Geometry of Lagrangian manifolds and the canonical Maslov operator in complex phase space

1980 ◽  
Vol 13 (1) ◽  
pp. 1-23
Author(s):  
A. S. Mishchenko ◽  
B. Yu. Sternin ◽  
V. E. Shatalov
Keyword(s):  
Phase Space ◽  
Complex Phase ◽  
Canonical Maslov Operator ◽  
Lagrangian Manifolds ◽  
Maslov Operator

Canonical Maslov operator on Lagrangian manifolds with Hilbert model

1990 ◽  
Vol 48 (6) ◽  
pp. 1206-1213 ◽  
Author(s):  
A. Yu. Daletskii
Keyword(s):  
Canonical Maslov Operator ◽  
Lagrangian Manifolds ◽  
Maslov Operator

scholarly journals Tunneling mechanism due to chaos in a complex phase space

2001 ◽  
Vol 64 (2) ◽  
Author(s):  
T. Onishi ◽  
A. Shudo ◽  
K. S. Ikeda ◽  
K. Takahashi
Keyword(s):  
Phase Space ◽  
Complex Phase ◽  
Tunneling Mechanism

Quantum trajectories in complex phase space: Multidimensional barrier transmission

2007 ◽  
Vol 127 (4) ◽  
pp. 044103 ◽  
Author(s):  
Robert E. Wyatt ◽  
Brad A. Rowland
Keyword(s):  
Phase Space ◽  
Quantum Trajectories ◽  
Complex Phase

Generalizing the Boltzmann equation in complex phase space

2016 ◽  
Vol 94 (2) ◽  
Author(s):  
Abed Zadehgol
Keyword(s):  
Boltzmann Equation ◽  
Phase Space ◽  
Complex Phase ◽  
The Boltzmann Equation

scholarly journals Chaotic systems in complex phase space

Pramana ◽  
2009 ◽  
Vol 73 (3) ◽  
pp. 453-470 ◽  
Author(s):  
Carl M. Bender ◽  
Joshua Feinberg ◽  
Daniel W. Hook ◽  
David J. Weir
Keyword(s):  
Phase Space ◽  
Chaotic Systems ◽  
Complex Phase

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.

Lie Series and Canonical Transformations in Complex Phase Space

1988 ◽  
Vol 43 (5) ◽  
pp. 411-418 ◽  
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.

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.

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