The Experts below are selected from a list of 9981 Experts worldwide ranked by ideXlab platform
Dominique Manchon - One of the best experts on this subject based on the ideXlab platform.
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Poisson Bracket deformed Bracket and gauge group actions in kontsevich deformation quantization
Letters in Mathematical Physics, 2000Co-Authors: Dominique ManchonAbstract:We express the difference between the Poisson Bracket and a deformed Bracket for Kontsevich deformation quantization on any Poisson manifold by means of the second derivative of the formality quasi-isomorphism. The counterpart in star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated.
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Poisson Bracket, deformed Bracket and gauge group actions in Kontsevich deformation quantization
Letters in Mathematical Physics, 2000Co-Authors: Dominique ManchonAbstract:We express the difference between Poisson Bracket and deformed Bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated.
V. A. Soroka - One of the best experts on this subject based on the ideXlab platform.
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supersymmetry and the odd Poisson Bracket
arXiv: High Energy Physics - Theory, 2002Co-Authors: V. A. SorokaAbstract:Some applications of the odd Poisson Bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd Bracket and the dynamics formulation with the Grassmann-odd Lagrangian. Quantum representations of the odd Bracket are also constructed and applied for the quantization of classical systems based on the odd Bracket and for the realization of the idea of a composite spinor structure of space-time. At last, the linear odd Bracket, corresponding to a semi-simple Lie group, is introduced on the Grassmann algebra.
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Supersymmetry and the odd Poisson Bracket
arXiv: High Energy Physics - Theory, 2001Co-Authors: V. A. SorokaAbstract:Abstract Some applications of the odd Poisson Bracket developed by Kharkov's theorists are represented.
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degenerate odd Poisson Bracket on grassmann variables
Physics of Atomic Nuclei, 2000Co-Authors: V. A. SorokaAbstract:A linear degenerate odd Poisson Bracket (antiBracket) realized solely on Grassmann variables is proposed. It is revealed that this Bracket has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, second and third orders with respect to the Grassmann derivatives. It is shown that these Δ-like operators, together with the Grassmann-odd nilpotent Casimir function of this Bracket, form a finite-dimensional Lie superalgebra.
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linear odd Poisson Bracket on grassmann variables
Physics Letters B, 1999Co-Authors: V. A. SorokaAbstract:Abstract A linear odd Poisson Bracket (antiBracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the Bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent Δ -like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson Bracket having the only Grassmann-odd nilpotent differential Δ -operator of the second order. It is shown that these Δ -like operators together with a Grassmann-odd nilpotent Casimir function of this Bracket form a finite-dimensional Lie superalgebra.
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linear odd Poisson Bracket on grassmann variables
arXiv: High Energy Physics - Theory, 1998Co-Authors: V. A. SorokaAbstract:A linear odd Poisson Bracket (antiBracket) realized solely in terms of Grassmann variables is suggested. It is revealed that the Bracket, which corresponds to a semi-simple Lie group, has at once three Grassmann-odd nilpotent $\Delta$-like differential operators of the first, the second and the third orders with respect to Grassmann derivatives, in contrast with the canonical odd Poisson Bracket having the only Grassmann-odd nilpotent differential $\Delta$-operator of the second order. It is shown that these $\Delta$-like operators together with a Grassmann-odd nilpotent Casimir function of this Bracket form a finite-dimensional Lie superalgebra.
P J Morrison - One of the best experts on this subject based on the ideXlab platform.
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beatification flattening the Poisson Bracket for two dimensional fluid and plasma theories
Physics of Plasmas, 2017Co-Authors: Thiago F Viscondi, I L Caldas, P J MorrisonAbstract:A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely, the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson Bracket and replaces it with a fixed dependence on a chosen state in the phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.
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beatification flattening the Poisson Bracket for two dimensional fluid and plasma theories
arXiv: Fluid Dynamics, 2016Co-Authors: Thiago F Viscondi, I L Caldas, P J MorrisonAbstract:A perturbative method called beatification is presented for a class of two-dimensional fluid and plasma theories. The Hamiltonian systems considered, namely the Euler, Vlasov-Poisson, Hasegawa-Mima, and modified Hasegawa-Mima equations, are naturally described in terms of noncanonical variables. The beatification procedure amounts to finding the correct transformation that removes the explicit variable dependence from a noncanonical Poisson Bracket and replaces it with a fixed dependence on a chosen state in phase space. As such, beatification is a major step toward casting the Hamiltonian system in its canonical form, thus enabling or facilitating the use of analytical and numerical techniques that require or favor a representation in terms of canonical, or beatified, Hamiltonian variables.
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higher order hamiltonian fluid reduction of vlasov equation
Annals of Physics, 2014Co-Authors: M Perin, P J Morrison, Cristel Chandre, Emanuele TassiAbstract:From the Hamiltonian structure of the Vlasov equation, we build a Hamiltonian model for the first three moments of the Vlasov distribution function, namely, the density, the momentum density and the specific internal energy. We derive the Poisson Bracket of this model from the Poisson Bracket of the Vlasov equation, and we discuss the associated Casimir invariants.
Cristina M Marchetti - One of the best experts on this subject based on the ideXlab platform.
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Poisson Bracket formulation of the dynamics of fluids of deformable particles
arXiv: Soft Condensed Matter, 2020Co-Authors: Arthur Hernandez, Cristina M MarchettiAbstract:Using the Poisson Bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations of individual particles from regular shapes and a shape tensor density field that quantifies both particle elongation and nematic alignment of elongated shapes. We explicitly consider the example of a dense biological tissue as described by the Vertex model energy, where cell shape has been proposed as a structural order parameter for a liquid-solid transition. The hydrodynamic model of biological tissue proposed here captures the coupling of cell shape to flow, and provides a starting point for modeling the rheology of dense tissue.
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Poisson Bracket approach to the dynamics of bent core molecules
Physical Review E, 2007Co-Authors: William Kung, Cristina M MarchettiAbstract:We generalize our previous work on the phase stability and hydrodynamic of polar liquid crystals possessing local uniaxial C infinity v symmetry to biaxial systems exhibiting local C2v symmetry. Our work is motivated by the recently discovered examples of thermotropic biaxial nematic liquid crystals comprising bent-core mesogens, whose molecular structure is characterized by a non-polar-body axis (n) as well as a polar axis (p) along the bisector of the bent mesogenic core which is coincident with a large, transverse dipole moment. The free energy for this system differs from that of biaxial nematic liquid crystals in that it contains terms violating the p-->-p symmetry. We show that, in spite of a general splay instability associated with these parity-odd terms, a uniform polarized biaxial state can be stable in a range of parameters. We then derive the hydrodynamic equations of the system, via the Poisson-Bracket formalism, in the polarized state and comment on the structure of the corresponding linear hydrodynamic modes. In our Poisson-Bracket derivation, we also compute the flow-alignment parameters along the three symmetry axes in terms of microscopic parameters associated with the molecular geometry of the constituent biaxial mesogens.
Young Min Rhee - One of the best experts on this subject based on the ideXlab platform.
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improving long time behavior of Poisson Bracket mapping equation a mapping variable scaling approach
Journal of Chemical Physics, 2014Co-Authors: Hyunwoo Kim, Weongyu Lee, Young Min RheeAbstract:Semiclassical approaches are widely employed for understanding nonadiabatic processes in complex systems. However, many semiclassical approaches may suffer from various unphysical behaviors especially in the long time limit. For example, the Poisson Bracket mapping equation (PBME), an example of semiclassical approaches that can be usefully adopted in simulating large systems, sometimes displays negative populations in long simulations. Here, to reduce the error in such population dynamics, we present a mapping variable scaling approach for PBME. We demonstrate that our approach yields the equilibrium population reliably in the long time limit by simulating energy transfers in a series of model systems. Based on error analyses of the system density matrices, we determine conditions for reliable dynamics in model two-state systems. We then apply our scheme to following the energy transfer dynamics in a more realistic seven state model with parameters that reflect experimental situations. With this, we confirm that the modified PBME provides correct equilibrium populations in the long time limit, with acceptable deterioration in the short time dynamics. We also test how the initial bath energy distribution changes in time depending on the schemes of sampling the initial bath modes, and try to see its effect on the system dynamics. Finally, we discuss the applicability of our scaling scheme to all-atom style semiclassical simulations of complex systems.
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improving long time behavior of Poisson Bracket mapping equation a non hamiltonian approach
Journal of Chemical Physics, 2014Co-Authors: Hyunwoo Kim, Young Min RheeAbstract:Understanding nonadiabatic dynamics in complex systems is a challenging subject. A series of semiclassical approaches have been proposed to tackle the problem in various settings. The Poisson Bracket mapping equation (PBME) utilizes a partial Wigner transform and a mapping representation for its formulation, and has been developed to describe nonadiabatic processes in an efficient manner. Operationally, it is expressed as a set of Hamilton's equations of motion, similar to more conventional classical molecular dynamics. However, this original Hamiltonian PBME sometimes suffers from a large deviation in accuracy especially in the long time limit. Here, we propose a non-Hamiltonian variant of PBME to improve its behavior especially in that limit. As a benchmark, we simulate spin-boson and photosynthetic model systems and find that it consistently outperforms the original PBME and its Ehrenfest style variant. We explain the source of this improvement by decomposing the components of the mapping Hamiltonian and by assessing the energy flow between the system and the bath. We discuss strengths and weaknesses of our scheme with a viewpoint of offering future prospects.
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behavior of Poisson Bracket mapping equation in studying excitation energy transfer dynamics of cryptophyte phycocyanin 645 complex
Bulletin of The Korean Chemical Society, 2012Co-Authors: Weongyu Lee, Aaron Kelly, Young Min RheeAbstract:Recently, it has been shown that quantum coherence appears in energy transfers of various photosynthetic lightharvesting complexes at from cryogenic to even room temperatures. Because the photosynthetic systems are inherently complex, these findings have subsequently interested many researchers in the field of both experiment and theory. From the theoretical part, simplified dynamics or semiclassical approaches have been widely used. In these approaches, the quantum-classical Liouville equation (QCLE) is the fundamental starting point. Toward the semiclassical scheme, approximations are needed to simplify the equations of motion of various degrees of freedom. Here, we have adopted the Poisson Bracket mapping equation (PBME) as an approximate form of QCLE and applied it to find the time evolution of the excitation in a photosynthetic complex from marine algae. The benefit of using PBME is its similarity to conventional Hamiltonian dynamics. Through this, we confirmed the coherent population transfer behaviors in short time domain as previously reported with a more accurate but more time-consuming iterative linearized density matrix approach. However, we find that the site populations do not behave according to the Boltzmann law in the long time limit. We also test the effect of adding spurious high frequency vibrations to the spectral density of the bath, and find that their existence does not alter the dynamics to any significant extent as long as the associated reorganization energy is changed not too drastically. This suggests that adopting classical trajectory based ensembles in semiclassical simulations should not influence the coherence dynamics in any practical manner, even though the classical trajectories often yield spurious high frequency vibrational features in the spectral density.
