Search Results (39)

This manuscript reviews our recently developed theory, the dynamical projective operatorial approach (DPOA), for studying pump–probe setups in ultra-fast regimes. After reviewing the general formulation of the DPOA, we focus on its lattice version and provide a formalism that is particularly suitable for several pumped semiconductors. Within the DPOA, we also compute the TR-ARPES signal through out-of-equilibrium Green’s functions and establish an out-of-equilibrium counterpart of the fluctuation–dissipation theorem. Moreover, we generalize the linear response theory to pumped systems and address, within the DPOA, the differential transient optical properties, providing an overall robust theoretical and computational framework for studying pump–probe setups. Considering a minimal model for a semiconductor, we illustrate the capabilities of the DPOA and discuss several features emerging in this case study that are relevant to real materials. Full article

This study concerns Riemannian manifolds with two types of tangent vectors. Let it be given that there are two subspaces of a tangent space with the property that each tangent vector has a unique decomposition as the sum of a vector in one subspace and a vector in the other subspace. Then, these tangent spaces can be complexified in such a way that the theory of the modular operator applies and that the complexified subspaces are invariant for the modular automorphism group. Notions coming from Kubo–Mori theory are introduced. In particular, the admittance function and the inner product of the Kubo–Mori theory can be generalized to the present context. The parallel transport operators are complexified as well. Suitable basis vectors are introduced. The real and imaginary contributions to the connection coefficients are identified. A version of the fluctuation–dissipation theorem links the admittance function to the path dependence of the eigenvalues and eigenvectors of the Hamiltonian generator of the modular automorphism group. Full article

The magnetic acceleration noise (MAN) that stems from the eddy current dissipation of a test mass (TM) serves as an important source of noise for space inertial sensors. Given the problem that the eddy current dissipation magnetic acceleration noise (ECDMAN) of a cubic TM defies analytical solutions, an analytical model of ECDMAN for a spherical TM, which has the same volume as the cubic TM, is systematically derived on the basis of the principles of electromagnetism and the fluctuation-dissipation theorem, and this model can be used as an approximate analytical model for the evaluation of this noise term. Based on the approximate analytical model, with the TM of the LISA Pathfinder (LPF) as the research object, this paper obtains a modification coefficient using the approach of combining the analytical method with the finite element method (FEM), and establishes a semi-analytical model of ECDMAN for the cubic TM. Using the parameters of the LPF’s TM, the calculation error of the semi-analytical model is reduced by about 4.64% compared with the approximate analytical model. Finally, a generalized modeling approach for the semi-analytical model of ECDMAN is put forward, which is applicable to TMs with different parameters and can realize the real-time and rapid evaluation of ECDMAN during in-orbit experiments. Full article

In a multivariable system, there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux–force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables in such a way that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof that Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics. Full article

Mechanical stress governs the dynamics of viscoelastic polymer systems and supercooled glass-forming fluids. It was recently established that liquids with long terminal relaxation times are characterized by transiently frozen stress fields, which, moreover, exhibit long-range correlations contributing to the dynamically heterogeneous nature of such systems. Recent studies show that stress correlations and relaxation elastic moduli are intimately related in isotropic viscoelastic systems. However, the origin of these relations (involving spatially resolved material relaxation functions) is non-trivial: some relations are based on the fluctuation-dissipation theorem (FDT), while others involve approximations. Generalizing our recent results on 2D systems, we here rigorously derive three exact FDT relations (already established in our recent investigations and, partially, in classical studies) between spatio-temporal stress correlations and generalized relaxation moduli, and a couple of new exact relations. We also derive several new approximate relations valid in the hydrodynamic regime, taking into account the effects of thermal conductivity and composition fluctuations for arbitrary space dimension. One approximate relation was heuristically obtained in our previous studies and verified using our extended simulation data on two-dimensional (2D) glass-forming systems. As a result, we provide the means to obtain, in any spatial dimension, all stress-correlation functions in terms of relaxation moduli and vice versa. The new approximate relations are tested using simulation data on 2D systems of polydisperse Lennard–Jones particles. Full article

The theoretical basis for the Eddy Damped Markovian Anisotropic Closure (EDMAC) is formulated for two-dimensional anisotropic turbulence interacting with Rossby waves in the presence of advection by a large-scale mean flow. The EDMAC is as computationally efficient as the Eddy Damped Quasi Normal Markovian (EDQNM) closure, but, in contrast, is realizable in the presence of transient waves. The EDMAC is arrived at through systematic simplification of a generalization of the non-Markovian Direct Interaction Approximation (DIA) closure that has its origin in renormalized perturbation theory. Markovian Anisotropic Closures (MACs) are obtained from the DIA by using three variants of the Fluctuation Dissipation Theorem (FDT) with the information in the time history integrals instead carried by Markovian differential equations for two relaxation functions. One of the MACs is simplified to the EDMAC with analytical relaxation functions and high numerical efficiency, like the EDQNM. Sufficient conditions for the EDMAC to be realizable in the presence of Rossby waves are determined. Examples of the numerical integration of the EDMAC compared with the EDQNM are presented for two-dimensional isotropic and anisotropic turbulence, at moderate Reynolds numbers, possibly interacting with Rossby waves and large-scale mean flow. The generalization of the EDMAC for the statistical dynamics of other physical systems to higher dimension and higher order nonlinearity is considered. Full article

The Kardar–Parisi–Zhang (KPZ) equation describes a wide range of growth-like phenomena, with applications in physics, chemistry and biology. There are three central questions in the study of KPZ growth: the determination of height probability distributions; the search for ever more precise universal growth exponents; and the apparent absence of a fluctuation–dissipation theorem (FDT) for spatial dimension $d>1$. Notably, these questions were answered exactly only for $1+1$ dimensions. In this work, we propose a new FDT valid for the KPZ problem in $d+1$ dimensions. This is achieved by rearranging terms and identifying a new correlated noise which we argue to be characterized by a fractal dimension $d_n$. We present relations between the KPZ exponents and two emergent fractal dimensions, namely $d_f$, of the rough interface, and $d_n$. Also, we simulate KPZ growth to obtain values for transient versions of the roughness exponent $\alpha$, the surface fractal dimension $d_f$ and, through our relations, the noise fractal dimension $d_n$. Our results indicate that KPZ may have at least two fractal dimensions and that, within this proposal, an FDT is restored. Finally, we provide new insights into the old question about the upper critical dimension of the KPZ universality class. Full article

The fluctuation relation stands as a fundamental result in nonequilibrium statistical physics. Its derivation, particularly in the stationary state, places stringent conditions on the physical systems of interest. On the other hand, numerical analyses usually do not directly reveal any specific connection with such physical properties. This study proposes an investigation of such a connection with the fundamental ingredients of the derivation of the fluctuation relation for the dissipation, which includes the decay of correlations, in the case of heat transport in one-dimensional systems. The role of the heat baths in connection with the system’s inherent properties is then highlighted. A crucial discovery of our research is that different lattice models obeying the steady-state fluctuation relation may do so through fundamentally different mechanisms, characterizing their intrinsic nature. Systems with normal heat conduction, such as the lattice ${\varphi }^4$ model, comply with the theorem after surpassing a certain observational time window, irrespective of lattice size. In contrast, systems characterized by anomalous heat conduction, such as Fermi–Pasta–Ulam–Tsingou-$\beta$ and harmonic oscillator chains, require extended observation periods for theoretical alignment, particularly as the lattice size increases. In these systems, the heat bath’s fluctuations significantly influence the entire lattice, linking the system’s fluctuations with those of the bath. Here, the current autocorrelation function allows us to discern the varying conditions under which different systems satisfy with the fluctuation relation. Our findings significantly expand the understanding of the stationary fluctuation relation and its broader implications in the field of nonequilibrium phenomena. Full article

In this article, we address the reliance on probability density functions to obtain macroscopic properties in systems with multiple degrees of freedom as plasmas, and the limitations of expensive techniques for solving Equations such as Vlasov’s. We introduce the Ehrenfest procedure as an alternative tool that promises to address these challenges more efficiently. Based on the conjugate variable theorem and the well-known fluctuation-dissipation theorem, this procedure offers a less expensive way of deriving time evolution Equations for macroscopic properties in systems far from equilibrium. We investigate the application of the Ehrenfest procedure for the study of adiabatic invariants in magnetized plasmas. We consider charged particles trapped in a dipole magnetic field and apply the procedure to the study of adiabatic invariants in magnetized plasmas and derive Equations for the magnetic moment, longitudinal invariant, and magnetic flux. We validate our theoretical predictions using a test particle simulation, showing good agreement between theory and numerical results for these observables. Although we observed small differences due to time scales and simulation limitations, our research supports the utility of the Ehrenfest procedure for understanding and modeling the behavior of particles in magnetized plasmas. We conclude that this procedure provides a powerful tool for the study of dynamical systems and statistical mechanics out of equilibrium, and opens perspectives for applications in other systems with probabilistic continuity. Full article

This study analyzed the relationship between characteristics of annual tree ring time series and the intensity of attacks on forest stands by forest insects. Using tenets of the fluctuation–dissipation theorem (which is widely used in physics), time series parameters are proposed that can help to assess the susceptibility of a forest stand to insect pests. The proposed approach was applied to evaluate differences in parameters of tree ring widths among outbreaks of the pine looper, Siberian silk moth, and spongy moth. A comparison of trees characteristics between outbreak locations and undamaged forest stands (control) showed that the tested parameters statistically significantly differed between the outbreak locations and control stands and can be used to assess the risk of pest outbreaks in forest stands. Full article

We discuss the generalized quantum Lyapunov exponents $L_q$, 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 $L_q$ 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. Full article

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. Full article

Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the performance of state-of-the-art ultra-narrow linewidth lasers, we derive an expression of the TN for a cylindrical spacer according to the fluctuation–dissipation theorem, which takes into account the front face area of the spacer. This estimation is more suitable for the TN of the cylindrical USC than the previous one. Meanwhile, we perform detailed studies of the influence of the four support pads on the TN in cylindrical USCs for the first time by numerical simulations. For a 400 mm long cylindrical USC with an ultra-low expansion spacer and fused silica substrates, the displacement noise contributed from the four support pads is roughly four times that of the substrates and the GaAs/AlGaAs crystalline coating. The results show that the four support pads are the primary TN contributors under some materials and geometries of USCs. Full article

In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation–dissipation theorem and the Donsker–Furutsu–Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures. Full article

Physical aging deals with slow property changes over time caused by molecular rearrangements. This is relevant for non-crystalline materials such as polymers and inorganic glasses, both in production and during subsequent use. The Narayanaswamy theory from 1971 describes physical aging—an inherently nonlinear phenomenon—in terms of a linear convolution integral over the so-called material time $\xi$. The resulting “Tool–Narayanaswamy (TN) formalism” is generally recognized to provide an excellent description of physical aging for small, but still highly nonlinear, temperature variations. The simplest version of the TN formalism is single-parameter aging according to which the clock rate $d\xi /dt$ is an exponential function of the property monitored. For temperature jumps starting from thermal equilibrium, this leads to a first-order differential equation for property monitored, involving a system-specific function. The present paper shows analytically that the solution to this equation to first order in the temperature variation has a universal expression in terms of the zeroth-order solution, $R_0\left(t\right)$. Numerical data for a binary Lennard–Jones glass former probing the potential energy confirm that, in the weakly nonlinear limit, the theory predicts aging correctly from $R_0\left(t\right)$ (which by the fluctuation–dissipation theorem is the normalized equilibrium potential-energy time-autocorrelation function). Full article