Lasers

Fain, V. M.; Khanin, Ya I

doi:10.1016/b978-0-08-012238-0.50009-8

Cited by 18 publications

(29 citation statements)

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“…The formula (3.27) is the extension of (3.29) for a quantum perturbation of the form (1.2). The spectral power, which, for a classical stationary random function, is just the Fourier transform of the correlation function, is replaced here by the quantum symmetric correlation function [14]. The energy relaxation rate due to reservoir fluctuations is exactly what we would expect on a physical basis : it is the power absorbed by 8 when it is driven by reservoir fluctuations.…”

Section: Relaxation Rates Of Energymentioning

confidence: 99%

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Dynamics of a small system coupled to a reservoir : reservoir fluctuations and self-reaction

1984

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Section: Relaxation Rates Of Energymentioning

confidence: 99%

“…When the emission process is completed, the angular momentum ends in the lower level J, -J & # x 3 E ; . Vacuum fluctuation effects play again a very important role ; they exactly balance the energy loss due to self reaction, ensuring the stability of the ground state [14]. Appendix A.…”

Section: Early Stage Of the Emission Processmentioning

confidence: 99%

Dynamics of a small system coupled to a reservoir : reservoir fluctuations and self-reaction

1984

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“…The canonical variables are p = n ω 1 n 0 ω 3 and q = ϕ 1 + ϕ 2 − 2ϕ 3 , where ϕ j are the phases of complex amplitudes, n ω j are the photon flux densities in the corresponding modes, and the normalization n 0 ω 3 corresponds to the boundary value of the pump photon flux density. The parameters are 2 = (n ω 1 − n ω 2 )/n 0 ω 3 , 3 = (n ω 3 /2 + n ω 1 )/n 0 ω 3 , χ is the coupling coefficient for the four-wave mixing, κ EIT is the standard coefficient of absorption of the probe wave in the regime of electromagnetically induced transparency, D = 1 ν 0 (ω 21 21 is the frequency of the transition 1-2 (see Fig. 1), and 0 R is the boundary value of the pumping wave Rabi frequency.…”

Section: B Generalization Of the Universal Model Of Nonlinear Resonamentioning

confidence: 99%

“…,ω M due to the dependence of the function U( P) on polarization in any odd power. Thus, taking into account the cubic nonlinearity, i.e., δP (3) ∝ E 3 , is usually sufficient for the description of this effect [20,21]. Moreover, under the condition of frequency synchronism Eq.…”

Section: Appendix A: Excitation Of Polarization In a Nonlinear Anisotmentioning

confidence: 99%

Modification of the adiabatic invariants method in the studies of resonant dissipative systems

Tokman

Erukhimova

2011

Phys. Rev. E

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We study the system of equations for the canonically conjugate variables p and q specified by the one-dimensional Hamiltonian H=H(p,q,Λ(1),...,Λ(N)) dependent on Nself-consistent slightly changing parameters obeying the equations: Λ(n)=εf(n)(Λ(1),...,Λ(N),p,q). A broad range of oscillatory and wave processes with weak dissipation is described by analogous systems. The general method of adiabatic invariant construction for this system is proposed. Self-consistent averaged equations for the evolution of the action integral and the parameters Λ(n) are obtained. The constructed theory is applied to a generalized model of the nonlinear resonance. The autoresonance (phase locking) regime of decay parametric instability in a dissipative medium is revealed.

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“…To deal with this problem one must start from the kinetic equation for the density matrix (T of the spin system, from which under certain conditions the rate equations can be derived [6]. The kinetic equation itself follows from the Liouville equation for the density matrix of the closed system of spins and phonons (we shall consider the phonon system as a thermostat with the constant temperature T).…”

Section: Introductionmentioning

confidence: 99%

On the kinetics of systems with discrete energy levels

Aminov

1972

Physica Status Solidi (b)

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The nonlinear generalization of the Konstantinov and Perel diagram method is used for a derivation of the quantum kinetic equation. Under definite conditions this equation may be rewritten as a differential equation analogous to that known from the theory of paramagnetism as the Wangsness-Bloch equation, but the relaxation term of which is not limited by the second order in a corresponding interaction. This fact allows to investigate the contribution of multiphonon relaxation processes to the rate equations for populations of the energy levels of systems with discrete energy levels. It is made clear that the relaxation parameters of the rate equations in general do not coincide with the total probabilities of transitions between levels calculated by the perturbation theory. It is shown how the procedure of the calculation of two-phonon (Raman) transitions is modified when an intermediate level occurs inside a frequency spectrum of the lattice vibrations.HeJIHHefiHOe 0 6 0 6 n l e~~e AHarpaMMHOfi TeXHHKH KOHCTaHTHHOBa M n[epeJIfl HCIIOJIb30BaHO AJIFI BbIBOAa KBaHTOBOrO KHHeTH9eCHOrO YpaBHeHHfI. rIpH 0npe.Ife-JIeHHJdX YCJIOBHFIX 3 T 0 YpaBHeHHe MOXeT 6bITb 3aIlHCaHO B @OpMe AM@@epeHUHaJIb-Horo ypaBHeHm, aHanormHoro M~BBCTHOMY B Teopm n a p a~a r~e~m~a ypame-HHIO BaHrcHecca-Ihoxa, HO penaKcaqmoHHbrfi qneH HoToporo He orpaHmeix BTOPbIM npH6JIHXeHHeM no COOTBeTCTBYIOUeMY B3aHMOAefiCTBHK). 3 T 0 06CTORTeZb-CTBO Il03BOJIfIeT HCCJIeAOBaTb BHJlaA MHOrO@OHOHHbIX PeJIaKCaUHOHHbIX IlpO-geCCOB B YpaBHeHHfI AJIR 3aCeJIeHHOCTefi YpOBHeB 3HeprHH CHCTeM, 0 6 n a~a 1 o w~x HHCKpeTHbIMH YPOBHRMH 3HeprHM. BbIfICHeHO, 9 T O peJIaHCaUHOHHbIe IIapaMeTpbI YpaBHeHMfi nJIH 3aCeJIeHHOCTefi B o 6~e~ CJIy9ae He COBIIaHaIoT C BbIYHCJIReMbIMH IlO TeOpHH BO3MyWeHHfi IlOJIHbIMM BePORTHOCTJXMH IIepeXOAOB MeXEy YPOBHfIMH. n[OKa3aHO, KaIC MOAH@HUHPYeTCR IlpOQenypa paCseTa BepOHTHOCTH AByX@OHOHHOrO (PaMaHOBCHOrO) IIepeXOAa, KOrAa IIpOMeXyTOYHbIfi YpOBeHb OHa3bIBaeTCfI B npenenax cnempa YacToT perueTosabIx ~o n e 6 a~~i i .

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Lasers

Cited by 18 publications

References 0 publications

Dynamics of a small system coupled to a reservoir : reservoir fluctuations and self-reaction

Dynamics of a small system coupled to a reservoir : reservoir fluctuations and self-reaction

Modification of the adiabatic invariants method in the studies of resonant dissipative systems

On the kinetics of systems with discrete energy levels

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