Quantum Field Theory of Thermal Diffusion

F. C. Khanna, Adolfo P. C. Malbouisson, J. M. C. Malbouisson +1 more

Luca V. Delacrétaz, Ruchira Mishra

Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved densities. We uncover a simple scaling behavior of correlators at late times, and, focusing on three and four-point functions, derive the asymptotically exact universal scaling functions that characterize nonlinear response in diffusive systems. This allows for precision tests of thermalization beyond linear response in quantum and classical many-body systems. We confirm our predictions in a classical lattice gas.

Ismail Abbas

The modern theory of quantum mechanics is incomplete. It is capable of describing the quantum energy field on the microscopic scale via the Schrödinger equation and its derivatives but is not capable of describing the energy field on the macroscopic scale such as the domain of thermal diffusion and sound intensity in audio rooms. . etc. On the other hand, in previous articles we have shown that the so-called theory of Cairo techniques and its chains of B matrices are more complete. They can numerically resolve both the macroscopic energy field on the thermodynamic scale, such as the energy field in thermal diffusion PDEs, and the sound energy field of PDEs in audio rooms. . etc. In a precise and revolutionary way. Additionally, they are also capable of describing and resolving the quantum energy distribution at the microscopic scale initially described via the Schrödinger equation and its derivatives. Considering that they can describe and solve pure mathematical problems such as numerical integration and infinite integer series in more detail, we better conclude that the numerical statistical methods of Cairo techniques and its B matrix chains are capable of describing almost all fields with the exception of the gravitational field (of general relativity) which will be the subject of the next article. Therefore, we propose that the Cairo techniques and their B-matrix chains constitute the required foundations of a unified field theory. It's logical and it makes sense. In this paper, we present detailed theoretical and numerical studies of six diverse physical and mathematical studies where the numerical results are surprisingly accurate. In conclusion, B-matrix strings and numerical statistical theory of Cairo techniques provide a framework for a unified energy density field theory. Schrödinger's equation can be considered as a diffusion equation with a diffusion coefficient β 2 = ħ / 2 m . D=(6.65E-34/2 Pi/2.9.31E-31=E-34/18.6 E-31=E- 3/18.6=5.6E-4. . !! SQRT Mue 0/Eps 0)=377 Ohm = Z01/Z0 =2.65 E-3 mho

Francesco Paolo Mancini, M. Marinaro, H. Matsumoto

Richard A. Davison, Subir Sachdev A, Michael Andrew Blake

We study the thermal diffusivity D[subscript T] in models of metals without quasiparticle excitations (“strange metals”). The many-body quantum chaos and transport properties of such metals can be efficiently described by a holographic representation in a gravitational theory in an emergent curved spacetime with an additional spatial dimension. We find that at generic infrared fixed points D[subscript T] is always related to parameters characterizing many-body quantum chaos: the butterfly velocity v[subscript B] and Lyapunov time τ[subscript L] through D[subscript T]∼v[subscript B][superscript 2]τ[subscript L]. The relationship holds independently of the charge density, periodic potential strength, or magnetic field at the fixed point. The generality of this result follows from the observation that the thermal conductivity of strange metals depends only on the metric near the horizon of a black hole in the emergent spacetime and is otherwise insensitive to the profile of any matter fields.

Piotr Garbaczewski