The Experts below are selected from a list of 117030 Experts worldwide ranked by ideXlab platform
Yuri Trakhinin - One of the best experts on this subject based on the ideXlab platform.
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Structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics
Zeitschrift für angewandte Mathematik und Physik, 2020Co-Authors: Yuri TrakhininAbstract:We study the structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics (SMHD) in the sense of the local-in-time existence and uniqueness of discontinuous solutions satisfying corresponding jump conditions. The equations of SMHD form a Symmetric hyperbolic System which is formally analogous to the System of 2D compressible elastodynamics for particular nonphysical deformations. Using this analogy and the recent results in [25] for shock waves in 2D compressible elastodynamics, we prove that shock waves in SMHD are structurally stable if and only if the fluid height increases across the shock front. For current-vortex sheets the fluid height is continuous whereas the tangential components of the velocity and the magnetic field may have a jump. Applying a so-called secondary symmetrization of the Symmetric System of SMHD equations, we find a condition sufficient for the structural stability of current-vortex sheets.
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structural stability of shock waves and current vortex sheets in shallow water magnetohydrodynamics
arXiv: Analysis of PDEs, 2019Co-Authors: Yuri TrakhininAbstract:We study the structural stability of shock waves and current-vortex sheets in shallow water magnetohydrodynamics (SMHD) in the sense of the local-in-time existence and uniqueness of discontinuous solutions satisfying corresponding jump conditions. The equations of SMHD form a Symmetric hyperbolic System which is formally analogous to the System of 2D compressible elastodynamics for particular nonphysical deformations. Using this analogy and the recent results in [Morando A., Trakhinin Y., Trebeschi P. Math. Ann. (2019), this https URL] for shock waves in 2D compressible elastodynamics, we prove that shock waves in SMHD are structurally stable if and only if the fluid height increases across the shock front. For current-vortex sheets the fluid height is continuous whereas the tangential components of the velocity and the magnetic field may have a jump. Applying a so-called secondary symmetrization of the Symmetric System of SMHD equations, we find a condition sufficient for the structural stability of current-vortex sheets.
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symmetrizations of rmhd equations and stability of relativistic current vortex sheets
Classical and Quantum Gravity, 2013Co-Authors: Heinrich Freistuhler, Yuri TrakhininAbstract:We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. Starting by computations in the fluid's rest frame and then applying Lorentz transformations, we derive a covariant Symmetric formulation of RMHD in terms of the primitive (physical) variables. This Symmetric System is important for the study of various initial boundary value problems. We also find a so-called secondary symmetrization whose direct consequence is the extension of the sufficient stability condition obtained earlier for non-relativistic planar current–vortex sheets to the relativistic case. As in non-relativistic settings, this implies the local-in-time existence of corresponding smooth nonplanar current–vortex sheets.
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symmetrizations of rmhd equations and stability of relativistic current vortex sheets
arXiv: Analysis of PDEs, 2012Co-Authors: Heinrich Freistuhler, Yuri TrakhininAbstract:We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a Symmetric System for the vector of primitive (physical) variables. By applying the Lorentz transformation to this System we find a concrete form of Symmetric matrices in the LAB-frame. The resulting Symmetric System in terms of primitive variables is important for the study of various initial boundary value problems for the RMHD equations. We also find a so-called secondary symmetrization whose direct consequence is the extension of the sufficient stability condition obtained earlier for non-relativistic planar current-vortex sheets to the relativistic case. As in non-relativistic settings, this implies the local-in-time existence of corresponding smooth nonplanar current-vortex sheets.
Gui Lu Long - One of the best experts on this subject based on the ideXlab platform.
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experimental demonstration of a digital quantum simulation of a general pt Symmetric System
Physical Review A, 2019Co-Authors: Jingwei Wen, Chao Zheng, Xiangyu Kong, Shijie Wei, Tao Xin, Gui Lu LongAbstract:$\mathcal{PT}$-Symmetric Systems are one of the most interesting research fields in modern quantum physics, where various theoretical and experimental progress has been made. In our work, we experimentally demonstrate how to realize a general $\mathcal{PT}$-Symmetric two-level operation in a quantum computation frame with a universal circuit model. It is based on enlarging the System with ancillary qubits and encoding the subSystem with the non-Hermitian Hamiltonian with postselection. Furthermore, we use the general formula to demonstrate one particular interesting issue, entanglement restoration induced by local $\mathcal{PT}$-Symmetric operation in our four-qubit liquid nuclear magnetic resonance platform, and a theoretical explanation for the physical characteristics has been proposed. We also extend the protocol to the realization of an arbitrary two-level Hamiltonian evolution without a Hermitian restriction by an appropriate modification of the original quantum circuit. Our work lays the foundation for quantum simulation of the general $\mathcal{PT}$-Symmetric problem in realistic quantum simulators, and the scheme can be extended to other quantum computation platforms.
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observation of a fast evolution in a parity time Symmetric System
Bulletin of the American Physical Society, 2013Co-Authors: Chao Zheng, Liang Hao, Gui Lu LongAbstract:In parity-time-Symmetric (PT-Symmetric) Hamiltonian theory, the optimal evolution time can be reduced drastically and can even be zero. In this article, we report our experimental simulation of the fast evolution of a PT-Symmetric Hamiltonian in a nuclear magnetic resonance quantum System. The experimental results demonstrate that the PT-Symmetric Hamiltonian System can indeed evolve much faster than the quantum System, and the evolution time can be arbitrarily close to zero.
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Reply on Comments on "Observation of a Fast Evolution in a Parity-time-Symmetric System"(Aixiv.1106.1550)
2011Co-Authors: Zheng Chao, Hao Liang, Gui Lu LongAbstract:Masillo [1] commented on our manuscript [2] "Observation of a Fast Evolution in a Parity-time-Symmetric System", pointing out a contradiction of our work with Ref.[3]. In this reply, we pointed out there is no disagreement between Masillo's comment and our work in Ref. [2]. The efficiency cost pointed out in Ref.\cite{masillo} exists, namely to obtain the PT-Symmetric hamiltonian evolution, one has to make a measurement on the auxiliary qubit and the auxiliary qubit is at state $|0\ket$ only probabilistically. This is reflected in the amplitude of the spectrum in the NMR quantum simulation. As a result, we made a small modification in a new version of the Ref. [2], and Fig. 2 of Ref.[2] has been replaced by spectra of two different $\alpha$'s in order to illustrate this fact.Comment: 1 page, 0 pictur
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observation of fast evolution in parity time Symmetric System
arXiv: Quantum Physics, 2011Co-Authors: Chao Zheng, Liang Hao, Gui Lu LongAbstract:To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In the parity-time-Symmetric(PT-Symmetric) Hamiltonian theory, it was predicted that the optimized evolution time can be reduced drastically comparing to the bound in the Hermitian case, and can become even zero. In this Letter, we report the experimental observation of the fast evolution of a PT-Symmetric Hamiltonian in an nuclear magnetic resonance (NMR) quantum System. The experimental results demonstrate that the PT-Symmetric Hamiltonian can indeed evolve much faster than that in a quantum System, and time it takes can be arbitrary close to zero.
Heinrich Freistuhler - One of the best experts on this subject based on the ideXlab platform.
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symmetrizations of rmhd equations and stability of relativistic current vortex sheets
Classical and Quantum Gravity, 2013Co-Authors: Heinrich Freistuhler, Yuri TrakhininAbstract:We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. Starting by computations in the fluid's rest frame and then applying Lorentz transformations, we derive a covariant Symmetric formulation of RMHD in terms of the primitive (physical) variables. This Symmetric System is important for the study of various initial boundary value problems. We also find a so-called secondary symmetrization whose direct consequence is the extension of the sufficient stability condition obtained earlier for non-relativistic planar current–vortex sheets to the relativistic case. As in non-relativistic settings, this implies the local-in-time existence of corresponding smooth nonplanar current–vortex sheets.
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symmetrizations of rmhd equations and stability of relativistic current vortex sheets
arXiv: Analysis of PDEs, 2012Co-Authors: Heinrich Freistuhler, Yuri TrakhininAbstract:We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a Symmetric System for the vector of primitive (physical) variables. By applying the Lorentz transformation to this System we find a concrete form of Symmetric matrices in the LAB-frame. The resulting Symmetric System in terms of primitive variables is important for the study of various initial boundary value problems for the RMHD equations. We also find a so-called secondary symmetrization whose direct consequence is the extension of the sufficient stability condition obtained earlier for non-relativistic planar current-vortex sheets to the relativistic case. As in non-relativistic settings, this implies the local-in-time existence of corresponding smooth nonplanar current-vortex sheets.
Peng Xue - One of the best experts on this subject based on the ideXlab platform.
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quantum information dynamics in a high dimensional parity time Symmetric System
Physical Review A, 2020Co-Authors: Zhihao Bian, Lei Xiao, Kunkun Wang, Franck Assogba Onanga, Frantisek Ruzicka, Yogesh N Joglekar, Peng XueAbstract:Non-Hermitian Systems with parity-time ($\mathcal{PT}$) symmetry give rise to exceptional points (EPs) with exceptional properties that arise due to the coalescence of eigenvectors. Such Systems have been extensively explored in the classical domain, where second- or higher-order EPs have been proposed or realized. In contrast, quantum information studies of $\mathcal{PT}$-Symmetric Systems have been confined to Systems with a two-dimensional Hilbert space. Here, by using a single-photon interferometry setup, we simulate the quantum dynamics of a four-dimensional $\mathcal{PT}$-Symmetric System across a fourth-order exceptional point. By tracking the coherent, nonunitary evolution of the density matrix of the System in $\mathcal{PT}$-symmetry unbroken and broken regions, we observe the entropy dynamics for both the entire System, and the gain and loss subSystems. Our setup is scalable to the higher-dimensional $\mathcal{PT}$-Symmetric Systems, and our results point towards the rich dynamics and critical properties.
Chao Zheng - One of the best experts on this subject based on the ideXlab platform.
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experimental demonstration of a digital quantum simulation of a general pt Symmetric System
Physical Review A, 2019Co-Authors: Jingwei Wen, Chao Zheng, Xiangyu Kong, Shijie Wei, Tao Xin, Gui Lu LongAbstract:$\mathcal{PT}$-Symmetric Systems are one of the most interesting research fields in modern quantum physics, where various theoretical and experimental progress has been made. In our work, we experimentally demonstrate how to realize a general $\mathcal{PT}$-Symmetric two-level operation in a quantum computation frame with a universal circuit model. It is based on enlarging the System with ancillary qubits and encoding the subSystem with the non-Hermitian Hamiltonian with postselection. Furthermore, we use the general formula to demonstrate one particular interesting issue, entanglement restoration induced by local $\mathcal{PT}$-Symmetric operation in our four-qubit liquid nuclear magnetic resonance platform, and a theoretical explanation for the physical characteristics has been proposed. We also extend the protocol to the realization of an arbitrary two-level Hamiltonian evolution without a Hermitian restriction by an appropriate modification of the original quantum circuit. Our work lays the foundation for quantum simulation of the general $\mathcal{PT}$-Symmetric problem in realistic quantum simulators, and the scheme can be extended to other quantum computation platforms.
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observation of a fast evolution in a parity time Symmetric System
Bulletin of the American Physical Society, 2013Co-Authors: Chao Zheng, Liang Hao, Gui Lu LongAbstract:In parity-time-Symmetric (PT-Symmetric) Hamiltonian theory, the optimal evolution time can be reduced drastically and can even be zero. In this article, we report our experimental simulation of the fast evolution of a PT-Symmetric Hamiltonian in a nuclear magnetic resonance quantum System. The experimental results demonstrate that the PT-Symmetric Hamiltonian System can indeed evolve much faster than the quantum System, and the evolution time can be arbitrarily close to zero.
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observation of fast evolution in parity time Symmetric System
arXiv: Quantum Physics, 2011Co-Authors: Chao Zheng, Liang Hao, Gui Lu LongAbstract:To find and realize the optimal evolution between two states is significant both in theory and application. In quantum mechanics, the minimal evolution is bounded by the gap between the largest and smallest eigenvalue of the Hamiltonian. In the parity-time-Symmetric(PT-Symmetric) Hamiltonian theory, it was predicted that the optimized evolution time can be reduced drastically comparing to the bound in the Hermitian case, and can become even zero. In this Letter, we report the experimental observation of the fast evolution of a PT-Symmetric Hamiltonian in an nuclear magnetic resonance (NMR) quantum System. The experimental results demonstrate that the PT-Symmetric Hamiltonian can indeed evolve much faster than that in a quantum System, and time it takes can be arbitrary close to zero.
