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Hamiltonian Systems with Convex Hamiltonians
2004A well-known theorem states that if a level surface of a Hamiltonian is convex, then it contains a periodic trajectory of the Hamiltonian system [142], [147]. In this chapter we prove a more general statement as an application of optimal control theory for linear systems.
Andrei A. Agrachev, Yuri L. Sachkov
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Stochastic surrogate Hamiltonian
The Journal of Chemical Physics, 2008The surrogate Hamiltonian is a general scheme to simulate the many body quantum dynamics composed of a primary system coupled to a bath. The method has been based on a representative bath Hamiltonian composed of two-level systems that is able to mimic the true system-bath dynamics up to a prespecified time.
Gil, Katz +3 more
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Physical Review E, 1993
The method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by Ott, Grebogi, and Yorke (OGY) is not directly applicable to chaotic Hamiltonian systems. The reason is that an unstable periodic orbit in such systems often exhibits complex-conjugate eigenvalues at one or more of its orbit points.
, Lai, , Ding, , Grebogi
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The method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by Ott, Grebogi, and Yorke (OGY) is not directly applicable to chaotic Hamiltonian systems. The reason is that an unstable periodic orbit in such systems often exhibits complex-conjugate eigenvalues at one or more of its orbit points.
, Lai, , Ding, , Grebogi
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MEMRISTOR HAMILTONIAN CIRCUITS
International Journal of Bifurcation and Chaos, 2011We prove analytically that 2-element memristive circuits consisting of a passive linear inductor in parallel with a passive memristor, or an active memristive device, can be described explicitly by a Hamiltonian equation, whose solutions can be periodic or damped, and can be represented analytically by the constants of the motion along the circuit ...
Itoh, Makoto, Chua, Leon O.
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Generalized Hamiltonian dynamics
Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1950The author’s procedure for passing from the Lagrangian to the Hamiltonian when the momenta are not independent functions of the velocities is put into a simpler and more practical form, the main results being obtained by a direct solution of the equations provided by the consistency requirements.
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Proceedings of the London Mathematical Society, 1984
The mathematical setup is as follows. A self-adjoint operator \(H\geq 0\) is given on the Hilbert space \(L_ 2=L_ 2(X,dx)\) on a \(\sigma\)-finite countably generated measure space. It is assumed that \[ (1)\quad e^{- tH}f\geq 0\quad for\quad all\quad t\geq 0,\quad f\geq 0\quad in\quad L_ 2. \] Certain admissible partitions of X are introduced, leading
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The mathematical setup is as follows. A self-adjoint operator \(H\geq 0\) is given on the Hilbert space \(L_ 2=L_ 2(X,dx)\) on a \(\sigma\)-finite countably generated measure space. It is assumed that \[ (1)\quad e^{- tH}f\geq 0\quad for\quad all\quad t\geq 0,\quad f\geq 0\quad in\quad L_ 2. \] Certain admissible partitions of X are introduced, leading
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Discrete Hamiltonian-assisted Hamiltonian sampling
Sampling from discrete distributions is a fundamental task in many statistical applications, with Markov Chain Monte Carlo (MCMC) being one of the primary approaches. We introduce two novel MCMC algorithms that address key challenges in efficient sampling from discrete spaces.openaire +1 more source
Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature
Nature Materials, 2022Louis Haeberlé, , Dafei Jin
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Floquet Hamiltonian engineering of an isolated many-body spin system
Science, 2021Sebastian Geier +2 more
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