scholarly journals Origin of the anomalies: The modified Heisenberg equation

2002 ◽  
Vol 66 (12) ◽  
Author(s):  
J. G. Esteve
Keyword(s):  
Heisenberg Equation

Wigner Representation for Investigation of Entangled Photon Evolution in Four-Wave Mixing Process within a Fiber Ring Resonator

2015 ◽  
Vol 804 ◽  
pp. 316-320
Author(s):  
Chatchawal Sripakdee
Keyword(s):  
Ring Resonator ◽  
Equations Of Motion ◽  
Numerical Approach ◽  
Equation Of Motion ◽  
Nonlinear Susceptibility ◽  
Heisenberg Equation ◽  
Fiber Ring ◽  
Wigner Representation ◽  
Fiber Ring Resonator ◽  
Photon States

The aim of this study is to analyze the quantum correlation of entangled photons for four-wavemixing process within Kerr nonlinear susceptibility χ(3) of an optical fiber ring resonator. The main system Hamiltonian composes of two types of coupling photon modes, including pumping and parametric-down conversion. Wigner representation is applied to the Heisenberg equation of motion derived from the system Hamiltonian in order to obtain the corresponding stochastic equations of motion in a c-number. Quantum trajectories obtained from the stochastic equation of motion of photon states are then derived. Finally, the entanglement inseparability criteria for a pair of entangled photonfrom a numerical approach is also satisfied.

scholarly journals Non-Markovian features in semiconductor quantum optics: quantifying the role of phonons in experiment and theory

Nanophotonics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 655-683 ◽  
Author(s):  
Alexander Carmele ◽  
Stephan Reitzenstein
Keyword(s):  
Quantum Electrodynamics ◽  
Theoretical Models ◽  
Cavity Quantum Electrodynamics ◽  
Heisenberg Equation ◽  
Linear Absorption ◽  
Electron Phonon Interaction ◽  
Two Photon ◽  
Quantum State Preparation ◽  
Path Integral Method

AbstractWe discuss phonon-induced non-Markovian and Markovian features in QD-based quantum nanooptics. We cover lineshapes in linear absorption experiments, phonon-induced incoherence in the Heitler regime, and memory correlations in two-photon coherences. To qualitatively and quantitatively understand the underlying physics, we present several theoretical models that capture the non-Markovian properties of the electron–phonon interaction accurately in different regimes. Examples are the Heisenberg equation of motion approach, the polaron master equation, and Liouville propagator techniques in the independent boson limit and beyond via the path integral method. Phenomenological modeling overestimates typically the dephasing due to the finite memory kernel of phonons and we give instructive examples of phonon-mediated coherence such as phonon-dressed anticrossings in Mollow physics, robust quantum state preparation, cavity feeding, and the stabilization of the collapse and revival phenomenon in the strong coupling limit of cavity quantum electrodynamics.

On the solutions of the anisotropic Heisenberg equation

1994 ◽  
Vol 27 (16) ◽  
pp. 5607-5621 ◽  
Author(s):  
N A Belov ◽  
A N Leznov ◽  
W J Zakrzewski
Keyword(s):  
Heisenberg Equation

scholarly journals NOISE AND DISSIPATION IN QUANTUM THEORY

1990 ◽  
Vol 02 (02) ◽  
pp. 127-176 ◽  
Author(s):  
LUIGI ACCARDI
Keyword(s):  
Quantum Theory ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Langevin Equation ◽  
Equations Of Motion ◽  
Natural Generalization ◽  
Usual Sense ◽  
Heisenberg Equation ◽  
Generalized Langevin Equation ◽  
Solid State Physics

A model independent generalization of quantum mechanics, including the usual as well as the dissipative quantum systems, is proposed. The theory is developed deductively from the basic principles of the standard quantum theory, the only new qualitative assumption being that we allow the wave operator at time t of a quantum system to be non-differentiable (in t) in the usual sense, but only in an appropriately defined (Sec. 5) stochastic sense. The resulting theory is shown to lead to a natural generalization of the usual quantum equations of motion, both in the form of the Schrödinger equation in interaction representation (Sec. 6) and of the Heisenberg equation (Sec. 8). The former equation leads in particular to a quantum fluctuation-dissipation relation of Einstein’s type. The latter equation is a generalized Langevin equation, from which the known form of the generalized master equation can be deduced via the quantum Feynmann-Kac technique (Secs. 9 and 10). For quantum noises with increments commuting with the past the quantum Langevin equation defines a closed system of (usually nonlinear) stochastic differential equations for the observables defining the coefficients of the noises. Such systems are parametrized by certain Lie algebras of observables of the system (Sec. 10). With appropriate choices of these Lie algebras one can deduce generalizations and corrections of several phenomenological equations previously introduced at different times to explain different phenomena. Two examples are considered: the Lie algebra [q, p]=i (Sec. 12), which is shown to lead to the equations of the damped harmonic oscillator; and the Lie algebra of SO(3) (Sec. 13) which is shown to lead to the Bloch equations. In both cases the equations obtained are independent of the model of noise. Moreover, in the former case, it is proved that the only possible noises which preserve the commutation relations of p, q are the quantum Brownian motions, commonly used in laser theory and solid state physics.

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