Axiomatic construction of quantum Langevin equations

Araújo, Rúbia; Wald, Sascha; Henkel, Malte

doi:10.1088/1742-5468/ab11dc

Cited by 11 publications

(17 citation statements)

References 90 publications

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“…Therefore, the introduction of stochastic differentials [32] converts (15) into a Langevin equation [33][34][35][36]…”

Section: Equations Of Motion With Thermal Noisementioning

confidence: 99%

“…A mathematically rigorous derivation of Langevin molecular dynamics, for the case of a composite quantum system that is weakly coupled to a heat bath of many fast particles, has been recently developed by Hoel and Szepessy [54]. Thus, we maintain the view that the system of equations ( 27) and ( 28) represents a quantum Langevin model [34][35][36] of protein α-helix immersed in water-based solvent at physiological temperature.…”

Section: Three-spine Model With Lateral Couplingmentioning

confidence: 99%

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Thermal stability of solitons in protein $α$-helices

Georgiev,

Glazebrook

2022

Preprint

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Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of stochastic differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T = 310 K, for either a single isolated α-helix spine of hydrogen bonded peptide groups or the full protein α-helix comprised of three parallel α-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated α-helix spine, the cooperative action of three amide I exciton quanta in the full protein α-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long α-helix. Thus, macromolecular protein complexes, which are built up of protein α-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems.

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“…Therefore, the introduction of stochastic differentials [32] converts (15) into a Langevin equation [33][34][35][36]…”

Section: Equations Of Motion With Thermal Noisementioning

confidence: 99%

Section: Three-spine Model With Lateral Couplingmentioning

confidence: 99%

Thermal stability of solitons in protein $α$-helices

Georgiev,

Glazebrook

2022

Preprint

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“…HLE for resonant optical systems are often nonlinear in operators, which makes them difficult for solving analytically. Several methods of solving HLE are proposed [3,[20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Perturbation approach in Heisenberg equations for lasers

Protsenko,

Uskov

2022

Preprint

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Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier-expansion for the laser in the LED regime. Fluctuations of populations of lasing levels are taken into account as perturbations. Spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons and broad the spectrum of a bad cavity thresholdless and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.

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“…The extension of the Langevin equation to describe quantum open system and quantum dissipation [5][6][7][8][9] has been addressed but the quantum description has brought problems that were not present in the classical case, and the approach to quantum open system and quantum dissipation does not seem to be completely solved [10]. For instance, an equation that governs the time evolution of the probability density, the Fokker-Planck-Kramers equation, can immediately be obtained from the classical Langevin equation.…”

Section: Introductionmentioning

confidence: 99%

Quantum Langevin equation

Oliveira

2020

J. Stat. Mech.

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We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the classical case. It is a white noise with a variance proportional to the temperature. The dissipation force is not restricted to be proportional to the velocity and is determined in a way as to guarantee that the stationary state is given by a density operator of the Gibbs canonical type. To this end we derived an equation that gives the time evolution of the density operator, which turns out to be a quantum Fokker-Planck-Kramers equation. The approach is applied to the harmonic oscillator in which case the dissipation force is found to be non Hermitian and proportional to the velocity and position.

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Axiomatic construction of quantum Langevin equations

Cited by 11 publications

References 90 publications

Thermal stability of solitons in protein $α$-helices

Thermal stability of solitons in protein $α$-helices

Perturbation approach in Heisenberg equations for lasers

Quantum Langevin equation

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