Annalen der Physik最新文献

{"title":"Magnon Blockade in a Hybrid Magnon-Superconducting Qubit System","authors":"Xinxin Zheng,&nbsp;Mei-Rong Wei,&nbsp;Qi Guo","doi":"10.1002/andp.70185","DOIUrl":"10.1002/andp.70185","url":null,"abstract":"<div>\u0000 \u0000 <p>We propose a scheme to realize magnon blockade in a hybrid system composed of a transmon-type superconducting qubit directly coupled to the magnon mode of a single-crystalline yttrium-iron-garnet sphere. By applying two-tone driving to the qubit, we engineer an effective Hamiltonian for the magnon mode including both single-magnon and two-magnon interaction. Due to the destructive interference between two transition paths, the two-magnon excitation is suppressed, and thus the unconventional magnon blockade can be achieved. We also demonstrate that the intrinsic anharmonicity of the qubit can be transferred to the magnon mode through their coherent hybridization, but this anharmonicity has almost no influence on the blockade effect. Through solving the second-order correlation function analytically and numerically, we show that the scheme can be realized under experimentally feasible conditions and remains robust against system dissipations and environment temperature. Therefore, the presented work provides a viable path toward generating single-magnon sources and advancing quantum information processing with magnonic platforms.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Issue Information: Ann. Phys. 4/2026","authors":"","doi":"10.1002/andp.70191","DOIUrl":"10.1002/andp.70191","url":null,"abstract":"","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/andp.70191","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Casimir Effect in ModMax Electrodynamics: Background Magnetic Field Dependence","authors":"Sharmistha Modak,&nbsp;Francesco Sorge","doi":"10.1002/andp.70188","DOIUrl":"10.1002/andp.70188","url":null,"abstract":"<div>\u0000 \u0000 <p>We study the corrections to the vacuum energy density and the corresponding force between the plates in a Casimir apparatus in the framework of the ModMax model. We linearize the theory around a background magnetic field <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mover>\u0000 <mi>B</mi>\u0000 <mo>⃗</mo>\u0000 </mover>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$vec{B}_0$</annotation>\u0000 </semantics></math> fixed along an arbitrary direction with respect to the z axis, taken perpendicular to the plates of the Casimir cavity. We find the mode dispersion relations of the confined electromagnetic field, from which we derive the Casimir (vacuum) energy density and the attractive force between the plates. Our results reveal that, even though the energy density and the attractive force are independent of the magnitude of the background magnetic field <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>B</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <annotation>$B_0$</annotation>\u0000 </semantics></math> (due to conformal invariance), they do depend on its direction. These corrections generalize the results found in a previous study, [Phys. Rev. D 110, 116006 (2024)], where the background magnetic field was only considered either parallel or perpendicular to the <span></span><math>\u0000 <semantics>\u0000 <mi>z</mi>\u0000 <annotation>$z$</annotation>\u0000 </semantics></math> axis. We compare the results with those of linear Maxwell electrodynamics for various directions of the background magnetic field. We investigate the possibility of superluminal motion of the electromagnetic field modes propagating inside the Casimir cavity in the framework of the nonlinear ModMax model.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Phase-Sensitive Superposition of Quantum States","authors":"Xiaotong Wang,&nbsp;Shunlong Luo,&nbsp;Yue Zhang","doi":"10.1002/andp.70170","DOIUrl":"10.1002/andp.70170","url":null,"abstract":"<div>\u0000 \u0000 <p>Although the principle of superposition lies at the heart of quantum mechanics and is the root of almost all quantum phenomena such as coherence and entanglement, its quantification, except for that related to the resource theory of coherence and interference, remains relatively less studied. In this work, we address quantification of superposition from an information-theoretic perspective. We introduce a family of quantifiers of superposition, the phase-sensitive superposition, by taking into account the phases of amplitudes in superposition of fixed basis states (e.g., computational basis states). We establish a conservation relation for the phase-sensitive superposition, which is a kind of complementary relation and is reminiscent of wave-particle duality. We evaluate explicitly the second moment of phase-sensitive superposition and show that it is intrinsically related to the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>l</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$l^2$</annotation>\u0000 </semantics></math>-norm coherence. We characterize the dephasing channel induced by the maximally superposed states. We investigate the minimal and maximal superpositions, reveal their basic properties, and illustrate them through various examples. We further explore the dynamics of superposition in the Grover search algorithm, and demonstrate a complementary relation between superposition and success probability of the search algorithm. These results and quantifiers offer tools for analyzing structural features and implications of quantum superposition.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Spatial Modulation Suppression Concept for Multi-Pump Interference Effect Mitigation in Stimulated Brillouin Amplification Beam Combining","authors":"Can Cui,&nbsp;Yue Wang,&nbsp;Yongkang Dong,&nbsp;Yulei Wang,&nbsp;Zhiwei Lü","doi":"10.1002/andp.202500611","DOIUrl":"10.1002/andp.202500611","url":null,"abstract":"<div>\u0000 \u0000 <p>High pulse energy, high average power lasers with low spatial modulation have attracted many advanced applications in scientific research, and beam combination through stimulated Brillouin amplification (SBA) offers the potential for energy scaling with repetitive operation. However, attaining low-modulation beam combining output remains a significant challenge due to the near-field interference induced by the overlapping configuration of multiple pump beams with identical frequencies during the SBA process. Here, the method for reducing spatial modulation intensity via optimizing the structure parameters in the SBA beam combination system is proposed. In the proof-of-principle nine-channel SBA beam combination experiment, a low-modulation near-field output with an <i>M</i>_T value of 1.088 was demonstrated through adjustment, which is nearly identical to the <i>M</i>_T value of the incident Stokes seed. This work introduces a promising methodology for achieving high-pulse energy and high-average power lasers via SBA beam combining techniques, ensuring exceptional beam quality, which have profound implications for petawatt laser pumping, material processing, and laser-matter interaction.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Self-Consistent Theoretical Framework for Third-Order Nonlinear Susceptibility in CdSe/ZnS–MOF Quantum Dot Composites","authors":"Jingxu Wu,&nbsp;Yifan Yang,&nbsp;Jie Shi,&nbsp;Yuwei Yin,&nbsp;Yifan He,&nbsp;Chenjia Li","doi":"10.1002/andp.202500587","DOIUrl":"10.1002/andp.202500587","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This work presents a fully theoretical and self-consistent framework for calculating the third-order nonlinear susceptibility &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$chi ^{(3)}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of CdSe/ZnS–MOF composite quantum dots. The approach unifies finite-potential quantum confinement, the Liouville-von Neumann density matrix expansion to third order, and effective-medium electrodynamics (Maxwell–Garnett and Bruggeman) within a single Hamiltonian-based model, requiring no empirical fitting. Electron-hole quantized states and dipole matrix elements are obtained under the effective-mass approximation with BenDaniel–Duke boundary conditions; closed analytic forms for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$chi ^{(3)}(omega)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (including Lorentzian/Voigt broadening) follow from the response expansion. Homogenization yields macroscopic scaling laws &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mi&gt;eff&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;∼&lt;/mo&gt;\u0000 &lt;mi&gt;ϕ&lt;/mi&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;ω&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;χ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Dynamic Multifunctional Metasurface for Terahertz Holography, Vortex, and Grayscale Imaging","authors":"Dingkun Chen,&nbsp;Jianliang Zhuo,&nbsp;Zhengyong Song","doi":"10.1002/andp.70165","DOIUrl":"10.1002/andp.70165","url":null,"abstract":"<div>\u0000 \u0000 <p>Metasurfaces offer unprecedented capabilities for manipulating electromagnetic wave, but simultaneous and independent generation of diverse functionalities like holography, orbital angular momentum (OAM), and grayscale imaging (GI) within a single platform remains a challenge. Here, we demonstrate a terahertz bilayer metasurface. It leverages insulator-metal phase transition of vanadium dioxide (VO₂) for dynamic control. The metasurface integrates spin-decoupled theory and Malus’ law to achieve multifunctional wavefront engineering. As VO₂ is metallic, a vortex beam (VB) with topological charge (TC) of <i>l</i> = 1 is gained under left-handed circular polarization (LCP) incidence, while a distinct hologram image (HI) A is obtained under right-handed circular polarization (RCP) incidence. Concurrently, GI 6 is observed in near field under x-polarized incidence. As VO₂ is insulating, it dynamically reconfigures metasurface's response. HI H is generated in LCP channel, and VB with TC = −2 is formed in RCP channel. Meanwhile, GI 3 with x polarization appears in near field. Through rigorous numerical simulations, we validate independent control and high-quality performance of each channel. This work demonstrates a versatile platform for achieving complex and switchable optical operations.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"A Three-Party Lightweight Quantum Key Distribution Protocol in a Restricted Quantum Environment","authors":"Mustapha Anis Younes,&nbsp;Sofia Zebboudj,&nbsp;Abdelhakim Gharbi","doi":"10.1002/andp.202500502","DOIUrl":"10.1002/andp.202500502","url":null,"abstract":"<div>\u0000 \u0000 <p>This study proposes a new lightweight quantum key distribution (LQKD) protocol based on the four-particle cluster state within a quantum-restricted environment. The protocol enables a quantum-capable user to simultaneously establish two separate secret keys with two “classical” users, who are limited to performing only the Hadamard operation and measurements in the <span></span><math>\u0000 <semantics>\u0000 <mi>Z</mi>\u0000 <annotation>$Z$</annotation>\u0000 </semantics></math> basis. By adopting a one-way qubit transmission approach, the proposed protocol addresses several limitations of existing semi-quantum key distribution (SQKD) schemes that rely on two-way or circular transmission methods: (1) it eliminates the need for classical participants to be equipped with costly quantum devices to defend against quantum Trojan horse attacks; (2) it reduces the qubit transmission distance; and (3) it achieves higher qubit efficiency. Consequently, the proposed LQKD protocol is both more lightweight and practical than existing SQKD protocols. Furthermore, the security analysis shows that, in the ideal case, the protocol achieves the same level of security as fully quantum protocols. Finally, the study proves the unconditional security of the protocol in the non-ideal case, demonstrating a noise tolerance close to that of the BB84 protocol.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"High-Order Above-Threshold Ionization by Thermal Light","authors":"Dejan B. Milošević,&nbsp;Wilhelm Becker","doi":"10.1002/andp.202500620","DOIUrl":"10.1002/andp.202500620","url":null,"abstract":"<div>\u0000 \u0000 <p>Strong-field ionization by thermal light is studied. Even though thermal light can be considered as completely classical stochastic light, it can also be treated as quantum light in the sense that it can be represented by a superposition of coherent states, similarly as has been done for the bright squeezed vacuum light, for example. Such a distribution over coherent states contains components with an intensity much higher than the average intensity of the thermal light. This increases the ionization probability by many orders of magnitude. For low intensities, in the multiphoton regime, the enhancement is by the factor of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>!</mo>\u0000 </mrow>\u0000 <annotation>$K!$</annotation>\u0000 </semantics></math>, with <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math> the multiphoton order of the process. This result is in agreement with an old experiment [<i>Phys. Rev. Lett</i>. <b>32</b> (1974): 265] in which a similar enhancement factor appears if a multimode laser pulse is used instead of a single-mode pulse. It is also shown that the plateau length in high-order above-threshold ionization by thermal light is extended by an order of magnitude in comparison with that of coherent laser light with the same average intensity.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Microscopic Theory of Pure Dephasing in Particle Plasmons","authors":"Weixiang Ye","doi":"10.1002/andp.70163","DOIUrl":"10.1002/andp.70163","url":null,"abstract":"<div>\u0000 \u0000 <p>Particle plasmons, the collective oscillations of conduction electrons in metal nanoparticles, are central to nanophotonics and quantum technologies. Their quantum coherence is degraded by both energy relaxation and pure dephasing. While the former is well described by classical and semiclassical models, a fundamental microscopic understanding of pure dephasing, which destroys phase coherence without energy exchange, remains elusive. This work establishes a microscopic theory by identifying stochastic resonance frequency fluctuations as the physical origin of pure dephasing in particle plasmons. Starting from a many-body electron Hamiltonian, we map the plasmon onto a quantum harmonic oscillator via collective coordinates and the random phase approximation. We demonstrate that environmental perturbations commuting with the plasmon number operator induce random frequency shifts, leading to phase diffusion. We then microscopically derive contributions from three dominant mechanisms: electron-phonon scattering, defect scattering, and surface roughness scattering. These contributions are unified into a general scaling law that predicts the pure dephasing rate as a function of nanoparticle size and geometry, revealing a crossover between dominant mechanisms. This law provides a microscopic foundation for empirical damping formulas and clarifies the fundamental distinction between energy relaxation and pure dephasing, thereby completing the quantum mechanical picture of plasmon decoherence.</p>\u0000 </div>","PeriodicalId":7896,"journal":{"name":"Annalen der Physik","volume":"538 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147564290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}