Fluctuation-dissipation Theorem Research Articles

Kinetic theory of two-dimensional point vortices and fluctuation–dissipation theorem

We complete the kinetic theory of two-dimensional (2D) point vortices initiated in previous works. We use a simpler and more physical formalism. We consider a system of 2D point vortices submitted to a small external stochastic perturbation and determine the response of the system to the perturbation. We derive the diffusion coefficient and the drift by polarization of a test vortex. We introduce a general Fokker–Planck equation involving a diffusion term and a drift term. When the drift by polarization can be neglected, we obtain a secular dressed diffusion equation sourced by the external noise. When the external perturbation is created by a discrete collection of N point vortices, we obtain a Lenard–Balescu-like kinetic equation reducing to a Landau-like kinetic equation when collective effects are neglected. We consider a multi-species system of point vortices. We discuss the process of kinetic blocking in the single and multi-species cases. When the field vortices are at statistical equilibrium (thermal bath), we establish the proper expression of the fluctuation–dissipation theorem for 2D point vortices relating the power spectrum of the fluctuations to the response function of the system. In that case, the drift coefficient and the diffusion coefficient satisfy an Einstein-like relation and the Fokker–Planck equation reduces to a Smoluchowski-like equation. We mention the analogy between 2D point vortices and stellar systems. In particular, the drift of a point vortex in 2D hydrodynamics (Chavanis in Phys Rev E 58:R1199, 1998) is the counterpart of the Chandrasekhar dynamical friction in astrophysics. We also consider a gas of 2D Brownian point vortices described by N coupled stochastic Langevin equations and determine its mean and mesoscopic evolution. In the present paper, we treat the case of unidirectional flows, but our results can be straightforwardly generalized to axisymmetric flows.

Periodic potential can enormously boost free-particle transport induced by active fluctuations.

Active fluctuations are detected in a growing number of systems due to self-propulsion mechanisms or collisions with an active environment. They drive the system far from equilibrium and can induce phenomena that are forbidden at equilibrium states by, e.g., fluctuation-dissipation relations and detailed balance symmetry. Understanding their role in living matter is emerging as a challenge for physics. Here we demonstrate a paradoxical effect in which a free-particle transport induced by active fluctuations can be boosted by many orders of magnitude when the particle is additionally subjected to a periodic potential. In contrast, within the realm of only thermal fluctuations, the velocity of a free particle exposed to a bias is reduced when the periodic potential is switched on. The presented mechanism is significant for understanding nonequilibrium environments such as living cells, where it can explain from a fundamental point of view why spatially periodic structures known as microtubules are necessary to generate impressively effective intracellular transport. Our findings can be readily corroborated experimentally, e.g., in a setup comprising a colloidal particle in an optically generated periodic potential.

Linear response functions respecting Ward-Takahashi identity and fluctuation-dissipation theorem within the GW approximation

Fundamental equalities, such as the Ward-Takahashi identity (WTI) and the fluctuation-dissipation theorem (FDT), are important in the calculation of the response functions, which are defined as the variations of physical quantities with respect to the external sources. In this paper, the formalism of calculating the response functions according to their original definitions is presented, based on the generalized $GW$ (GGW) method which was developed for the electronic systems including spin-dependent interaction. This formalism automatically ensures the FDT, and is theorectically proved to respect the WTI. By contrast, the commonly used random phase approximation (RPA) within the GGW method violates both the WTI and the FDT, and the Bethe-Salpeter equation (BSE) satisfies the WTI but does not fulfill the FDT. The validity of this methodology is demonstrated on the two-dimensional one-band Hubbard model, and the results show that our formalism makes significant improvements over the RPA formula. Due to the similar computational cost to the BSE, our formalism is expected to be applied to realistic materials.

Direct Modeling of Thermal-Radiation Reception by Antenna in Close Range

In this work, an interesting near-field propagation problem in the microwave radiometer calibration is addressed, which is the antenna reception of thermal radiation from calibration target. Efforts in simultaneously modeling the target and antenna within the same 2-D full-wave scenario are reported. Specifically, the coated pyramids and horn antennas are considered. Based on the incoherent nature of local thermal sources in the coating layer and the fluctuation-dissipation theorem (FDT), the direct modeling of receiving power and further brightness temperature ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$BT$ </tex-math></inline-formula> ) at the antenna waveguide port can be achieved. The direct modeling is then quantified based on the classic concept of antenna reception in an ideal blackbody chamber. Further, it is shown in the results that mutual coupling affects the antenna reception in a fluctuating manner, and the target structural radiation raises the antenna reception in a very close distance. That means, the thermal reception can be affected by both the antenna and target structures in the near field. Also, the Lambertian radiation properties of the coated pyramidal blackbody are clarified in the direct calculated results. This work reveals the complex scenario of close range <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$BT$ </tex-math></inline-formula> transfer, and opens the possibility of quantitatively modeling it for practical applications with further investigations.

Formalism for stochastic perturbations and analysis in relativistic stars

Perturbed Einstein’s equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out. These perturbations which are stochastic in nature, are of significance for building a non-equilibrium statistical mechanics theory in connections with relativistic astrophysics. A fluctuation dissipation relation for a spherically symmetric star in its simplest form is obtained. The FD relation shows how the random velocity fluctuations in the background of the unperturbed star can dissipate into Lagrangian displacement of fluid trajectories of the dense matter. Interestingly in a simple way, a constant (in time) coefficient of dissipation is obtained without a delta correlated noise. This formalism is also extended for perturbed TOV equations which have a stochastic contribution, and show up in terms of the effective or root mean square pressure perturbations. Such contributions can shed light on new ways of analysing the equation of state for dense matter. One may obtain contributions of first and second order in the equation of state using this stochastic approach.

Quantum Bounds on the Generalized Lyapunov Exponents

We discuss the generalized quantum Lyapunov exponents Lq, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents Lq via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger q are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.

Fluctuation-Dissipation Relation for a Bose-Einstein Condensate of Photons

For equilibrium systems, the magnitude of thermal fluctuations is closely linked to the dissipative response to external perturbations. This fluctuation-dissipation relation has been described for material particles in a wide range of fields. Here, we experimentally probe the relation between the number fluctuations and the response function for a Bose-Einstein condensate of photons coupled to a dye reservoir, demonstrating the fluctuation-dissipation relation for a quantum gas of light. The observed agreement of the scale factor with the environment temperature both directly confirms the thermal nature of the optical condensate and demonstrates the validity of the fluctuation-dissipation theorem for a Bose-Einstein condensate.

Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

Equilibrium and out-of-equilibrium realistic phonon self-energy free from overscreening

In model Hamiltonians, like Fr\"ohlich's, the electron-phonon interaction is assumed to be screened from the beginning. The same occurs when this interaction is obtained by using the state-of-the-art density functional perturbation theory as starting point. In this work I formally demonstrate that these approaches are affected by a severe overscreening error. By using an out-of-equilibrium many-body technique I discuss how to merge the many-body approach with density functional perturbation theory in order to correct the overscreening error. A symmetric statically screened phonon self-energy is obtained by downfolding the exact Baym-Kadanoff equations. The statically screened approximation proposed here is shown to have the same long-range spatial limit of the exact self-energy and to respect the fluctuation-dissipation theorem. The doubly screened approximation, commonly used in the literature, is shown, instead, to be overscreened, to violate several many-body properties and to have a wrong spatial long-range decay. The accuracy of the proposed approximation is tested against the exact solution of an extended model Fr\"ohlich Hamiltonian and it is applied to a paradigmatic material: ${\mathrm{MgB}}_{2}$. I find that the present treatment enhances the linewidths by $57%$ with respect to what has been previously reported for the anomalous ${E}_{2g}$ mode. I further discover that the ${A}_{2u}$ mode is also anomalous (its strong coupling being completely quenched by the overscreened expression). The present results deeply question methods based on state-of-the-art approaches and impact a wide range of fields such as thermal conductivity, phononic instabilities, and nonequilibrium lattice dynamics.

Revisiting thermal charge carrier refractive noise in semiconductor optics for gravitational-wave interferometers

The test masses in next-generation gravitational-wave interferometers may have a semiconductor substrate, most likely silicon. The stochastic motion of charge carriers within the semiconductor will cause random fluctuations in the material's index of refraction, introducing a noise source called thermal charge carrier refractive (TCCR) noise. TCCR noise was previously studied in 2020 by Bruns et al., using a Langevin force approach. Here we compute the power spectral density of TCCR noise by both using the fluctuation-dissipation theorem and accounting for previously neglected effects of the standing wave of laser light produced by reflections along the direction of beam propagation. We quantify our results with parameters from Einstein Telescope, and we show that at temperatures of 10 K the amplitude of TCCR noise is up to a factor of $\sqrt{2}$ times greater than what was previously claimed. From 77 K to 300 K the amplitude is around 5 to 7 orders of magnitude lower than previously claimed when we choose to neglect the standing wave, and is up to a factor of 6 times lower if the standing wave is included. Despite these differences, we still conclude like Bruns et al. that TCCR noise should not be a limiting noise source for next-generation gravitational-wave interferometers.

Bounding Variance and Skewness of Fluctuations in Nonlinear Dynamical Systems with Stochastic Thermodynamics*

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterisation such as the fluctuation-dissipation theorem (also called Johnson-Nyquist law, or Einstein's law in specific contexts). Using results from stochastic thermodynamics, we show that the variance of these fluctuations exceeds the variance predicted by a suitably extended version of Johnson-Nyquist's formula, by an amount that is controlled by the skewness (third moment) of the fluctuations. As a consequence, symmetric fluctuations necessarily obey the extended Johnson-Nyquist formula. This shows the physical inconsistency of Gaussian approximation for the noise arising in some nonlinear models, such as MOS transistors or chemical reactions. More generally, this suggests the need for a stochastic nonlinear systems theory that is compatible with the teachings of thermodynamics.

Fluctuation-dissipation in thermoelectric sensors

Thermoelectric materials exhibit correlated transport of charge and heat. The Johnson-Nyquist noise formula 4k B T R for the spectral density of voltage fluctuations accounts for fluctuations associated solely with Ohmic dissipation. Applying the fluctuation-dissipation theorem, we generalize the Johnson-Nyquist formula for thermoelectrics, finding an enhanced voltage fluctuation spectral density 4k B T R(1 + Z D T) at frequencies below a thermal cut-off frequency f T , where Z D T is the dimensionless thermoelectric device figure of merit. The origin of the enhancement in voltage noise is thermoelectric coupling of temperature fluctuations. We use a wideband , integrated thermoelectric micro-device to experimentally confirm our findings. Measuring the Z D T enhanced voltage noise, we experimentally resolve temperature fluctuations with a root mean square amplitude of at a mean temperature of 295 K. We find that thermoelectric devices can be used for thermometry with sufficient resolution to measure the fundamental temperature fluctuations described by the fluctuation-dissipation theorem.

Adiabatic limit collapse and local interaction effects in non-linear active microrheology molecular simulations of two-dimensional fluids.

Nonlinear active microrheology molecular dynamics simulations of high-density two-dimensional fluids show that the presence of strong confining forces and an external pulling force induces a correlation between the velocity and position dynamics of the tracer particle. This correlation manifests in the form of an effective temperature and an effective mobility of the tracer particle, which is responsible for the breaking of the equilibrium fluctuation-dissipation theorem. This fact is shown by measuring the tracer particle's temperature and mobility directly from the first two moments of the velocity distribution of a tracer particle and by formulating a diffusion theory in which effective thermal and transport properties are decoupled from the velocity dynamics. Furthermore, the flexibility of the attractive and repulsive forces in the tested interaction potentials allowed us to relate the temperature and mobility behaviors to the nature of the interactions and the structure of the surrounding fluid as a function of the pulling force. These results provide a refreshing physical interpretation of the phenomena observed in non-linear active microrheology.

Qubit dynamics driven by dipole field in thermal noise environment

Quantum computing is a new way to process quantum information by using superposition and entanglement of the quantum system. Quantum state’s vast Hilbert space allows it to perform operations that classical computers cannot. The quantum computing has unique advantages in dealing with some complex problems, so it has attracted wide attention. Computing a single qubit is the first of seven fundamental stages needed to achieve a large-scale quantum computer that is universal, scalable and fault-tolerant. In other words, the primary task of quantum computing is the careful preparation and precise regulation of qubits. At present, the physical systems that can be used as qubits include superconducting qubits, semiconductor qubits, ion trap systems and nitrogen-vacancy (NV) color centers. These physical systems have made great progress of decoherence time and scalability. Owing to the vulnerability of qubits, ambient thermal noise can cause quantum decoherence, which greatly affects the fidelity of qubits. Improving the fidelity of qubits is therefore a key step towards large-scale quantum computing. Based on the dipole field driven qubit, the stochastic dynamic structure decomposition method is adopted and the Kubo-Einstein fluctuation-dissipation theorem is used to study the qubit control in a thermal noise environment. The dipole field has components in three directions, not just in one plane, which allows more flexible control of quantum states. Without considering the noise, the quantum state can reach the target state 100%. In the noisy environment, thermal noise will cause the deviation between the actual final state and the target final state caused by thermal fluctuation, which becomes the main factor affecting the quantum fidelity. The influence of thermal noise is related to temperature and the evolution trajectory of quantum state. Therefore, this paper proposes an optimal scheme to improve the qubit fidelity in the thermal noise environment. The feasibility of this method is verified by numerical calculation, which can provide a new solution for further guiding and evaluating the experiment. The scheme is suitable for qubit systems of various physical control fields, such as semiconductor qubits and nitrogen vacancy center qubits. This work may have more applications in the development of quantum manipulation technology and can also be extended to multi-qubit systems, the details of which will appear in the future work.

Activation/Inhibition of Gene Expression Caused by Alcohols: Relationship with the Viscoelastic Property of a DNA Molecule

Alcohols are used in the life sciences because they can condense and precipitate DNA. Alcohol consumption has been linked to many diseases and can alter genetic activity. In the present report, we carried out experiments to make clear how alcohols affect the efficiency of transcription-translation (TX-TL) and translation (TL) by adapting cell-free gene expression systems with plasmid DNA and RNA templates, respectively. In addition, we quantitatively analyzed intrachain fluctuations of single giant DNA molecules based on the fluctuation-dissipation theorem to gain insight into how alcohols affect the dynamical property of a DNA molecule. Ethanol (2-3%) increased gene expression levels four to five times higher than the control in the TX-TL reaction. A similar level of enhancement was observed with 2-propanol, in contrast to the inhibitory effect of 1-propanol. Similar alcohol effects were observed for the TL reaction. Intrachain fluctuation analysis through single DNA observation showed that 1-propanol markedly increased both the spring and damping constants of single DNA in contrast to the weak effects observed with ethanol, whereas 2-propanol exhibits an intermediate effect. This study indicates that the activation/inhibition effects of alcohol isomers on gene expression correlate with the changes in the viscoelastic mechanical properties of DNA molecules.

A reduction scheme for coupled Brownian harmonic oscillators

We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original dynamics and is written in terms of suitable transport coefficients. The proposed procedure is twofold: while the deterministic component of the dynamics is obtained by a direct application of the invariant manifold method, the diffusion terms are determined via the fluctuation-dissipation theorem. We highlight the behavior of the coefficients up to a critical value of the coupling parameter, which marks the endpoint of the interval in which a contracted description is available. The study of the weak coupling regime is addressed and the commutativity of alternative reduction paths is also discussed.

Stochastic thermodynamics of fractional Brownian motion

This paper is concerned with the stochastic thermodynamics of nonequilibrium Gaussian processes that can exhibit anomalous diffusion. In the systems considered, the noise correlation function is not necessarily related to friction. Thus there is no conventional fluctuation-dissipation relation (FDR) of the second kind and no unique way to define a temperature. We start from a Markovian process with time-dependent diffusivity (an example being scaled Brownian motion). It turns out that standard stochastic thermodynamic notions can be applied rather straightforwardly by introducing a time-dependent temperature, yielding the integral fluctuation relation. We then proceed to our focal system, that is, a particle undergoing fractional Brownian motion (FBM). In this case, the noise is still Gaussian, but the noise correlation function is nonlocal in time, defining a non-Markovian process. We analyze in detail the consequences when using the conventional notions of stochastic thermodynamics with a constant medium temperature. In particular, the heat calculated from dissipation into the medium differs from the log ratio of path probabilities of forward and backward motion, yielding a deviation from the standard integral fluctuation relation for the total entropy production if the latter is defined via system entropy and heat exchange. These apparent inconsistencies can be circumvented by formally defining a time-nonlocal temperature that fulfills a generalized FDR. To shed light on the rather abstract quantities resulting from the latter approach, we perform a perturbation expansion in terms of $\ensuremath{\epsilon}=H\ensuremath{-}1/2$, where $H$ is the Hurst parameter of FBM and $1/2$ corresponds to the Brownian case. This allows us to calculate analytically, up to linear order in $\ensuremath{\epsilon}$, the generalized temperature and the corresponding heat exchange. By this, we provide explicit expressions and a physical interpretation for the leading corrections induced by non-Markovianity.

Theory of thermal radiation from a nanoparticle array

Thermal radiation has diffusive and broad emission characteristics. Controlling emission spectrum and direction is essential for various applications. Nanoparticle arrays, supporting collective lattice resonances, can be employed for controlling optical properties. However, thermal emission characteristics remain unexplored due to the lack of a theoretical model. Here, we develop an analytical model to predict thermal radiation from a nanoparticle array using fluctuation–dissipation theorem and lattice Green's functions. Our findings reveal that the periodicity and particle size of the particle array are main parameters to control both emission spectrum and direction. The derived simple expression for thermal emission enables insightful interpretation of physics. This model will lay a foundation for analytical derivation of thermal radiation from metasurfaces. Our study can be useful in engineering infrared thermal sources and radiative cooling applications.

Brownian axionlike particles

We study the non-equilibrium dynamics of a pseudoscalar axion-like particle (ALP) weakly coupled to degrees of freedom in thermal equilibrium by obtaining its reduced density matrix. Its time evolution is determined by the in-in effective action which we obtain to leading order in the (ALP) coupling but to \emph{all orders} in the couplings of the bath to other fields within or beyond the standard model. The effective equation of motion for the (ALP) is a Langevin equation with noise and friction kernels obeying the fluctuation dissipation relation. A ``misaligned'' initial condition yields damped coherent oscillations, however, the (ALP) population increases towards thermalization with the bath. As a result, the energy density features a mixture of a cold component from misalignment and a hot component from thermalization with proportions that vary in time $(cold)\,e^{-\Gamma t}+(hot)\,(1-e^{-\Gamma t})$, providing a scenario wherein the ``warmth'' of the dark matter evolves in time from colder to hotter. As a specific example we consider the (ALP)-photon coupling $g a \vec{E}\cdot \vec{B}$ to lowest order, valid from recombination onwards. For $T \gg m_a$ the long-wavelength relaxation rate is substantially enhanced $\Gamma_T = \frac{g^2\,m^2_a\,T}{16\pi} $. The ultraviolet divergences of the (ALP) self-energy require higher order derivative terms in the effective action. We find that at high temperature, the finite temperature effective mass of the (ALP) is $m^2_a(T) = m^2_a(0)\Big[ 1-(T/T_c)^4\Big]$, with $T_c \propto \sqrt{m_a(0)/g}$, \emph{suggesting} the possibility of an inverted phase transition, which when combined with higher derivatives may possibly indicate exotic new phases. We discuss possible cosmological consequences on structure formation, the effective number of relativistic species and birefringence of the cosmic microwave background.

Electric field influenced coordinate jump of the guiding centre and magnetotransport

ABSTRACT Our studies formulate a classical theory to study the influence of in-plane electric field on electron-impurity scattering process and magnetotransport in a two-dimensional space, in the presence of a strong out-of-plane magnetic field. Our studies connect classical scattering and quantum Landau Level broadening, as will be reviewed in this report. We derived an electric current formula in agreement with the current derived from the Drude theory under a strong magnetic field. Our electric current formula is derived microscopically from the migration of the guiding centres at strong magnetic field regime . The electron-impurity scattering under electromagnetic field not only shifts the guiding centre coordinates X and Y, but also changes cyclotron radius R. The change of cyclotron radius R compensates the change of the electric potential energy during the scattering process. The broadening of cyclotron radius is a classical manifestation of Landau Levels broadening. Our conductivity derived from our current formula in the linear response regime results in the same as the current derived from Kubo current fluctuation theory, providing a special case of the fluctuation-dissipation theorem.