<sub>4</sub> detection, with favorable recovery times and sensitivity. These findings provide theoretical foundations for developing high-performance gas sensors to monitor power equipment conditions, showcasing the potential of modified PtSe<sub>2</sub> monolayers in practical applications.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130987"},"PeriodicalIF":2.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral properties of the ladder-like Josephson junction array 阶梯状约瑟夫森结阵列的光谱特性
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-17 DOI: 10.1016/j.physleta.2025.130983
Daryna Bukatova, Ivan O. Starodub, Yaroslav Zolotaryuk
{"title":"Spectral properties of the ladder-like Josephson junction array","authors":"Daryna Bukatova,&nbsp;Ivan O. Starodub,&nbsp;Yaroslav Zolotaryuk","doi":"10.1016/j.physleta.2025.130983","DOIUrl":"10.1016/j.physleta.2025.130983","url":null,"abstract":"<div><div>In this paper theoretical analysis of the ladder-like multirow array of inductively coupled Josephson junctions is presented. An external dc current is applied at the top to each of the columns of the array and is extracted at the bottom of that column. The density of states of the Josephson plasma waves has a <em>δ</em>-function term due to the flat band and <span><math><mn>3</mn><mi>N</mi><mo>−</mo><mn>2</mn></math></span> singularities where <em>N</em> is the number of rows. The spatial distribution of the amplitudes of the plasmon wave is computed analytically for any given value of the wavenumber <em>q</em>. It is expressed through the orthogonal polynomials that have a recurrence relation similar to the Chebyshev polynomials.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"562 ","pages":"Article 130983"},"PeriodicalIF":2.6,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed-mode oscillations and its mechanism in an axially accelerating beam system 轴向加速束流系统的混模振荡及其机理
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-16 DOI: 10.1016/j.physleta.2025.130978
Yanpeng Li , Denghui Li , Qiong Yang , Biliu Zhou
{"title":"Mixed-mode oscillations and its mechanism in an axially accelerating beam system","authors":"Yanpeng Li ,&nbsp;Denghui Li ,&nbsp;Qiong Yang ,&nbsp;Biliu Zhou","doi":"10.1016/j.physleta.2025.130978","DOIUrl":"10.1016/j.physleta.2025.130978","url":null,"abstract":"<div><div>This paper investigates the complex dynamics of an axially accelerating beam under periodic excitation and reveals two types of Mixed-mode oscillations: the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-type (featuring <em>L</em> large-amplitude oscillations followed by one small-amplitude oscillation) and the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-type (consisting of two sets of <em>L</em> large oscillations each followed by a small oscillation). The former is induced by a saddle-node bifurcation, while the latter arises from a reverse period-doubling bifurcation. Within the chaotic region of the parameter plane, a self-similar shrimp-like structure is identified, where isolated solutions multiply with parameter changes, suggesting possible Devil's staircase emergence. These findings may contribute to the establishment of oscillation mode boundaries in such systems, preventing resonance and excessive vibrations.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130978"},"PeriodicalIF":2.6,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Influence of layered spacer on correlated electrical conductivity of bilayer graphene double layer systems 层状间隔层对双层石墨烯双层体系相关电导率的影响
IF 2.6 3区 物理与天体物理
Physics Letters A Pub Date : 2025-09-16 DOI: 10.1016/j.physleta.2025.130986
Le Thi Kieu Oanh , Nguyen Nhu Tan Lanh , Dang Khanh Linh
{"title":"Influence of layered spacer on correlated electrical conductivity of bilayer graphene double layer systems","authors":"Le Thi Kieu Oanh ,&nbsp;Nguyen Nhu Tan Lanh ,&nbsp;Dang Khanh Linh","doi":"10.1016/j.physleta.2025.130986","DOIUrl":"10.1016/j.physleta.2025.130986","url":null,"abstract":"<div><div>We study the conductivity of the first layer, <span><math><mrow><msub><mi>σ</mi><mn>1</mn></msub><mrow><mo>(</mo><msub><mi>n</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></math></span>, as a function of its electron density <span><math><msub><mi>n</mi><mn>1</mn></msub></math></span> in double-layer bilayer graphene systems, with a particular focus on the effects of correlated charged impurity scattering and an inhomogeneous spacer. Previously, the universal characteristics of conductivity σ(n), considering correlated charged impurity scattering in bilayer graphene, had been calculated by Qiuzi Li et al. Subsequently, we investigated <span><math><mrow><msub><mi>σ</mi><mn>1</mn></msub><mrow><mo>(</mo><msub><mi>n</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></math></span>, considering the correlated charged impurity scattering in the first layer of double-layer bilayer graphene structures. However, in modern materials research, spacers may exhibit multilayered structures. In this manuscript, we show that <span><math><msub><mi>σ</mi><mn>1</mn></msub></math></span> increases with increasing <span><math><msub><mi>n</mi><mn>1</mn></msub></math></span>, dielectric constants <span><math><mrow><msub><mi>ϵ</mi><mn>21</mn></msub><mo>,</mo><mspace></mspace><msub><mi>ϵ</mi><mn>22</mn></msub></mrow></math></span>. We also show that <span><math><msub><mi>σ</mi><mn>1</mn></msub></math></span> decreases with increasing thickness <span><math><mi>w</mi></math></span> of the dielectric layer <span><math><msub><mi>ϵ</mi><mn>22</mn></msub></math></span>, while it increases with the thickness d of the spacer. Finally, our results reveal the connection between the conductivities of bilayer graphene double layers with homogeneous and layered spacers.</div></div>","PeriodicalId":20172,"journal":{"name":"Physics Letters A","volume":"561 ","pages":"Article 130986"},"PeriodicalIF":2.6,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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