On the phase-space catastrophes in dynamics of the quantum particle in an optical lattice potential

2020 ◽  
Vol 30 (10) ◽  
pp. 103107
Author(s):  
M. Ćosić ◽  
S. Petrović ◽  
S. Bellucci
Keyword(s):  
Phase Space ◽  
Optical Lattice ◽  
Quantum Particle ◽  
Lattice Potential

scholarly journals The geometry of the Wigner caustic and a decomposition of a curve into parallel arcs

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Wojciech Domitrz ◽  
Michał Zwierzyński
Keyword(s):  
Rotation Number ◽  
Optical Lattice ◽  
Quantum Particle ◽  
Singular Points ◽  
Planar Curves ◽  
Lattice Potential ◽  
Global Properties ◽  
Important Object ◽  
Cusp Singularities ◽  
Regular Closed

AbstractIn this paper we study global properties of the Wigner caustic of parameterized closed planar curves. We find new results on its geometry and singular points. In particular, we consider the Wigner caustic of rosettes, i.e. regular closed parameterized curves with non-vanishing curvature. We present a decomposition of a curve into parallel arcs to describe smooth branches of the Wigner caustic. By this construction we can find the number of smooth branches, the rotation number, the number of inflexion points and the parity of the number of cusp singularities of each branch. We also study the global properties of the Wigner caustic on shell (the branch of the Wigner caustic connecting two inflexion points of a curve). We apply our results to whorls—the important object to study the dynamics of a quantum particle in the optical lattice potential.

Regular and chaotic solutions in BEC for tilted bichromatical optical lattice

2018 ◽  
Vol 32 (23) ◽  
pp. 1850254
Author(s):  
Eren Tosyali ◽  
Fatma Aydogmus ◽  
Ayberk Yilmaz
Keyword(s):  
Shock Wave ◽  
Phase Space ◽  
Power Spectrum ◽  
Lyapunov Exponents ◽  
Optical Lattice ◽  
Einstein Condensate ◽  
System Parameters ◽  
Lattice Potential ◽  
Bose Einstein Condensate ◽  
Bose Einstein

We investigate a Bose–Einstein condensate held in a 1D tilted bichromatical optical lattice potential by constructing its Poincaré sections in phase space. We explore dynamic of the system based on the relations between the system parameters and the solution behaviors. It is demonstrated that the system exhibits shock-wave like dynamic. The power spectrum graphs, bifurcation and Lyapunov exponents of BEC system are also presented.

A REPRESENTATION OF THE BELAVKIN EQUATION VIA PHASE SPACE FEYNMAN PATH INTEGRALS

2004 ◽  
Vol 07 (04) ◽  
pp. 507-526 ◽  
Author(s):  
S. ALBEVERIO ◽  
G. GUATTERI ◽  
S. MAZZUCCHI
Keyword(s):  
Phase Space ◽  
Continuous Measurement ◽  
Quantum Particle ◽  
Oscillatory Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Infinite Dimensional ◽  
Feynman Path Integrals ◽  
Characteristics Method ◽  
Stochastic Characteristics

The Belavkin equation, describing the continuous measurement of the momentum of a quantum particle, is studied. The existence and uniqueness of its solution is proved via analytic tools. A stochastic characteristics method is applied. A rigorous representation of the solution by means of an infinite dimensional oscillatory integral (Feynman path integral) defined on the phase space is also given.

scholarly journals Atoms trapped by a spin-dependent optical lattice potential: Realization of a ground-state quantum rotor

2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Igor Kuzmenko ◽  
Tetyana Kuzmenko ◽  
Y. Avishai ◽  
Y. B. Band
Keyword(s):  
Ground State ◽  
Optical Lattice ◽  
Lattice Potential

scholarly journals High Phase-Space Density of Laser-Cooled Molecules in an Optical Lattice

2021 ◽  
Vol 127 (26) ◽  
Author(s):  
Yewei Wu ◽  
Justin J. Burau ◽  
Kameron Mehling ◽  
Jun Ye ◽  
Shiqian Ding
Keyword(s):  
Phase Space ◽  
Optical Lattice ◽  
Phase Space Density ◽  
Space Density ◽  
High Phase

EQUIVALENCE OF STOCHASTIC, KLAUDER AND GEOMETRIC QUANTIZATION

1992 ◽  
Vol 07 (06) ◽  
pp. 1267-1285 ◽  
Author(s):  
K. HAJRA ◽  
P. BANDYOPADHYAY
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Gauge Field ◽  
Quantum Particle ◽  
Group Structure ◽  
Relativistic Quantum ◽  
Geometric Quantization ◽  
Geometrical Approach ◽  
Sharp Point ◽  
Space Formulation

The relativistic generalization of stochastic quantization helps us to introduce a stochastic-phase-space formulation when a relativistic quantum particle appears as a stochastically extended one. The nonrelativistic quantum mechanics is obtained in the sharp point limit. This also helps us to introduce a gauge-theoretical extension of a relativistic quantum particle when for a fermion the group structure of the gauge field is SU(2). The sharp point limit is obtained when we have a minimal contribution of the residual gauge field retained in the limiting procedure. This is shown to be equivalent to the geometrical approach to the phase-space quantization introduced by Klauder if it is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher-dimensional configuration space when quantization corresponds to freezing the particle to its first Landau level. The geometric quantization then appears as a natural consequence of these two formalisms, since the Hermitian line bundle introduced there finds a physical meaning in terms of the inherent gauge field in stochastic-phase-space formulation or in the interaction with the magnetic field in Klauder quantization.

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