WAVE FUNCTION OF THE PARTICLE TRAPPED BY OSCILLATING FIELDS

1994 ◽  
Vol 08 (25) ◽  
pp. 1549-1553
Author(s):  
CÉLIA M.A. DANTAS ◽  
V.S. BAGNATO ◽  
B. BASEIA
Keyword(s):  
Wave Function ◽  
Linear Time ◽  
Recent Model ◽  
Time Dependent ◽  
Squeezing Effect ◽  
Particle Trapping ◽  
Present Procedure

In a previous paper [Quantum Opt.5, 155 (1993)] we have employed a recent model by Glauber for particle trapping by oscillating fields to investigate the occurrence of the squeezing effect for this system. Here we construct a linear time-dependent invariant which allows us to obtain the wave function of the system. The treatment is general for a class of time-dependent Hamiltonian, the application to our previous work being a particularization of the present procedure.

DISSIPATIVE DYNAMICS OF A SINGLE PARTICLE IN AN ION TRAP

2000 ◽  
Vol 14 (09) ◽  
pp. 993-1006
Author(s):  
C. F. LO ◽  
D. KIANG
Keyword(s):  
Time Evolution ◽  
Single Particle ◽  
Ion Trap ◽  
Time Dependent ◽  
Squeezing Effect ◽  
Particle Trapping ◽  
Model Particle ◽  
Dissipative Dynamics ◽  
Quantum Time

In this paper we have investigated the time evolution of a dissipative quantum time-dependent oscillator which can be used to model particle trapping in an ion trap. Our analysis shows that the nonadiabatic changes in the oscillator mass and/or frequency as well as the dissipation constitute two competing forces on the squeezing properties of the system — the former helps generate the squeezing effect whereas the latter tries to destroy it.

GEOMETRIC PHASES, SQUEEZED QUANTUM STATES AND GAUSSIAN WAVE PACKET STATES OF RELIC GRAVITONS

2012 ◽  
Vol 18 ◽  
pp. 13-17
Author(s):  
K. BAKKE ◽  
I. A. PEDROSA ◽  
C. FURTADO
Keyword(s):  
Wave Packet ◽  
Linear Time ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Gaussian Wave Packet ◽  
Geometric Phases ◽  
Uncertainty Product ◽  
Quantized Field ◽  
Generalized Time

In this contribution, we discuss quantum effects on relic gravitons described by the Friedmann-Robertson-Walker (FRW) spacetime background by reducing the problem to that of a generalized time-dependent harmonic oscillator, and find the corresponding Schrödinger states with the help of the dynamical invariant method. Then, by considering a quadratic time-dependent invariant operator, we show that we can obtain the geometric phases and squeezed quantum states for this system. Furthermore, we also show that we can construct Gaussian wave packet states by considering a linear time-dependent invariant operator. In both cases, we also discuss the uncertainty product for each mode of the quantized field.

scholarly journals LINEAR TIME-DEPENDENT INVARIANTS FOR SCALAR FIELDS AND NOETHER’S THEOREM

1994 ◽  
Vol 09 (19) ◽  
pp. 1785-1790 ◽  
Author(s):  
O. CASTAÑOS ◽  
R. LÓPEZ-PEÑA ◽  
V.I. MAN’KO
Keyword(s):  
Scalar Field ◽  
Infinite Number ◽  
Linear Time ◽  
Scalar Fields ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure.

Properties of Linear Time-Dependent Systems

2020 ◽  
pp. 271-290
Author(s):  
Sandor Molnar ◽  
Mark Molnar
Keyword(s):  
Linear Time ◽  
Time Dependent
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