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.

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.

scholarly journals Negative heat capacity for a Klein–Gordon oscillator in non-commutative complex phase space

2017 ◽  
Vol 14 (10) ◽  
pp. 1750141 ◽  
Author(s):  
Slimane Zaim ◽  
Hakim Guelmamene ◽  
Yazid Delenda
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Phase Space ◽  
Energy Levels ◽  
Two Dimensional ◽  
Complex Phase ◽  
First Order ◽  
Klein Gordon

We obtain exact solutions to the two-dimensional (2D) Klein–Gordon oscillator in a non-commutative (NC) complex phase space to first order in the non-commutativity parameter. We derive the exact NC energy levels and show that the energy levels split to [Formula: see text] levels. We find that the non-commutativity plays the role of a magnetic field interacting automatically with the spin of a particle induced by the non-commutativity of complex phase space. The effect of the non-commutativity parameter on the thermal properties is discussed. It is found that the dependence of the heat capacity [Formula: see text] on the NC parameter gives rise to a negative quantity. Phenomenologically, this effectively confirms the presence of the effects of self-gravitation induced by the non-commutativity of complex phase space.

Noise-induced phase space transport in two-dimensional Hamiltonian systems

1999 ◽  
Vol 60 (2) ◽  
pp. 1567-1578 ◽  
Author(s):  
Ilya V. Pogorelov ◽  
Henry E. Kandrup
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
Two Dimensional ◽  
Phase Space Transport

Identification of semiclassical chaos in two-dimensional PT-symmetric systems

2003 ◽  
Vol 81 (6) ◽  
pp. 835-846 ◽  
Author(s):  
Asiri Nanayakkara ◽  
Chula Abayaratne
Keyword(s):  
Phase Space ◽  
Complex Systems ◽  
Quantum Level ◽  
Two Dimensional ◽  
Level Spacing ◽  
Chaotic Motions ◽  
Complex Phase ◽  
Wigner Distributions ◽  
Symmetric Complex ◽  
Symmetric Systems

Identification of regular and chaotic motions of two-dimensional PT-symmetric complex systems was investigated. New definitions have been introduced to study properties of trajectories in complex phase space. Projections of these trajectories on complex x- and y-planes, Lyapunov exponents, and surfaces of section have been used for identifying regular and irregular (chaotic) motions in complex phase space. Quantum level spacing distributions of these systems have also been calculated for finding out the connection between regular and irregular states with standard distributions such as Poisson and Wigner distributions. It has been found that the PT-symmetric complex systems behave in the same way as the real systems. PACS No.: 05.45.Ac

Negative temperature states of two-dimensional plasmas and vortex fluids

1974 ◽  
Vol 336 (1606) ◽  
pp. 257-271 ◽  
Keyword(s):  
Phase Space ◽  
Statistical Mechanics ◽  
Hamiltonian Systems ◽  
Ideal Fluid ◽  
Negative Temperature ◽  
Two Dimensional

The two-dimensional guiding centre plasma and a system of interacting line vortices in an ideal fluid are examples of Hamiltonian systems with bounded phase space. The statistical mechanics of such systems is investigated. An interesting feature is that they can exist in negative temperature states which show observable intrinsic characteristics, such as the formation of clusters of particles.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Computer Assisted Image Reconstruction of Oligomer Structure

1976 ◽  
Vol 34 ◽  
pp. 472-473
Author(s):  
A.M. Jones ◽  
A. Max Fiskin
Keyword(s):  
Three Dimensional ◽  
Depth Of Field ◽  
Computer Assisted ◽  
Projection Data ◽  
Two Dimensional ◽  
Single Particles ◽  
Dimensional Reconstruction ◽  
Computer Assisted Image ◽  
The Fourier Transform ◽  
Space Approach

If the tilt of a specimen can be varied either by the strategy of observing identical particles orientated randomly or by use of a eucentric goniometer stage, three dimensional reconstruction procedures are available (l). If the specimens, such as small protein aggregates, lack periodicity, direct space methods compete favorably in ease of implementation with reconstruction by the Fourier (transform) space approach (2). Regardless of method, reconstruction is possible because useful specimen thicknesses are always much less than the depth of field in an electron microscope. Thus electron images record the amount of stain in columns of the object normal to the recording plates. For single particles, practical considerations dictate that the specimen be tilted precisely about a single axis. In so doing a reconstructed image is achieved serially from two-dimensional sections which in turn are generated by a series of back-to-front lines of projection data.

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