Quantum trajectories in complex phase space: Multidimensional barrier transmission

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.

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Integrability of a Coupled Harmonic Oscillator in Extended Complex Phase Space

The interdisciplinary journal of Discontinuity Nonlinearity and Complexity ◽

10.5890/dnc.2015.03.004 ◽

2015 ◽

Vol 4 (1) ◽

pp. 35-48

Author(s):

Ram Mehar Singh

Keyword(s):

Phase Space ◽

Harmonic Oscillator ◽

Complex Phase ◽

Extended Complex ◽

Coupled Harmonic Oscillator

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Lie Series and Canonical Transformations in Complex Phase Space

Zeitschrift für Naturforschung A ◽

10.1515/zna-1988-0504 ◽

1988 ◽

Vol 43 (5) ◽

pp. 411-418 ◽

Cited By ~ 1

Author(s):

B. Bruhn

Keyword(s):

Phase Space ◽

Generating Function ◽

Series Representation ◽

Canonical Transformations ◽

Lie Series ◽

Complex Phase ◽

Lie Transformations ◽

Complex Valued

This paper considers the Lie series representation of the canonical transformations in a complex phase space. A condition is given which selects the canonical mappings from the Lie transformations associated with a complex-valued generating function. Some special types of mappings and some simple algebraic tools are discussed.

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

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887817501419 ◽

2017 ◽

Vol 14 (10) ◽

pp. 1750141 ◽

Cited By ~ 1

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.

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Complex dynamical invariants for two-dimensional nonhermitian Hamiltonian systems

Canadian Journal of Physics ◽

10.1139/p11-152 ◽

2012 ◽

Vol 90 (2) ◽

pp. 151-157 ◽

Cited By ~ 6

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.

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