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[en] For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion collisional timescales for cross-field multiple-species transport, the maximum-entropy state is instead given by the classic impurity pinch relation. The maximum-entropy derivation, unlike previous approaches, does not rely on the details of the collision operator or the dynamics of the system, only on the presence of certain conservation properties.
[en] Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g_1"2/2(ψ̄ψ)"2+g_2"2/2(Φ̄Φ)"2+g_3"2(ψ̄ψ)(Φ̄Φ) as well as vector–vector interactions g_1"2/2(ψ̄γμψ)(ψ̄γμψ)+g_2"2/2(Φ̄γμΦ)(Φ̄γμΦ)+g_3"2(ψ̄γμψ)(Φ̄γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e"–"i"ω"1"tR_1cosθ,R_1sinθφ=e"–"i"ω"2"tR_2cosη,R_2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g_3"2/g"2_2 and g_3"2/g_1"2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.
[en] In this work, we obtain the exact one-spin intrinsic localized excitation in an anisotropic Heisenberg ferromagnetic spin chain in a constant/variable external magnetic field with Gilbert damping included. We also point out how an appropriate magnitude spin current term in a spin transfer nano-oscillator (STNO) can stabilize the tendency towards damping. Further, we show how this excitation can be sustained in a recently suggested PT -symmetric magnetic nanostructure. We also briefly consider more general spin excitations.
[en] Highlights: • We introduce the concept of symmetry for a quantum Boltzmann machine and develop a group theory to describe the symmetry. We also answer what the symmetry implies for a quantum Boltzmann machine. • For the Boltzmann machines built on qubits, we propose a systematic procedure to construct the group and develop a numerical algorithm to verify the completeness of our construction. • We give an idea of how does the symmetry group of a quantum Boltzmann machine applies in simulating physical data. Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine and develop a group theory to describe the symmetry. This symmetry implies not only that all the target states related with the symmetry transformations are equivalent, but also that for a given target state all the optimal solutions related with the symmetry transformations that keep the target state invariant are equivalent. For the Boltzmann machines built on qubits, we propose a systematic procedure to construct the group, and develop a numerical algorithm to verify the completeness of our construction.
[en] Highlights: • DS in SRR based metamaterials secured under higher order nonlinearity and randomness. • Model mimics experimental situation, hence can reduce gap of theory and experiment. • Influence of TPA on DS may lead to design metamaterial based imaging devices. • DS found in presence of diffusion, sensing devices can be made using this property. Compound dissipative soliton (DS) is obtained theoretically in Split Ring Resonator based metamaterial having higher order nonlinearities, multi-photon absorption and diffusion. Effects of both the multi-photon absorption and diffusion on the DS are found to be detrimental however can be compensated by a suitable external gain to stabilize the DS. The interaction dynamics of two DSs is studied for different phase difference and initial separation. The phase controlled soliton switching is demonstrated. Notably, a weak solitonic beam is demonstrated to control a strong one. The DSs are robust against the randomness of the metamaterial. The outcome of this investigation may be useful to design experiments that employ DS in higher order nonlinear metamaterials.
[en] Highlights: • Quantum algorithm for measuring out of time ordered correlators giving exponential speed up. • Efficient quantum algorithm to estimate gate fidelities. • Efficient quantum circuit to estimate eigenvalue spectrum of OTOCs. Out-of-time-ordered correlators (OTOC) are a quantifier of quantum information scrambling and are useful in characterizing quantum chaos. We propose an efficient quantum algorithm to measure OTOCs that provides an exponential speed-up over the best known classical algorithm provided the OTOC operator to be estimated admits an efficient gate decomposition. We also discuss a scheme to obtain information about the eigenvalue spectrum and the spectral density of OTOCs as well as an efficient algorithm to estimate gate fidelities.
[en] Highlights: • The (2+1)-dimensional Bogoyavlenskii's breaking soliton (BBS) model. • Bilinear form of the model by using the Hirota bilinear approach. • The collision among lump, periodic and kink soliton solutions are investigated. • Fission properties of the lump and periodic waves have been also observed. • Physical natures of the results have been analyzed and depicted graphically. In this manuscript, the (2+1)-dimensional Bogoyavlenskii's breaking soliton (BBS) model is considered. At-first, we reduce the model into its bilinear form using the Hirota bilinear approach. We then analytically construct lump waves and collision of lump with periodic waves via the Hirota scheme. We also present collision between lump wave and single-, double-kink soliton solutions, and the collision among lump, periodic and single-, double-kink soliton solutions of the model. In addition, we explain the fission properties of the collisions. It is noticed that collision of lump-kink waves split into double kinky-lump waves and gradually increases the number of such waves as the increase of λ, which was not found in the previous literature. Finally, we graphically present the nature of the collision solutions of the model in 3D and contour plots. The derived such wave solutions may have much more important for controlling unpredictable harmful waves arises in nature.
[en] Highlights: • Graph states generated by operator of evolution with Ising Hamiltonian are examined. • Entanglement of a spin with other spins in graph state is found on quantum computer. • The results of quantum calculations are in good agreement with the theoretical ones. • Entanglement of graph states is related with properties of the corresponding graphs. We consider graph states generated by operator of evolution with Ising Hamiltonian. The geometric measure of entanglement of a spin with other spins in the graph state is obtained analytically and quantified on IBM's quantum computer, IBM Q Valencia. The results of quantum calculations are in good agreement with the theoretical ones. We conclude that the geometric measure of entanglement of a spin with other spins in the graph state is related with degree of vertex representing the spin in the corresponding graph.
[en] Highlights: • Laser Wake Field Acceleration is studied in a colliding target with colliding laser beam setup. • The setup is advantageous for laser driven fusion. • Non-thermal ignition rate can be higher than in usual configurations for laser fusion. • Benefits of embedding resonant nano-antennas is discussed. Recently NAno-Plasmonic, Laser Inertial Fusion Experiments (NAPLIFE) were proposed, as an improved way to achieve laser driven fusion. The improvement is the combination of two basic research discoveries: (i) the possibility of detonations on space-time hyper-surfaces with time-like normal (i.e. simultaneous detonation in a whole volume) and (ii) to increase this volume to the whole target, by regulating the laser light absorption using nanoshells or nanorods as antennas. These principles can be realized in a one dimensional configuration, in the simplest way with two opposing laser beams as in particle colliders. Such, opposing laser beam experiments were also performed recently. Here we study the consequences of the Laser Wake Field Acceleration (LWFA) if we experience it in a colliding laser beam set-up. These studies can be applied to laser driven fusion, but also to other rapid phase transition, combustion, or ignition studies in other materials.