scholarly journals New Neumerical Method to Calculate Time-Dependent Quantum Properties in Finite Temperature Based on the Heisenberg Equation of Motion

2012 ◽  
Vol 03 (10) ◽  
pp. 1537-1549 ◽  
Author(s):  
Shin-Ichiro Kondo
Keyword(s):  
Finite Temperature ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Quantum Properties

WEHRL ENTROPY AND ENTANGLEMENT OF A TIME-DEPENDENT TWO-LEVEL TRAPPED ION INTERACTING WITH A LASER FIELD

2008 ◽  
Vol 06 (02) ◽  
pp. 331-339
Author(s):  
MAHMOUD ABDEL-ATY ◽  
SAYED ABDEL-KHALEK ◽  
ABDEL-SHAFY F. OBADA
Keyword(s):  
Exact Solution ◽  
Time Evolution ◽  
Laser Field ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Wehrl Entropy ◽  
Entanglement Generation ◽  
Trapped Ion ◽  
Cat States

The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.

COMMUTATION RELATIONS AND SELF-CONSISTENCY IN ELECTRODYNAMICS FOR THE FIELDS IN TIME-VARYING MEDIA

2008 ◽  
Vol 22 (03) ◽  
pp. 267-280 ◽  
Author(s):  
JEONG RYEOL CHOI ◽  
JUN-YOUNG OH
Keyword(s):  
Commutation Relation ◽  
Operator Method ◽  
Equation Of Motion ◽  
Invariant Operator ◽  
Time Dependent ◽  
Heisenberg Equation ◽  
Time Varying ◽  
Commutation Relations ◽  
Self Consistent ◽  
Self Consistency

In linear media with time-dependent parameters, various commutation relations for the field operators obtained from the Lewis–Riesenfeld invariant operator method are calculated. We investigated whether our development is self-consistent or not by evaluating the Heisenberg equation of motion for field operators using the associated commutation relation.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster

2019 ◽  
Vol 15 (12) ◽  
pp. 6617-6624 ◽  
Author(s):  
Lauren N. Koulias ◽  
David B. Williams-Young ◽  
Daniel R. Nascimento ◽  
A. Eugene DePrince ◽  
Xiaosong Li
Keyword(s):  
Real Time ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Coupled Cluster

scholarly journals Finite-temperature time-dependent variation with multiple Davydov states

2017 ◽  
Vol 146 (12) ◽  
pp. 124127 ◽  
Author(s):  
Lu Wang ◽  
Yuta Fujihashi ◽  
Lipeng Chen ◽  
Yang Zhao
Keyword(s):  
Finite Temperature ◽  
Time Dependent ◽  
Temperature Time
Sign in / Sign up

Export Citation Format

Share Document