Fermionic and bosonic fluctuation-dissipation theorem from a deformed AdS holographic model at finite temperature and chemical potential

In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein–Maxwell–Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases, from which we obtain the short and large time approximations. For the long time, we obtain a sub-diffusive regime $$\sim \log t$$ ∼ log t . Combining the results from the admittance and the correlations functions we check the fluctuation-dissipation theorem for bosonic and fermionic systems.

Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures

We consider the problem of heat transport by vibrational modes between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature difference and thus be out of equilibrium. We develop a classical formalism based on the equation of motion method, the fluctuation–dissipation theorem and the Novikov theorem to describe heat flow in a multi-terminal geometry. We show that it is imperative to include a quartic term in the potential energy to insure stability and to properly describe thermal expansion. The latter also contributes to leading order in the thermal resistance, while the usually adopted cubic term appears in the second order. This formalism paves the way for accurate modeling of thermal transport across interfaces in highly non-equilibrium situations beyond perturbation theory.

Scrutinizing GW-Based Methods Using the Hubbard Dimer

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

The Fractal Geometry of Growth: Fluctuation–Dissipation Theorem and Hidden Symmetry

Growth in crystals can be usually described by field equations such as the Kardar-Parisi-Zhang (KPZ) equation. While the crystalline structure can be characterized by Euclidean geometry with its peculiar symmetries, the growth dynamics creates a fractal structure at the interface of a crystal and its growth medium, which in turn determines the growth. Recent work by Gomes-Filho et al. (Results in Physics, 104,435 (2021)) associated the fractal dimension of the interface with the growth exponents for KPZ and provides explicit values for them. In this work, we discuss how the fluctuations and the responses to it are associated with this fractal geometry and the new hidden symmetry associated with the universality of the exponents.

Conclusions

This concluding chapter focuses on the philosophical lessons to be had from the discussions in the previous chapters. Specifically, it suggests that one interesting and fruitful way to understand the relation “theory X is more fundamental than theory Y” is through mediated mesoscale modeling. This is in contrast to the kind of direction derivational connections often invoked in the debates about reduction that depend on “in principle” mathematical claims. The hierarchical ordering in terms of this relation of relative fundamentality can be understood in terms of the conception of relative autonomy discussed throughout the book. It highlights the fact that this point of view has its genesis in Einstein’s work on Brownian Motion and specifically in his determination of an effective material parameter and the first expression of the Fluctuation-Dissipation theorem. Finally, it recaps the conception of an engineering, middle-out approach to many-body physics and the physical arguments that certain mesoscale variables should be considered to be natural kinds.

Brownian Motion

This chapter discusses the phenomenon of Brownian motion and Einstein’s pioneering arguments that explained various aspects of it. It shows how Einstein presented two arguments that relate directly to the themes of this book. The first is the upscaling or homogenization to effective continuum parameters from correlational structures in representative volume elements at mesoscales. Einstein’s argument is shown to answer the question about autonomy raised in Chapter 2. The second relates to the Fluctuation-Dissipation theorem. This theorem justifies the mesoscale hydrodynamic description of many-body systems and Einstein provided the first statement of the theorem.

The fluctuation-dissipation theorem and the autocorrelation function of thermal radiation

A new relatively simple derivation of the fluctuation-dissipation theorem (FDT) is presented. The generalized coordinate of the system is changed by an external force and is expressed by means of causal susceptibility, its Fourier transform – the transfer function, generalized impedance and active resistance. These characteristics describe heat dissipation on the resistor and the result is generalized to the dissipative system which is under the action of macroscopic force. The fluctuation voltage on the resistor is obtained by decomposing the thermal chaotic motion of free charges along the conductor into a Fourier series. The number of standing waves and the average energy of the quantum oscillation state at a fixed temperature give the thermal power of charge transfer. By comparing with the Joule-Lenz law and by generalizing the result to an arbitrary isothermal system, the mean square of the fluctuating force and dispersion of the generalized coordinate caused by the thermal motion are obtained. The autocorrelation functions of the generalized coordinate and the random force, and their spectral densities are expressed through the considered characteristics. The content of FDT is that the power of heat release, the spectral densities of the fluctuating force and the autocorrelation are proportional to the imaginary part of the transfer function of the system. The result is used for thermal radiation in a cavity the walls of which contain electric dipoles excited by thermal motion. The transfer function, the fluctuating force acting on the charge, the dispersion of the electric field strength, time autocorrelation of the electric field strength and its spectral density are obtained. Real and imaginary components, the modulus and phase are found for complex relative autocorrelation of the electric field strength and the coherence time is determined.

Thermal Noise in Cubic Optical Cavities

Thermal noise in optical cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Numata et al. derived three equations based on strain energy and the fluctuation–dissipation theorem to estimate the thermal noise contributions of the spacer, substrates, and coating. These equations work well for cylindrical cavities. Extending from that, an expression for the thermal noise for a cubic spacer based on the fluctuation–dissipation theorem is derived, and the thermal noise in cubic optical cavities is investigated in detail by theoretical analysis and finite element simulation. The result shows that the thermal noise of the analytic estimate fits well with that of finite element analysis. Meanwhile, the influence of the compressive force Fp on the thermal noise in cubic optical cavities is analyzed for the first time. For a 50 mm long ultra-low expansion cubic cavity with fused silica substrates and GaAs/AlGaAs crystalline coating, the displacement noise contributed from every Fp of 100 N is about three times more than that of the substrate and coating.