scholarly journals Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems

2003 ◽  
Vol 44 (3) ◽  
pp. 1150-1172 ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov
Keyword(s):  
Hamiltonian Formalism ◽  
Hydrodynamic Type ◽  
Hamiltonian Operators ◽  
Linearly Degenerate

scholarly journals Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

2019 ◽  
Vol 21 (35) ◽  
pp. 18939-18957 ◽  
Author(s):  
Kun Wang ◽  
Tao Zeng
Keyword(s):  
Hamiltonian Formalism ◽  
Spin Orbit ◽  
Jahn Teller ◽  
Hamiltonian Operators

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

scholarly journals On the compatible weakly nonlocal Poisson brackets of hydrodynamic type

2002 ◽  
Vol 32 (10) ◽  
pp. 587-614 ◽  
Author(s):  
Andrei Ya. Maltsev
Keyword(s):  
Integrable Hierarchies ◽  
Riemannian Metrics ◽  
Riemannian Metric ◽  
Hydrodynamic Type ◽  
Poisson Brackets ◽  
Symplectic Structures ◽  
Symplectic Forms ◽  
Hamiltonian Functions ◽  
Hamiltonian Operators ◽  
Nonlocal Part

We consider the pairs of general weakly nonlocal Poisson brackets of hydrodynamic type (Ferapontov brackets) and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding “first” pseudo-Riemannian metricg(0) νμand also some nondegeneracy requirement for the nonlocal part, it is possible to introduce a “canonical” set of “integrable hierarchies” based on the Casimirs, momentum functional and some “canonical Hamiltonian functions.” We prove also that all the “higher” “positive” Hamiltonian operators and the “negative” symplectic forms have the weakly nonlocal form in this case. The same result is also true for “negative” Hamiltonian operators and “positive” symplectic structures in the case when both pseudo-Riemannian metricsg(0) νμandg(1) νμare nondegenerate.

scholarly journals A Unified Hamiltonian Formalism of Jahn-Teller and Pseudo-Jahn-Teller Problems in Axial Symmetries

2021 ◽  
Author(s):  
James Brown ◽  
Robert Lang ◽  
Tao Zeng
Keyword(s):  
Arbitrary Number ◽  
Quantum Dynamics ◽  
Hamiltonian Formalism ◽  
High Order ◽  
Dynamics Simulation ◽  
Simulation Program ◽  
Jahn Teller ◽  
User Friendly ◽  
Hamiltonian Operators

A formalism for expansions of all Jahn-Teller and pseudo-Jahn-Teller Hamiltonian operators in all axial symmetries is presented. The formalism provides Hamiltonian expansions up to arbitrarily high order and including an arbitrary number of vibra?tional modes, which are of arbitrary types. It consists of three equations and two tables. The formalism is user-friendly since it can be used without understanding its derivation. An example of E00 3 ⊗ e 0 1 Jahn-Teller interaction of cycloheptatrienyl cation is used to demonstrate the correctness of the formalism. A Python program is devel?oped to automate the generation of Hamiltonian expansions for all axial Jahn-Teller and pseodo-Jahn-Teller problems, , and interface the expansions to quantum dynamics simulation program. This is the first unified Hamiltonian formalism for axial Jahn?Teller and pseudo-Jahn-Teller problems. And it is the only one.

scholarly journals Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type

2010 ◽  
Vol 60 (9) ◽  
pp. 1112-1126 ◽  
Author(s):  
John Gibbons ◽  
Paolo Lorenzoni ◽  
Andrea Raimondo
Keyword(s):  
Hamiltonian Formalism ◽  
Hydrodynamic Type ◽  
Systems Of Hydrodynamic Type
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