This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋o...
详细信息
This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) ...
详细信息
Theoretical descriptions of the non-equilibrium dynamics of quantum many-body systems essentially employ either (i) explicit treatments, relying on the truncation of the expansion of the many-body wave function, (ii) compressed representations of the many-body wave function, or (iii) evolution of an effective (downfolded) representation through Green's functions. In this work, we select representative cases of each of the methods and address how these complementary approaches capture the dynamics driven by intense field perturbations to non-equilibrium states. Under strong driving, the systems are characterized by strong entanglement of the single-particle density matrix and natural populations approaching those of a strongly interacting equilibrium system. We generate a representative set of results that are numerically exact and form a basis for a critical comparison of the distinct families of methods. We demonstrate that the compressed formulation based on similarity-transformed Hamiltonians (coupled-cluster approach) is practically exact in weak fields and, hence, weakly or moderately correlated systems. Coupled cluster, however, struggles for strong driving fields, under which the system exhibits strongly correlated behavior, as measured by the von Neumann entropy of the single-particle density matrix. The dynamics predicted by Green's functions in the (widely popular) GW approximation are less accurate, but improve significantly upon the mean-field results in the strongly driven regime.
An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal ...
详细信息
An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.
We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging pow...
详细信息
We investigate the charging dynamics of Sachdev-Ye-Kitaev (SYK) models as quantum batteries, highlighting their capacity to achieve quantum charging advantages. By analytically deriving the scaling of the charging power in SYK batteries, we identify the two key mechanisms underlying this advantage: the use of operators scaling extensively with system size N and the facilitation of operator delocalization by specific graph structures. A graph-theoretic framework is introduced in which the charging process is recast as a random walk on a graph, enabling a quantitative analysis of operator spreading. Our results establish rigorous conditions for the quantum advantage in SYK batteries and extend these insights to graph-based SYK models, revealing broader implications for energy storage and quantum dynamics. This work opens avenues for leveraging quantum chaos and complex network structures in optimizing energy transfer processes.
In this paper,we study the Cauchy problem for the nonlinear Schrodinger equations with Coulomb potential i■_(t)u+△u+k/|x|u=λ/|u|^(p-l)u with 10,and the scattering theory when the Coulomb potential is repulsive,i.e....
详细信息
In this paper,we study the Cauchy problem for the nonlinear Schrodinger equations with Coulomb potential i■_(t)u+△u+k/|x|u=λ/|u|^(p-l)u with 10,and the scattering theory when the Coulomb potential is repulsive,i.e.,when K≤*** argument is based on the newlyestablished interaction Morawetz-type inequalities and the equivalence of Sobolev norms for the Laplacian operator with the Coulomb potential.
The Thermal expansion,Hugoniot state and 300 K isotherm of sodium have been calculated on the basis of:(i)the accurate calculations of 0 K total energies with the full-potential linearized augmented plane wave method ...
详细信息
The Thermal expansion,Hugoniot state and 300 K isotherm of sodium have been calculated on the basis of:(i)the accurate calculations of 0 K total energies with the full-potential linearized augmented plane wave method within the generalized gradient approximation to exchange-correlational functional and(ii)the newly developed classical mean-field statistics where both the cold and thermal parts of the Helmholtz free-energy are entirely derived from the 0 K total energy.A quite satisfactory agreement between calculation and experiment has been *** approach does not invoke any empirical parameter,which has long been a desirability on the field of material science.
The isotope shifts and hyperfine structures of seven optical transitions for all seven stable isotopes of Nd II were measured by using collinear fast-ion-beam laser *** nuclear parameterλwas obtained from the measure...
详细信息
The isotope shifts and hyperfine structures of seven optical transitions for all seven stable isotopes of Nd II were measured by using collinear fast-ion-beam laser *** nuclear parameterλwas obtained from the measured optical isotope shifts for all seven stable isotopes with improved ***λvalues were analysed by using the Fermi distribution for the nuclear charge *** values of δ,δand δwere determined.
Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale...
详细信息
Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale attention feature fusion medical image classification network(HMAC-Net),which effectively combines global features and local *** network framework consists of three parallel layers:The global feature extraction layer,the local feature extraction layer,and the multi-scale feature fusion layer.A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information *** the local feature extraction layer,a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent *** the multi-scale feature fusion layer,a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation *** double-branch iterative multi-scale classification block is used to improve the classification *** the brain glioma risk grading dataset,the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation *** the dataset of skin cancer classification,the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.
Using Bohmlan trajectory （151） method, we investigate the dynamic interference in nlgn-orcter narmonlc generauon from diatomic molecular ions. It is demonstrated that the main characteristics of the molecular harmon...
详细信息
Using Bohmlan trajectory （151） method, we investigate the dynamic interference in nlgn-orcter narmonlc generauon from diatomic molecular ions. It is demonstrated that the main characteristics of the molecular harmonic spectrum can be well reproduced by only two BTs which are located at the two ions. This haiapens because these two localized trajectories can receive and store the whole collision information coming from all of the other re-collision trajectories. Therefore, the amplitudes and frequencies of these two trajectories represent the intensity and frequency distribution of the harmonic generation. Moreover, the interference between these two trajectories shows a dip in the harmonic spectrum, which reveals the molecular structure information.
暂无评论