Fluctuations, Dissipation, and Noise

2019 ◽  
pp. 325-408
Author(s):  
Peter W. Milonni
Keyword(s):  
Brownian Motion ◽  
Noise Figure ◽  
Heat Bath ◽  
Radiation Reaction ◽  
Langevin Equations ◽  
Photon Statistics ◽  
Laser Linewidth ◽  
Homodyne Detection ◽  
Fluctuation Dissipation ◽  
Fundamental Laser

General concepts in the theory of fluctuations and dissipation are reviewed and applied to examples in quantum optics. Brownian motion, Fokker-Planck and Langevin equations, and the Wiener-Khintchine theorem are reviewed, followed by a derivation and discussion of the fluctuation-dissipation theorem. The general problem of an oscillator coupled to a heat bath is revisited, as is the nonrelativistic theory of radiation reaction. The general ideas about fluctuations and dissipation developed in the first part of the chapter are then applied to the theory of the fundamental laser linewidth, the photon statistics of linear amplifiers and attenuators, the noise figure, amplified spontaneous emission, and the quantum theory of the beam slitter and homodyne detection.

Interaction Hamiltonian and Spontaneous Emission

2019 ◽  
pp. 205-268
Author(s):  
Peter W. Milonni
Keyword(s):  
Field Theory ◽  
Spontaneous Emission ◽  
Electric Dipole ◽  
Radiation Reaction ◽  
Vacuum Field ◽  
Coupling Interaction ◽  
Fluctuation Dissipation ◽  
Level Shifts ◽  
Field Fluctuations ◽  
Quantized Field

The atom-field interaction is formulated within the fully quantized-field theory, starting from a detailed analysis of the transformation from the fundamental minimal coupling interaction Hamiltonian to the electric dipole Hamiltonian used extensively in quantum optics. Spontaneous emission, radiative level shifts, and the natural radiative lineshape are treated in both the Schrodinger and Heisenberg pictures, with emphasis on the roles of vacuum field fluctuations, radiation reaction, and the fluctuation-dissipation relation between them. The shortcomings of semiclassical radiation theories are discussed.

Sampling of photon statistics and density matrix using homodyne detection

1996 ◽  
Vol 127 (1-3) ◽  
pp. 144-160 ◽  
Author(s):  
U Leonhardt ◽  
M Munroe ◽  
T Kiss ◽  
Th Richter ◽  
M.G Raymer
Keyword(s):  
Density Matrix ◽  
Photon Statistics ◽  
Homodyne Detection

scholarly journals Energetics of Poisson–Kac Stochastic Processes Possessing Finite Propagation Velocity

2016 ◽  
Vol 41 (2) ◽  
Author(s):  
Antonio Brasiello ◽  
Massimiliano Giona ◽  
Silvestro Crescitelli
Keyword(s):  
Large Time ◽  
Coarse Grained ◽  
Langevin Equations ◽  
Stochastic Forcing ◽  
Stochastic Perturbations ◽  
Wiener Processes ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Almost Everywhere ◽  
Large Time Limit

AbstractA local fluctuation–dissipation theorem for the power delivered by a stochastic forcing is derived for Ornstein–Uhlenbeck processes driven by smooth, i. e. almost everywhere (a. e.)-differentiable stochastic perturbations (Poisson–Kac processes). An analytic expression for the probability density function of the fluctuational power is obtained in the large time limit. As these processes converge, in the Kac limit, toward classical Langevin equations driven by Wiener processes, a coarse-grained analysis of the statistical properties of the fluctuational work is developed.

scholarly journals QUANTUM-LIOUVILLE AND LANGEVIN EQUATIONS FOR GRAVITATIONAL RADIATION DAMPING

2002 ◽  
Vol 17 (26) ◽  
pp. 3729-3736 ◽  
Author(s):  
Z. HABA ◽  
H. KLEINERT
Keyword(s):  
Master Equation ◽  
Path Integral ◽  
Langevin Equation ◽  
Gravitational Radiation ◽  
Heat Bath ◽  
Radiation Damping ◽  
Langevin Equations ◽  
Quantum Object ◽  
Dense Stars

From a forward–backward path integral, we derive a master equation for the emission and absorption of gravitons by a massive quantum object in a heat bath of gravitons. Such an equation could describe the collapse phenomena of dense stars. We also present a useful approximate Langevin equation for such a system.

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