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Goldenfeld Phase Transitions Djvu Free [REPACK]

Goldenfeld Phase Transitions Djvu Free >

Goldenfeld Phase Transitions Djvu Free [REPACK]

We propose that the thermodynamics and the kinetics of the phase transition between wormhole and two black hole described by the two coupled SYK model can be investigated in terms of the stochastic dynamics on the underlying free energy landscape. We assume that the phase transition is a stochastic process under the thermal fluctuations. By quantifying the underlying free energy landscape, we study the phase diagram, the kinetic time and its fluctuations in details, which reveal the underlying thermodynamics and kinetics. It is shown that the first order phase transition between wormhole and two black hole described by two coupled SYK model is analogous to the Van der Waals phase transition. Therefore, the emergence of wormhole and two black hole phases, the phase transition and associated kinetics can be quantitatively addressed in our free energy landscape and kinetic framework through the dependence on the barrier height and the temperature.

Our work underscores not only the potential importance of zonal flows in other transitional turbulence situations9,10, but also shows the utility of coarse-grained effective models for non-equilibrium phase transitions, even to states as perplexing as fluid turbulence.

A good reference to applications is LatticeGas Cellular Automata: Simple Models of Complex Hydrodynamics by D. Rothman and S.Zaleski. These same authors have a somewhat different review article entitled Lattice-gasmodels of phase separation: interfaces, phase transitions, and multiphase flow inReviews of Modern Physics, 66, 1417 (1994).

The lecture course provides an introduction to the theory of classical and quantum phase transitions, to position-space as well as Wilson renormalisation-group theory. Emphasis will be set on broadly used spin models as well as bosonic field theories relevant in particular for applications in the field of ultracold atomic gases. Methodologically, the lecture will build on the basics of the operator as well as the path-integral approach to quantum field theory. Basic knowledge of quantum mechanics, statistical mechanics, and quantum field theory is presumed.

Content: Introduction- Classical phase transitions - phase diagram of water - Ehrenfest classification - continuous phase transitions - quantum phase transitionsPhase transition in the classical Ising model- Ising Hamiltonian - Spontaneous symmetry breaking - Thermodynamic properties - Phase transitions in the Ising model - Landau mean-field theory - Mean-field critical exponents - Correlation functions - Hubbard Stratonovich transformation - Functional-integral representation - Ginzburg-Landau-Wilson functional - Saddlepoint approximation and Gaussian effective action - Ginzburg criterionRenormalisation-group theory in position space- Block-spin transformation - Transfer-matrix solution of the 1D Ising chain - RG stepping for the 1D and 2D Ising models - Critical point - RG fixed points - Relevant and irrelevant couplings - Universality and universality class - Renormalisation-group flows - Scaling properties of the free energy and of the two-point correlation function - Scaling relations between critical exponents - The scaling hypothesisWilson's Renormalisation Group - Perturbation theory - Linked-Cluster and Wick's theorems - Dyson equation - One-loop critical properties - Dimensional analysis - Momentum-scale RG - Gaussian fixed point - Wilson-Fisher fixed point - Epsilon-expansion - Critical exponents - Wave function renormalisation and anomalous dimension - Suppl. Mat.: Asymptotic expansionsQuantum phase transitions- Quantum Ising model - Mapping of the classical Ising chain to a quantum spin model - Universal scaling behaviour - Thermal as time-ordered correlators - Quantum to classical mapping - Perturbative spectrum of the transverse-field Ising model - Jordan Wigner transformation and exact spectrum - Universal crossover functions near the quantum critical point - Anomal

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