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
2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Wojciech Domitrz ◽  
Michał Zwierzyński

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.


2018 ◽  
Vol 32 (23) ◽  
pp. 1850254
Author(s):  
Eren Tosyali ◽  
Fatma Aydogmus ◽  
Ayberk Yilmaz

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.


Author(s):  
S. ALBEVERIO ◽  
G. GUATTERI ◽  
S. MAZZUCCHI

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.


2019 ◽  
Vol 100 (3) ◽  
Author(s):  
Igor Kuzmenko ◽  
Tetyana Kuzmenko ◽  
Y. Avishai ◽  
Y. B. Band

2021 ◽  
Vol 127 (26) ◽  
Author(s):  
Yewei Wu ◽  
Justin J. Burau ◽  
Kameron Mehling ◽  
Jun Ye ◽  
Shiqian Ding

1992 ◽  
Vol 07 (06) ◽  
pp. 1267-1285 ◽  
Author(s):  
K. HAJRA ◽  
P. BANDYOPADHYAY

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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