scholarly journals Induction of chaotic fluctuations in particle dynamics in a uniformly accelerated frame

2020 ◽  
Vol 35 (18) ◽  
pp. 2050081 ◽  
Author(s):  
Surojit Dalui ◽  
Bibhas Ranjan Majhi ◽  
Pankaj Mishra
Keyword(s):  
Harmonic Oscillator ◽  
Integrable System ◽  
Chaotic Motion ◽  
Gravitational Effect ◽  
Particle Dynamics ◽  
Harmonic Potential ◽  
Intrinsic Curvature ◽  
Killing Horizon ◽  
Periodic State

The ongoing conjecture that the presence of horizon may induce chaos in an integrable system, is further investigated from the perspective of a uniformly accelerated frame. Particularly, we build up a model which consists of a particle (massless and chargeless) trapped in harmonic oscillator in a uniformly accelerated frame (namely Rindler observer). Here, the Rindler frame provides a Killing horizon without any intrinsic curvature to the system. This makes the present observations different from previous studies. We observe that for some particular values of parameters of the system (like acceleration, energy of the particle), the motion of the particle trapped in harmonic potential systematically goes from periodic state to the chaotic. This indicates that the existence of horizon alone, not the intrinsic curvature (i.e. the gravitational effect) in the background, is sufficient to induce the chaotic motion in the particle. We believe the present study further enlighten and balustrade the conjecture.

scholarly journals A COHERENT STATE PATH INTEGRAL FOR ANYONS

1995 ◽  
Vol 10 (12) ◽  
pp. 985-989 ◽  
Author(s):  
J. GRUNDBERG ◽  
T.H. HANSSON
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Path Integral ◽  
Coherent States ◽  
Integral Formula ◽  
Harmonic Potential ◽  
One Dimensional ◽  
Change Of Variables ◽  
The One ◽  
State Path

We derive an su (1, 1) coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to an su (1, 1) version of the Holstein-Primakoff transformation.

Particle dynamics in a virtual harmonic potential

2013 ◽  
Author(s):  
Momčilo Gavrilov ◽  
Yonggun Jun ◽  
John Bechhoefer
Keyword(s):  
Particle Dynamics ◽  
Harmonic Potential

Eigenvalues of the Potential Function V=z4±Bz2 and the Effect of Sixth Power Terms

1970 ◽  
Vol 24 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Jaan Laane
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Potential Function ◽  
Schrodinger Equation ◽  
Harmonic Potential ◽  
Reduced Form ◽  
Approximation Formula ◽  
One Dimensional ◽  
Ring Puckering ◽  
The One

The one-dimensional Schrödinger equation in reduced form is solved for the potential function V = z4+ Bz2 where B may be positive or negative. The first 17 eigenvalues are reported for 58 values of B in the range −50⩽ B⩽100. The interval of B between the tabulated values is sufficiently small so that the eigenvalues for any B in this range can be found by interpolation. At the limits of the range of B the potential function approaches that of a harmonic oscillator with only small anharmonicity. The effect of a small Cz6 term on this potential is studied and it is concluded that a previously reported approximation formula is quite applicable but only for positive values of B. The success of the quartic—harmonic potential function for the analysis of the ring-puckering vibration is shown; it is also demonstrated that the same potential serves as a useful approximation for many other systems, especially those of the double minimum type.

ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS

2000 ◽  
Vol 10 (09) ◽  
pp. 2075-2098 ◽  
Author(s):  
JAN WIERSIG
Keyword(s):  
Harmonic Oscillator ◽  
Energy Dependence ◽  
Invariant Tori ◽  
Low Energy ◽  
Action Space ◽  
Harmonic Potential ◽  
Classical Dynamics ◽  
Isotropic Harmonic Oscillator ◽  
Energy Surfaces ◽  
Action Variables

The classical dynamics of the triaxial ellipsoidal billiard with isotropic harmonic potential attracting to the center of the ellipsoid is discussed. The integrability preserving potential introduces an energy dependence to the foliation of energy shells into invariant tori. This foliation and the character of the corresponding motion is described in terms of 13 qualitatively different energy surfaces in the space of the action variables. Frequencies and the location of resonances are calculated. The consequences of the superintegrability of the low-energy case, the isotropic harmonic oscillator, for the energy surfaces in action space are investigated.

LATTICE EQUILIBRIUM THEORY AND SIZE EFFECTS FOR BOSONS IN A BOUNDED HARMONIC POTENTIAL

2006 ◽  
Vol 20 (02) ◽  
pp. 151-179 ◽  
Author(s):  
S. LUMB ◽  
S. K. MUTHU ◽  
K. K. SINGH
Keyword(s):  
Harmonic Oscillator ◽  
Size Effects ◽  
General Structure ◽  
Energy Levels ◽  
Ideal Gas ◽  
Harmonic Potential ◽  
Thermodynamic Quantities ◽  
Self Consistent ◽  
Spatial Size ◽  
Crossover Parameter

Effects of finite spatial size of boson assemblies in traps are studied in a self-consistent lattice theory by modeling the trap as a bounded harmonic potential of size R0. The thermodynamic quantities exhibit scaling and crossover from ideal gas behaviour at small (R0/a0) to that appropriate to an unbounded harmonic potential at large (R0/a0) with a crossover parameter [Formula: see text], a0 being the harmonic oscillator length, and τ denoting the dimensionless thermal energy. The numerical results obtained earlier by computing the energy levels of the bounded harmonic oscillator fit the general structure predicted by the theory very well. For a1>10, the spatial size effects are negligible but for a1<10 they become appreciable and experimentally measurable in suitably designed traps. At low temperatures the self consistent cell size is found to be about 2.5a0 implying that the condensate is essentially a single coherent state contained in the central cell.

scholarly journals QUANTUM GRAVITATIONAL CORRECTIONS TO THE HYDROGEN ATOM AND HARMONIC OSCILLATOR

2010 ◽  
Vol 19 (02) ◽  
pp. 137-151 ◽  
Author(s):  
MICHAEL MAZIASHVILI ◽  
ZURAB SILAGADZE
Keyword(s):  
Quantum Mechanics ◽  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Opposite Sign ◽  
Energy Levels ◽  
Gravitational Effect ◽  
Energy Shift ◽  
Space Time ◽  
Minimum Length ◽  
Time Dimension

It is shown that the rate of corrections to the hydrogen atom and harmonic oscillator energy levels due to the profound quantum gravitational effect of space–time dimension running/reduction coincides well with those obtained by means of minimum-length-deformed quantum mechanics. The rate of corrections is pretty much the same within the accuracy with which we can judge the quantum gravitational corrections at all. Such a convergence of results makes the concept of space–time dimension running more appreciable. As a remarkable distinction, the energy shift due to dimension reduction has the opposite sign as compared with the correction obtained by means of minimum-length-modified quantum mechanics. Therefore, the sign of total quantum gravitational correction remains somewhat obscure.

THE PATH INTEGRAL APPROACH TO AN N-PARTICLE IN A PT-SYMMETRIC HARMONIC OSCILLATOR

2010 ◽  
Vol 24 (28) ◽  
pp. 5579-5587
Author(s):  
SIKARIN YOO-KONG
Keyword(s):  
Harmonic Oscillator ◽  
Total Energy ◽  
Path Integral ◽  
Path Integrals ◽  
Harmonic Potential ◽  
Integral Approach ◽  
Path Integral Approach ◽  
System Of Particles

We study a path integral approach to a system of particles in a PT-symmetric harmonic potential: V(x)=mω2(x2±2iεx)/2. The eigenvalues and eigenstates of the system have been calculated. We find that the total energy of the system is real. The connection between the non-Hermitian and Hermitian Hamiltonians has been discussed and we also establish this connection in the context of path integrals via a considering model.

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