Heisenberg Equations Approach

2019 ◽  
pp. 73-84
Author(s):  
Aniello Lampo ◽  
Miguel Ángel García March ◽  
Maciej Lewenstein
Keyword(s):  
Heisenberg Equations

scholarly journals Exact density matrix elements for a driven dissipative system described by a quadratic Hamiltonian

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sh. Saedi ◽  
F. Kheirandish
Keyword(s):  
Density Matrix ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Characteristic Functions ◽  
Matrix Elements ◽  
Exact Density ◽  
Quadratic Hamiltonian ◽  
Heisenberg Equations ◽  
Reduced Density ◽  
Heisenberg Equations Of Motion

AbstractFor a prototype quadratic Hamiltonian describing a driven, dissipative system, exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations of motion and operator calculus. The special and limiting cases are discussed.

scholarly journals Exact Solutions of the Heisenberg Equations and Zitterbewegung of the Electron in a Constant Uniform Magnetic Field

1982 ◽  
Vol 35 (4) ◽  
pp. 353 ◽  
Author(s):  
AO Barut ◽  
AJ Bracken
Keyword(s):  
Magnetic Field ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Internal Motion ◽  
Mass Motion ◽  
Internal Dynamics ◽  
Classical Motion ◽  
Dirac Electron ◽  
Heisenberg Equations

For a free Dirac electron, the Heisenberg equations define an internal dynamical system in the rest frame, isomorphic to a finite three-dimensional oscillator with a compact SO(5) phase space, such that the spin of the electron is the orbital angular momentum of the internal dynamics (Barut and Bracken 1980, 1981a). In the present work, the change in this internal dynamics due to an external magnetic field is studied. In order that the internal motion can be distinguished from the centre of mass motion, the solutions of the corresponding Hamilton and Heisenberg equations for the relativistic classical motion and the relativistic quantum mechanical spinless motion are also presented. The solutions for the electron exhibit the effect of the spin terms both in the internal motion and external motion, and we are able to identify the properties of the Zitterbewegung in the external field.

scholarly journals Quantum fluctuations of elementary excitations in discrete media

2004 ◽  
Vol 2004 (1) ◽  
pp. 169-177
Author(s):  
Hermann Haken
Keyword(s):  
Quantum Noise ◽  
General Theorem ◽  
Polymer Chains ◽  
Quantum Mechanical ◽  
Projection Operators ◽  
Noise Sources ◽  
Elementary Excitations ◽  
Heisenberg Equations ◽  
Discrete Media

Elementary excitations (electrons, holes, polaritons, excitons, plasmons, spin waves, etc.) on discrete substrates (e.g., polymer chains, surfaces, and lattices) may move coherently as quantum waves (e.g., Bloch waves), but also incoherently (“hopping”) and may lose their phases due to their interaction with their substrate, for example, lattice vibrations. In the frame of Heisenberg equations for projection operators, these latter effects are often phenomenologically taken into account, which violates quantum mechanical consistency, however. To restore it, quantum mechanical fluctuating forces (noise sources) must be introduced, whose properties can be determined by a general theorem. With increasing miniaturization, in the nanotechnology of logical devices (including quantum computers) that use interacting elementary excitations, such fluctuations become important. This requires the determination of quantum noise sources in composite quantum systems. This is the main objective of my paper, dedicated to the memory of Ilya Prigogine.

Heisenberg equations of motion in the Caldirola-Montaldi procedure

1982 ◽  
Vol 67 (2) ◽  
pp. 161-172 ◽  
Author(s):  
A. Jannussis ◽  
A. Leodaris ◽  
P. Filippakis ◽  
Th. Filippakis ◽  
V. Zisis
Keyword(s):  
Equations Of Motion ◽  
Heisenberg Equations ◽  
Heisenberg Equations Of Motion

Thermal effect in the resonance fluorescence of a two-level system

1991 ◽  
Vol 69 (11) ◽  
pp. 1367-1372
Author(s):  
C. H. A. Fonseca ◽  
L. A. Amarante Ribeiro
Keyword(s):  
Equations Of Motion ◽  
Normal Modes ◽  
Thermal Fluctuations ◽  
Harmonic Oscillators ◽  
Thermal Bath ◽  
Resonance Fluorescence ◽  
Level System ◽  
Near Resonance ◽  
Intensity Correlation Function ◽  
Heisenberg Equations

The damped two-level system, driven by a strong incident classical field near resonance frequency is subjected to the effect of thermal fluctuations. To simulate the thermal bath we introduce a large system of harmonic oscillators that represents the normal modes of the thermal radiation field. From the Heisenberg equations of motion we calculate the power spectrum of the scattered field and the intensity correlation function. The results show that the presence of the bath dramatically modifies the light scattered by the two-level system when compared with the case without a thermal bath.

QUANTUM TREATMENT OF A TIME DEPENDENT SINGLE-TRAPPED ION INTERACTING WITH A BIMODAL CAVITY FIELD

2003 ◽  
Vol 17 (31n32) ◽  
pp. 5925-5941 ◽  
Author(s):  
MAHMOUD ABDEL-ATY ◽  
A.-S. F. OBADA ◽  
M. SEBAWE ABDALLA
Keyword(s):  
Cross Correlation ◽  
Analytic Solution ◽  
Coupling Parameter ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Field Interaction ◽  
Trapped Ion ◽  
Heisenberg Equations ◽  
Quantum Treatment ◽  
Heisenberg Equations Of Motion

In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.

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