scholarly journals One-photon wave packet interacting with two separated atoms in a one-dimensional waveguide: Influence of virtual photons

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
S. Derouault ◽  
M. A. Bouchene
Keyword(s):  
Wave Packet ◽  
One Dimensional ◽  
Virtual Photons

The motion of a particle in a periodic field of force

1928 ◽  
Vol 24 (3) ◽  
pp. 447-450
Author(s):  
S. L. Malurkar ◽  
J. Hargreaves
Keyword(s):  
Wave Packet ◽  
Uncertainty Relation ◽  
Classical Dynamics ◽  
Electron Theory ◽  
Periodic Field ◽  
Periodic Term ◽  
One Dimensional ◽  
De Broglie Waves ◽  
Suitable Combination

The electron theory of metals revived by Sommerfeld assumes that an electron moves in a metal as though this were an equipotential medium. Considering the nuclei fixed and regularly spaced we obtain a potential periodic in space coordinates. To study the effect of such fields we may simplify the problem so as to contain only one periodic term for each coordinate in its expression for potential. This problem can be reduced further to a one-dimensional one, of which the simplest example is the motion of an electron in a field with potential cos x or sin x. Darwin has shown that a suitable combination or packet of elementary de Broglie waves is capable of moving coherently in several instances. The motion of such a packet is found to be equivalent to that of a particle in classical dynamics with the Heissenberg uncertainty relation. The wave packet is used here for the motion of the electron in a periodic field. The result obtained is equivalent to that of classical dynamics. The wave packet again moves as a particle with an uncertainty relation.

Asymptotic estimate for the counting problems corresponding to the dynamical system on some decorated graphs

2017 ◽  
Vol 38 (5) ◽  
pp. 1697-1708 ◽  
Author(s):  
V. L. CHERNYSHEV ◽  
A. A. TOLCHENNIKOV
Keyword(s):  
Dynamical System ◽  
Wave Packet ◽  
General Theorem ◽  
Three Dimensional ◽  
Initial Time ◽  
Dimensional Torus ◽  
Counting Problems ◽  
One Dimensional ◽  
Moving Points ◽  
Narrow Wave

We study a topological space obtained from a graph via replacing vertices with smooth Riemannian manifolds, that is, a decorated graph. We consider the following dynamical system on decorated graphs. Suppose that, at the initial time, we have a narrow wave packet on a one-dimensional edge. It can be thought of as a point moving along the edge. When a packet arrives at the point of gluing, the expanding wavefront begins to spread on the Riemannian manifold. At the same time, there is a partial reflection of the wave packet. When the wavefront that propagates on the surface comes to another point of gluing, it generates a reflected wavefront and a wave packet on an edge. We study the number of Gaussian packets, that is, moving points on one-dimensional edges as time goes to infinity. We prove the asymptotic estimations for this number for the following decorated graphs: a cylinder with an interval, a two-dimensional torus with an interval and a three-dimensional torus with an interval. Also we prove a general theorem about a manifold with an interval and apply it to the case of a uniformly secure manifold.

scholarly journals Non-Markovianity induced by a single-photon wave packet in a one-dimensional waveguide

2016 ◽  
Vol 41 (13) ◽  
pp. 3126 ◽  
Author(s):  
D. Valente ◽  
M. F. Z. Arruda ◽  
T. Werlang
Keyword(s):  
Wave Packet ◽  
Single Photon ◽  
One Dimensional

QUANTUM EFFECTS OF A PARTICLE IN AN INFINITE SQUARE WELL WITH A MOVING WALL

2000 ◽  
Vol 14 (10) ◽  
pp. 1059-1065 ◽  
Author(s):  
JIAN ZOU ◽  
BIN SHAO
Keyword(s):  
Wave Packet ◽  
Boundary Conditions ◽  
Coherent State ◽  
Dynamical Behavior ◽  
Squeezed State ◽  
Initial State ◽  
One Dimensional ◽  
Moving Wall ◽  
Quantum Behavior ◽  
Square Well

The quantum behavior of a particle in a one-dimensional infinite square well potential with a moving wall is studied. The particle is assumed to be initially prepared in the coherent state (Gaussian wave packet) and although the boundary is far from the particle, it is shown that the changing of the boundary conditions can instantaneously affect the dynamical behavior of the particle. It is also shown that the initial state can evolve into a squeezed state, and in some cases the spreading of the wavepacket could be suppressed. Finally the Pancharatnam phase is also discussed.

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