In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.
{"title":"Coherent Phase States in the Coordinate and Wigner Representations","authors":"Miguel Citeli de Freitas, V. Dodonov","doi":"10.3390/quantum4040036","DOIUrl":"https://doi.org/10.3390/quantum4040036","url":null,"abstract":"In this paper, we numerically study the coordinate wave functions and the Wigner functions of the coherent phase states (CPS), paying particular attention to their differences from the standard (Klauder–Glauber–Sudarshan) coherent states, especially in the case of the high mean values of the number operator. In this case, the CPS can possess a strong coordinate (or momentum) squeezing, which is roughly twice weaker than for the vacuum squeezed states. The Robertson–Schrödinger invariant uncertainty product in the CPS logarithmically increases with the mean value of the number operator (whereas it is constant for the standard coherent states). Some measures of the (non)Gaussianity of CPS are considered.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43709475","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.
{"title":"Some Classical Models of Particles and Quantum Gauge Theories","authors":"A. Akhmeteli","doi":"10.3390/quantum4040035","DOIUrl":"https://doi.org/10.3390/quantum4040035","url":null,"abstract":"The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47506686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron–hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig–Hughes–Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of 2π, (b) the integer multiplier of π, and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand.
{"title":"Topological Properties of the 2D 2-Band System with Generalized W-Shaped Band Inversion","authors":"Z. Rukelj, D. Radić","doi":"10.3390/quantum4040034","DOIUrl":"https://doi.org/10.3390/quantum4040034","url":null,"abstract":"We report the topological properties, in terms of the Berry phase, of the 2D noninteracting system with electron–hole band inversion, described by the two-band generalized analogue of the low-energy Bernevig–Hughes–Zhang Hamiltonian, yielding the W-shaped energy bands in the form of two intersecting cones with the gap along the closed continuous loop. We identify the range of parameters where the Berry phase attains qualitatively different values: (a) the integer multiplier of 2π, (b) the integer multiplier of π, and (c) the nontrivial value between the latter two, which depends on the system parameters. The system thus exhibits the anomalous quantum Hall effect associated with the nontrivial geometric phase, which is presumably tunable through the choice of parameters at hand.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45757440","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The quantization of games expand the players strategy space, allowing the emergence of more equilibriums. However, finding these equilibriums is difficult, especially if players are allowed to use mixed strategies. The size of the exploration space expands so much for quantum games that makes far harder to find the player’s best strategy. In this work, we propose a method to learn and visualize mixed quantum strategies and compare them with their classical counterpart. In our model, players do not know in advance which game they are playing (pay-off matrix) neither the action selected nor the reward obtained by their competitors at each step, they only learn from an individual feedback reward signal. In addition, we study both the influence of entanglement and noise on the performance of various quantum games.
{"title":"Learning Mixed Strategies in Quantum Games with Imperfect Information","authors":"Agustin Silva, O. G. Zabaleta, C. Arizmendi","doi":"10.3390/quantum4040033","DOIUrl":"https://doi.org/10.3390/quantum4040033","url":null,"abstract":"The quantization of games expand the players strategy space, allowing the emergence of more equilibriums. However, finding these equilibriums is difficult, especially if players are allowed to use mixed strategies. The size of the exploration space expands so much for quantum games that makes far harder to find the player’s best strategy. In this work, we propose a method to learn and visualize mixed quantum strategies and compare them with their classical counterpart. In our model, players do not know in advance which game they are playing (pay-off matrix) neither the action selected nor the reward obtained by their competitors at each step, they only learn from an individual feedback reward signal. In addition, we study both the influence of entanglement and noise on the performance of various quantum games.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41934574","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s. The Schrödinger–Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism of how extended wave functions collapse on solitons. The gravity-related stochastic Schrödinger equation (1989) provides the spontaneous collapse, but the resulting solitons undergo a tiny diffusion, leading to an inconvenient steady increase in the kinetic energy. We propose the stochastic Schrödinger–Newton equation, which contains the above two gravity-related modifications together. Then, the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons, which perform inertial motion without momentum diffusion: conservation of momentum and energy is restored.
{"title":"Schrödinger–Newton Equation with Spontaneous Wave Function Collapse","authors":"L. Di'osi","doi":"10.3390/quantum4040041","DOIUrl":"https://doi.org/10.3390/quantum4040041","url":null,"abstract":"Based on the assumption that the standard Schrödinger equation becomes gravitationally modified for massive macroscopic objects, two independent proposals have survived from the 1980s. The Schrödinger–Newton equation (1984) provides well-localized solitons for free macro-objects but lacks the mechanism of how extended wave functions collapse on solitons. The gravity-related stochastic Schrödinger equation (1989) provides the spontaneous collapse, but the resulting solitons undergo a tiny diffusion, leading to an inconvenient steady increase in the kinetic energy. We propose the stochastic Schrödinger–Newton equation, which contains the above two gravity-related modifications together. Then, the wave functions of free macroscopic bodies will gradually and stochastically collapse to solitons, which perform inertial motion without momentum diffusion: conservation of momentum and energy is restored.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48341796","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer—a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons.
{"title":"Effect of a Moving Mirror on the Free Fall of a Quantum Particle in a Homogeneous Gravitational Field","authors":"J. Allam, A. Matzkin","doi":"10.3390/quantum5010001","DOIUrl":"https://doi.org/10.3390/quantum5010001","url":null,"abstract":"We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer—a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49569495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The T=0 excitation spectra of the antiferromagnetic (J>0) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for Δ=cos(π/n), n=3,4 and 5. The number of unknown functions is n−1 for Δ=cos(π/n) and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of c=1. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The “impurity” is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green’s function correctly.
{"title":"Excitation Spectra and Edge Singularities in the One-Dimensional Anisotropic Heisenberg Model for Δ = cos(π/n), n = 3,4,5","authors":"P. Schlottmann","doi":"10.3390/quantum4040032","DOIUrl":"https://doi.org/10.3390/quantum4040032","url":null,"abstract":"The T=0 excitation spectra of the antiferromagnetic (J>0) anisotropic Heisenberg chain of spins 1/2 are studied using the Bethe Ansatz equations for Δ=cos(π/n), n=3,4 and 5. The number of unknown functions is n−1 for Δ=cos(π/n) and can be solved numerically for a finite external field. The low-energy excitations form a Luttinger liquid parametrized by a conformal field theory with conformal charge of c=1. For higher energy excitations, the spectral functions display deviations from the Luttinger behavior arising from the curvature in the dispersion. Adding a corrective term of the form of a mobile impurity coupled to the Luttinger liquid modes corrects this difference. The “impurity” is an irrelevant operator, which if treated non-perturbatively, yields the threshold singularities in the one-spinwave particle and hole Green’s function correctly.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44289484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.
{"title":"Quantum-Inspired Classification Based on Voronoi Tessellation and Pretty-Good Measurements","authors":"R. Leporini, D. Pastorello","doi":"10.3390/quantum4040031","DOIUrl":"https://doi.org/10.3390/quantum4040031","url":null,"abstract":"In quantum machine learning, feature vectors are encoded into quantum states. Measurements for the discrimination of states are useful tools for classification problems. Classification algorithms inspired by quantum state discrimination have recently been implemented on classical computers. We present a local approach combining Vonoroi-type tessellation of a training set with pretty-good measurements for quantum state discrimination.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69807437","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Rietman, L. Schuum, Ayush Salik, M. Askenazi, H. Siegelmann
Stephen Wolfram (2002) proposed the concept of computational equivalence, which implies that almost any dynamical system can be considered as a computation, including programmable matter and nonlinear materials such as, so called, quantum matter. Memristors are often used in building and evaluating hardware neural networks. Ukil (2011) demonstrated a theoretical relationship between piezoelectrical materials and memristors. We review that work as a necessary background prior to our work on exploring a piezoelectric material for neural network computation. Our method consisted of using a cubic block of unpoled lead zirconate titanate (PZT) ceramic, to which we have attached wires for programming the PZT as a programmable substrate. We then, by means of pulse trains, constructed on-the-fly internal patterns of regions of aligned polarization and unaligned, or disordered regions. These dynamic patterns come about through constructive and destructive interference and may be exploited as a type of reservoir network. Using MNIST data we demonstrate a learning machine.
Stephen Wolfram(2002)提出了计算等效的概念，这意味着几乎任何动力系统都可以被认为是一种计算，包括可编程物质和非线性材料，如所谓的量子物质。忆阻器常用于硬件神经网络的构建和评估。Ukil(2011)证明了压电材料和忆阻器之间的理论关系。在我们探索用于神经网络计算的压电材料之前，我们回顾了这项工作作为必要的背景。我们的方法包括使用立方块的未极化锆钛酸铅(PZT)陶瓷，我们在其上附加了用于编程PZT的电线作为可编程基板。然后，我们通过脉冲序列，构建了对准极化区域和未对准或无序区域的动态内部模式。这些动态模式是通过建设性和破坏性干扰产生的，可以作为一种油藏网络进行开发。使用MNIST数据，我们演示了一个学习机。
{"title":"Machine Learning with Quantum Matter: An Example Using Lead Zirconate Titanate","authors":"E. Rietman, L. Schuum, Ayush Salik, M. Askenazi, H. Siegelmann","doi":"10.3390/quantum4040030","DOIUrl":"https://doi.org/10.3390/quantum4040030","url":null,"abstract":"Stephen Wolfram (2002) proposed the concept of computational equivalence, which implies that almost any dynamical system can be considered as a computation, including programmable matter and nonlinear materials such as, so called, quantum matter. Memristors are often used in building and evaluating hardware neural networks. Ukil (2011) demonstrated a theoretical relationship between piezoelectrical materials and memristors. We review that work as a necessary background prior to our work on exploring a piezoelectric material for neural network computation. Our method consisted of using a cubic block of unpoled lead zirconate titanate (PZT) ceramic, to which we have attached wires for programming the PZT as a programmable substrate. We then, by means of pulse trains, constructed on-the-fly internal patterns of regions of aligned polarization and unaligned, or disordered regions. These dynamic patterns come about through constructive and destructive interference and may be exploited as a type of reservoir network. Using MNIST data we demonstrate a learning machine.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42056230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation ∼md2 in the latter case, with m mass, d separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as m in place of the naive expectation m. In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Diósi and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when m becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine.
{"title":"Conditions for Graviton Emission in the Recombination of a Delocalized Mass","authors":"A. Pesci","doi":"10.3390/quantum5020028","DOIUrl":"https://doi.org/10.3390/quantum5020028","url":null,"abstract":"In a known gedanken experiment, a delocalized mass is recombined while the gravitational field sourced by it is probed by another (distant) particle; in it, this is used to explore a possible tension between complementarity and causality in case the gravitational field entangles with the superposed locations, a proposed resolution being graviton emission from quadrupole moments. Here, we focus on the delocalized particle (forgetting about the probe and the gedanken experiment) and explore the conditions (in terms of mass, separation, and recombination time) for graviton emission. Through this, we find that the variations of quadrupole moments in the recombination are generically greatly enhanced if the field is entangled compared to if it is sourced instead by the energy momentum expectation value on the delocalized state (moment variation ∼md2 in the latter case, with m mass, d separation). In addition, we obtain the (upper) limit recombination time for graviton emission growing as m in place of the naive expectation m. In this, the Planck mass acts as threshold mass (huge, for delocalized objects): no graviton emission is possible below it, however fast the recombination occurs. If this is compared with the decay times foreseen in the collapse models of Diósi and Penrose (in their basic form), one finds that no (quadrupole) graviton emission from recombination is possible in them. Indeed, right when m becomes large enough to allow for emission, it also becomes too large for the superposition to survive collapse long enough to recombine.","PeriodicalId":34124,"journal":{"name":"Quantum Reports","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49625498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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