Phase-space Distribution and the Liouville Equation
Parametric space for nonlinearly excited phase equation
... the phase of oscillators coupled by diffusion is generally described by a partial differential equation involving infinitely many ...the equation, namely a form based on nonlinear excitation and a ...
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Nonlinear Liouville Equation and Information Soliton
... 5. Application Generally, the above results provoke a constructive mechanism to realize a sort of self-organization from the non-equlibrium process for the open system. This may be useful, from physical justification, to ...
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Solution of the master equation for Wigner's quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential
... Fokker-Planck equation 共 known in this instance as the Klein-Kramers equation 兲 for the phase space distribution function W 共 x, p , t 兲 by continued fraction ...Langevin ...
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Heisenberg Uncertainty Relation in Quantum Liouville Equation
... the distribution function of the electrons fx, v, t and by introducing equations typical of the statistical mechanics whose solutions provide a more precise and correct description of the dynamics of these systems ...
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NUMERICAL SOLUTION OF AN INVERSE PROBLEM FOR THE LIOUVILLE EQUATION
... of distribution of the number of the particles in the phase space, H (x, v, t) is the Hamiltonian, λ(x, v, t) is a source function, x is the space coordinate vector, v and t denote the ...
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\(\operatorname{Spin}(7)\) structure equation and the vector elliptic Liouville equation
... u t = u × u s , u = (u 1 , u 2 , u 3 ) ∈ S 2 → R 3 (4) for the “staggered” spin field u(t, s). On the other hand, the Euclidean 3-space R 3 can be regarded as the imaginary part Im H of the quaternions H , and the ...
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The Foldy Wouthuysen Transformation of the Dirac Equation in Noncommutative Phase Space
... noncommutative phase-space are investigated and the Schrödinger-Pauli equation is found, knowing that the used methods for extracting the full phase-space noncom- mutative Dirac ...
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Asymptotic distributions of Neumann problem for Sturm-Liouville equation
... asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on [0, π] with Neumann conditions (y ′ (0) = y ′ (π) = 0) ...
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Properties of Phase Space Wavefunctions and Eigenvalue Equation of Momentum Dispersion Operator
... and phase space representation of quantum ...the phase space representation and the momentum dispersion operator, its representations and eigenvalue ...the phase space ...
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Phase space Langevin equation for spin relaxation in a dc magnetic field
... Langevin equation for the quantum Brownian motion of a spin of arbitrary size in a uniform external dc magnetic field is derived from the phase space master equation in the weak coupling and ...
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CiteSeerX — Fully adaptive propagation of the quantum-classical Liouville equation
... D. Case B For our second model problem, we provide numerical data from the nonadiabatic Marcus regime (V E r ), which we have studied recently. 25 According to Fig. 2, methods #2 and #3 perform at roughly the same ...
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CiteSeerX — Partial Wigner Transforms and the Quantum-Classical Liouville Equation
... QCL. This dis
ussion shows that the QCL solutions may be interpre- tated as lassi
al phase spa
e densities, at least near the adiabati limit. Third, it is demonstrated that the QCL yields good approximations of ...
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Continuity Equation in Presence of a Non Local Potential in Non Commutative Phase Space
... continuity equation in presence of a local potential, and a non-local potential arising from electron-electron interaction in both com- mutative and non-commutative ...the phase-space ...
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Mapping stationary axisymmetric phase space distribution functions by orbit libraries
... accurate phase-space volumes to individual orbits and to reconstruct the full three-integral phase-space distribution function (DF) of any axisymmetric orbit ...
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Solution of Dirac Equation with the Time Dependent Linear Potential in Non Commutative Phase Space
... 2 Laboratory for Photoelectric Technology and Application, Guizhou University, Guiyang, China Email: # [email protected] Received April 13, 2013; revised May 16, 2013; accepted June 15, 2013 Copyright © 2013 Xueling ...
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Semiclassical master equation in Wigner's phase space applied to the Brownian motion in a periodic potential
... “jump” rate 关45兴. The Kramers idea was later elaborated upon by Mel’nikov 关46兴 and Mel’nikov and Meshkov 关47兴. They proposed, based on a Wiener-Hopf equation, a univer- sal formula 共 that is valid for all values ...
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Liouville type theorem for a singular elliptic equation with finite Morse index
... There are few works on the elliptic equation with the p-Laplace operator and exponential growth. By choosing a special test function, the authors gave the result on the nonexistence of positive stable solution for ...
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Gradient estimates and Liouville type theorems for a weighted nonlinear elliptic equation
... elliptic equation on a smooth metric measure space (M, g, e –f dv): f u + au log u + bu = 0, where a, b are two real ...above equation must be constant under some suitable ...
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Sturm Liouville problem and numerical method of fractional diffusion equation on fractals
... 32. Jiang, L, Kong, DX, Chen, ZH: Applied Partial Differential Equations. Higer Education Press, Beijing (2008) 33. Zhuang, P, Liu, F, Anh, V, Turner, I: Numerical treatment for the fractional Fokker-Planck ...
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Liouville type theorem for some nonlinear systems in a half space
... By the method of moving planes in integral forms they derived that the positive solutions of (.) are radially symmetric and such solutions are nonexistent under some integrability conditions. In a recent paper of Chen ...
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