QUANTUM FLUCTUATION DISSIPATION THEOREM REVISITED: REMARKS AND CONTRADICTIONS

2012 ◽  
Vol 11 (03) ◽  
pp. 1242002 ◽  
Author(s):  
L. REGGIANI ◽  
P. SHIKTOROV ◽  
E. STARIKOV ◽  
V. GRUŽINSKIS
Keyword(s):  
Harmonic Oscillator ◽  
Quantum Fluctuation ◽  
Zero Point ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Accepted Form

The quantum fluctuation dissipation theorem (QFDT) in the Callen–Welton [ Phys. Rev.83 (1951) 34] form is critically revisited. We show that the role of the system eigenvalues is in general not correctly accounted for by the accepted form of the QFDT. As a consequence, a series of quantum results claimed in the literature, like the presence of zero point fluctuations, the violation of the quantum regression hypothesis, the non-white spectrum of the Langevin force, etc. emerge as a consequence of an incorrect application of the theorem. In this context the case of the single harmonic oscillator is illustrated as a typical example where the accepted form of the QFDT is proven to fail.

scholarly journals Molecular machines operating on the nanoscale: from classical to quantum

2016 ◽  
Vol 7 ◽  
pp. 328-350 ◽  
Author(s):  
Igor Goychuk
Keyword(s):  
Molecular Motors ◽  
High Performance ◽  
Molecular Machines ◽  
Thermal Fluctuations ◽  
Maximum Power ◽  
Thermodynamic Efficiency ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Physical Features

The main physical features and operating principles of isothermal nanomachines in the microworld, common to both classical and quantum machines, are reviewed. Special attention is paid to the dual, constructive role of dissipation and thermal fluctuations, the fluctuation–dissipation theorem, heat losses and free energy transduction, thermodynamic efficiency, and thermodynamic efficiency at maximum power. Several basic models are considered and discussed to highlight generic physical features. This work examines some common fallacies that continue to plague the literature. In particular, the erroneous beliefs that one should minimize friction and lower the temperature for high performance of Brownian machines, and that the thermodynamic efficiency at maximum power cannot exceed one-half are discussed. The emerging topic of anomalous molecular motors operating subdiffusively but very efficiently in the viscoelastic environment of living cells is also discussed.

scholarly journals Fluctuation Dissipation Theorem and Electrical Noise Revisited

2019 ◽  
Vol 18 (01) ◽  
pp. 1930001 ◽  
Author(s):  
Lino Reggiani ◽  
Eleonora Alfinito
Keyword(s):  
Electromagnetic Radiation ◽  
Linear Response ◽  
Casimir Effect ◽  
Zero Point ◽  
Absolute Temperature ◽  
Electrical Noise ◽  
Point Energy ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Kinetic Coefficients

The fluctuation dissipation theorem (FDT) is the basis for a microscopic description of the interaction between electromagnetic radiation and matter. By assuming the electromagnetic radiation in thermal equilibrium and the interaction in the linear-response regime, the theorem interrelates the macroscopic spontaneous fluctuations of an observable with the kinetic coefficients that are responsible for energy dissipation in the linear response to an applied perturbation. In the quantum form provided by Callen and Welton in their pioneering paper of 1951 for the case of conductors [H. B. Callen and T. A. Welton, Irreversibility and generalized noise, Phys. Rev. 83 (1951) 34], electrical noise in terms of the spectral density of voltage fluctuations, [Formula: see text], detected at the terminals of a conductor was related to the real part of its impedance, [Formula: see text], by the simple relation [Formula: see text] where [Formula: see text] is the Boltzmann constant, [Formula: see text] is the absolute temperature, [Formula: see text] is the reduced Planck constant and [Formula: see text] is the angular frequency. The drawbacks of this relation concern with: (i) the appearance of a zero-point contribution which implies a divergence of the spectrum at increasing frequencies; (ii) the lack of detailing the appropriate equivalent-circuit of the impedance, (iii) the neglect of the Casimir effect associated with the quantum interaction between zero-point energy and boundaries of the considered physical system; (iv) the lack of identification of the microscopic noise sources beyond the temperature model. These drawbacks do not allow to validate the relation with experiments, apart from the limiting conditions when [Formula: see text]. By revisiting the FDT within a brief historical survey of its formulation, since the announcement of Stefan–Boltzmann law dated in the period 1879–1884, we shed new light on the existing drawbacks by providing further properties of the theorem with particular attention to problems related with the electrical noise of a two-terminals sample under equilibrium conditions. Accordingly, among others, we will discuss the duality and reciprocity properties of the theorem, the role played by different statistical ensembles, its applications to the ballistic transport-regime, to the case of vacuum and to the case of a photon gas.

scholarly journals Numerical approximation and fast evaluation of the overdamped generalized Langevin equation with fractional noise

2020 ◽  
Vol 54 (2) ◽  
pp. 431-463 ◽  
Author(s):  
Di Fang ◽  
Lei Li
Keyword(s):  
Differential Equation ◽  
Langevin Equation ◽  
Numerical Approximation ◽  
Generalized Langevin Equation ◽  
Fractional Gaussian Noise ◽  
Fast Evaluation ◽  
Fractional Noise ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem

The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the movement of microparticles with sub-diffusion phenomenon. It has been proved that with fractional Gaussian noise (fGn) mostly considered by biologists, the overdamped Generalized Langevin equation satisfying fluctuation dissipation theorem can be written as a fractional stochastic differential equation (FSDE). In this work, we present both a direct and a fast algorithm respectively for this FSDE model in order to numerically study ergodicity. The strong orders of convergence are proven for both schemes, where the role of the memory effects can be clearly observed. We verify the convergence theorems using linear forces, and then verify the convergence to Gibbs measure algebraically for the double well potentials in both 1D and 2D setups. Our work is new in numerical analysis of FSDEs and provides a useful tool for studying ergodicity. The idea can also be used for other stochastic models involving memory.

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