Classical and quantum mechanics of complex hamiltonian systems: An extended complex phase space approach

Pramana ◽  
2009 ◽  
Vol 73 (2) ◽  
pp. 287-297 ◽  
Author(s):  
R. S. Kaushal
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Hamiltonian Systems ◽  
Complex Phase ◽  
Extended Complex ◽  
Classical And Quantum Mechanics ◽  
Space Approach

Complex dynamical invariants for two-dimensional nonhermitian Hamiltonian systems

2012 ◽  
Vol 90 (2) ◽  
pp. 151-157 ◽  
Author(s):  
J.S. Virdi ◽  
F. Chand ◽  
C.N. Kumar ◽  
S.C. Mishra
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
General Result ◽  
Two Dimensional ◽  
Complex Phase ◽  
Quartic Potential ◽  
Dynamical Invariants ◽  
Extended Complex ◽  
Space Approach

Keeping in view the importance of dynamical invariants, attempts have been made to investigate complex invariants for two-dimensional Hamiltonian systems within the framework of the extended complex phase space approach. The rationalization method has been used to derive an invariant of a general nonhermitian quartic potential. Invariants for three specific potentials are also obtained from the general result.

Classical invariants for non-Hermitian anharmonic potentials

2020 ◽  
Vol 98 (11) ◽  
pp. 1004-1008
Author(s):  
Ram Mehar Singh ◽  
S.B. Bhardwaj ◽  
Kushal Sharma ◽  
Anand Malik ◽  
Fakir Chand
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
One Dimension ◽  
Complex Dynamical Systems ◽  
Complex Phase ◽  
Extended Complex ◽  
Space Approach

Keeping in view the importance of complex dynamical systems, we investigate the classical invariants for some non-Hermitian anharmonic potentials in one dimension. For this purpose, the rationalization method is employed under the elegance of the extended complex phase space approach. The invariants obtained are expected to play an important role in studying complex Hamiltonian systems at the classical as well as quantum levels.

Invariance Groups in Classical and Quantum Mechanics

1973 ◽  
Vol 28 (3-4) ◽  
pp. 538-540 ◽  
Author(s):  
D. J. Simms
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Energy Levels ◽  
Classical Mechanics ◽  
Symmetry Groups ◽  
Casimir Invariants ◽  
Classical Phase Space ◽  
Invariance Groups ◽  
Classical And Quantum Mechanics

AbstractThis is a report on some new relations and analogies between classical mechanics and quantum mechanics which arise out of the work of Kostant and Souriau. Topics treated are i) the role of symmetry groups; ii) the notion of elementary system and the role of Casimir invariants; iii) energy levels; iv) quantisation in terms of geometric data on the classical phase space. Some applications are described.

Phase-Space Approach to Berry Phases

2006 ◽  
Vol 13 (01) ◽  
pp. 67-74 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Wigner Function ◽  
Berry Phase ◽  
Space Formulation ◽  
Berry Phases ◽  
Classical Phase Space ◽  
New Formula ◽  
Space Approach

We propose a new formula for the adiabatic Berry phase which is based on phase-space formulation of quantum mechanics. This approach sheds a new light onto the correspondence between classical and quantum adiabatic phases — both phases are related with the averaging procedure: Hannay angle with averaging over the classical torus and Berry phase with averaging over the entire classical phase space with respect to the corresponding Wigner function.

scholarly journals Lyapunov exponent in quantum mechanics. A phase-space approach

2000 ◽  
Vol 145 (3-4) ◽  
pp. 330-348 ◽  
Author(s):  
V.I. Man’ko ◽  
R. Vilela Mendes
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Lyapunov Exponent ◽  
Space Approach

Superoperator methods of calculating cross sections: III. Unified description of classical and quantal scattering

1980 ◽  
Vol 58 (8) ◽  
pp. 1171-1182 ◽  
Author(s):  
R. E. Turner ◽  
R. F. Snider
Keyword(s):  
Quantum Mechanics ◽  
Phase Space ◽  
Time Dependence ◽  
Stationary State ◽  
Cross Sections ◽  
Differential Cross ◽  
Density Operator ◽  
The Difference ◽  
Unified Description ◽  
Classical And Quantum Mechanics

It is shown how differential cross sections can be obtained from the time dependence of phase space packets. This procedure is valid both for classical and quantum mechanics. Two methods are described. In one the trajectory of the packet is emphasized, while in the second the packet is appropriately spread to infinite size. Both methods are applicable to either mechanics. It is shown how the quantal results agree with those of the stationary state approach as formulated in terms of the density operator. The description is also used to elucidate the difference between the scattered flux and the generalized flux that arises naturally in the superoperator formulation.

Canonical Transformations, Entropy and Quantization

1987 ◽  
Vol 42 (4) ◽  
pp. 333-340 ◽  
Author(s):  
B. Bruhn
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Arbitrary Function ◽  
Coordinate Transformations ◽  
Canonical Transformations ◽  
Integrable Hamiltonian Systems ◽  
Eigenvalue Spectrum ◽  
Complex Phase ◽  
Algebraic Treatment ◽  
Canonical Coordinate

This paper considers various aspects of the canonical coordinate transformations in a complex phase space. The main result is given by two theorems which describe two special families of mappings between integrable Hamiltonian systems. The generating function of these transformations is determined by the entropy and a second arbitrary function which we take to be the energy function. For simple integrable systems an algebraic treatment based on the group properties of the canonical transformations is given to calculate the eigenvalue spectrum of the energy.

Sign in / Sign up

Export Citation Format

Share Document