The Experts below are selected from a list of 120690 Experts worldwide ranked by ideXlab platform
Lior Klein - One of the best experts on this subject based on the ideXlab platform.
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stabilization of Exponential Number of discrete remanent states with localized spin orbit torques
Applied Physics Letters, 2020Co-Authors: Shubhankar Das, Ariel Zaig, Moty Schultz, Lior KleinAbstract:Using bilayer films of β-Ta/Ni0.8Fe0.2, we fabricate structures consisting of two, three, and four crossing ellipses, which exhibit shape-induced bi-axial, tri-axial, and quadro-axial magnetic anisotropy in the crossing area, respectively. Structures consisting of N crossing ellipses can be stabilized in 2N remanent states by applying (and removing) an external magnetic field. However, we show that with field-free spin–orbit torques induced by flowing currents in individual ellipses, the Number of remanent states grows to 2 N. Furthermore, when the current flows between the edges of different ellipses, the Number of remanent states jumps to 2 2 N, including states that exhibit a π-Neel domain wall in the overlap area. The very large Number of accessible remanent magnetic states that are exhibited by the relatively simple magnetic structures paves the way for intriguing spintronics applications including memory devices.
Christophe Texier - One of the best experts on this subject based on the ideXlab platform.
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Exponential Number of equilibria and depinning threshold for a directed polymer in a random potential
Annals of Physics, 2018Co-Authors: Yan V Fyodorov, Pierre Le Doussal, Alberto Rosso, Christophe TexierAbstract:Abstract By extending the Kac–Rice approach to manifolds of finite internal dimension, we show that the mean Number N tot of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension d = 1 + 1 , grows Exponentially N tot ∼ exp ( r L ) with its length L . The growth rate r is found to be directly related to the generalized Lyapunov exponent (GLE) which is a moment-generating function characterizing the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schrodinger operator of the 1D Anderson localization problem. For strong confinement, the rate r is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate r is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape “topology trivialization” phenomenon, we obtain an upper bound for the depinning threshold f c , in the presence of an applied force, for elastic lines and d -dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic Number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.
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Exponential Number of equilibria and depinning threshold for a directed polymer in a random potential
arXiv: Disordered Systems and Neural Networks, 2017Co-Authors: Yan V Fyodorov, Pierre Le Doussal, Alberto Rosso, Christophe TexierAbstract:By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean Number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows Exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic Number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.
Pan Zhang - One of the best experts on this subject based on the ideXlab platform.
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the solution space structure of random constraint satisfaction problems with growing domains
Journal of Statistical Mechanics: Theory and Experiment, 2015Co-Authors: Pan Zhang, Tian Liu, Fuzhou GongAbstract:In this paper we study the solution space structure of model RB, a standard prototype of the constraint satisfaction problem (CSP), with growing domains. Using the first moment method and the second moment method, we rigorously show that in the satisfiable phase close to the satisfiability transition, solutions are clustered into an Exponential Number of well-separated clusters, with each cluster containing a sub-Exponential Number of solutions. As a consequence, the system has a clustering (dynamical) transition but no condensation transition. This picture of the phase diagram is different to other classic random CSPs that possess a fixed domain size, such as the K-satisfiability (K-SAT) problem and the graph colouring problem, where a condensation transition exists and is distinctly different to the satisfiability transition. Our result verifies some non-rigorous results obtained using the cavity method from spin glass theory.
Shubhankar Das - One of the best experts on this subject based on the ideXlab platform.
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stabilization of Exponential Number of discrete remanent states with localized spin orbit torques
Applied Physics Letters, 2020Co-Authors: Shubhankar Das, Ariel Zaig, Moty Schultz, Lior KleinAbstract:Using bilayer films of β-Ta/Ni0.8Fe0.2, we fabricate structures consisting of two, three, and four crossing ellipses, which exhibit shape-induced bi-axial, tri-axial, and quadro-axial magnetic anisotropy in the crossing area, respectively. Structures consisting of N crossing ellipses can be stabilized in 2N remanent states by applying (and removing) an external magnetic field. However, we show that with field-free spin–orbit torques induced by flowing currents in individual ellipses, the Number of remanent states grows to 2 N. Furthermore, when the current flows between the edges of different ellipses, the Number of remanent states jumps to 2 2 N, including states that exhibit a π-Neel domain wall in the overlap area. The very large Number of accessible remanent magnetic states that are exhibited by the relatively simple magnetic structures paves the way for intriguing spintronics applications including memory devices.
Yan V Fyodorov - One of the best experts on this subject based on the ideXlab platform.
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Exponential Number of equilibria and depinning threshold for a directed polymer in a random potential
Annals of Physics, 2018Co-Authors: Yan V Fyodorov, Pierre Le Doussal, Alberto Rosso, Christophe TexierAbstract:Abstract By extending the Kac–Rice approach to manifolds of finite internal dimension, we show that the mean Number N tot of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension d = 1 + 1 , grows Exponentially N tot ∼ exp ( r L ) with its length L . The growth rate r is found to be directly related to the generalized Lyapunov exponent (GLE) which is a moment-generating function characterizing the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schrodinger operator of the 1D Anderson localization problem. For strong confinement, the rate r is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate r is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape “topology trivialization” phenomenon, we obtain an upper bound for the depinning threshold f c , in the presence of an applied force, for elastic lines and d -dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic Number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.
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Exponential Number of equilibria and depinning threshold for a directed polymer in a random potential
arXiv: Disordered Systems and Neural Networks, 2017Co-Authors: Yan V Fyodorov, Pierre Le Doussal, Alberto Rosso, Christophe TexierAbstract:By extending the Kac-Rice approach to manifolds of finite internal dimension, we show that the mean Number $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle$ of all possible equilibria (i.e. force-free configurations, a.k.a. equilibrium points) of an elastic line (directed polymer), confined in a harmonic well and submitted to a quenched random Gaussian potential in dimension $d=1+1$, grows Exponentially $\left\langle\mathcal{N}_\mathrm{tot}\right\rangle\sim\exp{(r\,L)}$ with its length $L$. The growth rate $r$ is found to be directly related to the generalised Lyapunov exponent (GLE) which is a moment-generating function characterising the large-deviation type fluctuations of the solution to the initial value problem associated with the random Schr\"odinger operator of the 1D Anderson localization problem. For strong confinement, the rate $r$ is small and given by a non-perturbative (instanton, Lifshitz tail-like) contribution to GLE. For weak confinement, the rate $r$ is found to be proportional to the inverse Larkin length of the pinning theory. As an application, identifying the depinning with a landscape "topology trivialization" phenomenon, we obtain an upper bound for the depinning threshold $f_c$, in the presence of an applied force, for elastic lines and $d$-dimensional manifolds, expressed through the mean modulus of the spectral determinant of the Laplace operators with a random potential. We also discuss the question of counting of stable equilibria. Finally, we extend the method to calculate the asymptotic Number of equilibria at fixed energy (elastic, potential and total), and obtain the (annealed) distribution of the energy density over these equilibria (i.e. force-free configurations). Some connections with the Larkin model are also established.
