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Register a new userLocal Equilibrium Spin Distribution From Detailed Balance
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As the core ingredient for spin polarization, the local equilibrium spin distribution function is derived from the detailed balance principle. The kinetic theory for interacting fermionic systems is applied to the Nambu--Jona-Lasinio model at quark level. Under the semi-classical expansion with respect to $hbar$ and non-perturbative expansion with respect to $N_c$, the kinetic equations for the vector and axial-vector distribution functions are derived with collision terms. It is found that, for an initially unpolarized system, non-zero spin polarization can be generated at the order of $hbar$ from the coupling between the vector and axial-vector charges. The local equilibrium spin polarization is derived from the requirement of detailed balance. It arises from the thermal vorticity and is orthogonal to the particle momentum.
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The principle of detailed balance is at the basis of equilibrium physics and is equivalent to the Kubo-Martin-Schwinger (KMS) condition (under quite general assumptions). In the present paper we prove that a large class of open quantum systems satisfies a dynamical generalization of the detailed balance condition ({it dynamical detailed balance}) expressing the fact that all the micro-currents, associated to the Bohr frequencies are constant. The usual (equilibrium) detailed balance condition is characterized by the property that this constant is identically zero. From this we deduce a simple and experimentally measurable relation expressing the microcurrent associated to a transition between two levels $epsilon_mtoepsilon_n$ as a linear combination of the occupation probabilities of the two levels, with coefficients given by the generalized susceptivities (transport coefficients). Finally, using a master equation characterization of the dynamical detailed balance condition, we show that this condition is equivalent to a local generalization of the usual KMS condition.
We analyse and interpret the effects of breaking detailed balance on the convergence to equilibrium of conservative interacting particle systems and their hydrodynamic scaling limits. For finite systems of interacting particles, we review existing results showing that irreversible processes converge faster to their steady state than reversible ones. We show how this behaviour appears in the hydrodynamic limit of such processes, as described by macroscopic fluctuation theory, and we provide a quantitative expression for the acceleration of convergence in this setting. We give a geometrical interpretation of this acceleration, in terms of currents that are emph{antisymmetric} under time-reversal and orthogonal to the free energy gradient, which act to drive the system away from states where (reversible) gradient-descent dynamics result in slow convergence to equilibrium.
Diffusive dynamics in presence of deep energy minima and weak nongradient forces can be coarse-grained into a mesoscopic jump process over the various basins of attraction. Combining standard weak-noise results with a path integral expansion around equilibrium, we show that the emerging transition rates satisfy local detailed balance (LDB). Namely, the log ratio of the transition rates between nearby basins of attractions equals the free-energy variation appearing at equilibrium, supplemented by the work done by the nonconservative forces along the typical transition path. When the mesoscopic dynamics possesses a large-size deterministic limit, it can be further reduced to a jump process over macroscopic states satisfying LDB. The persistence of LDB under coarse graining of weakly nonequilibrium states is a generic consequence of the fact that only dissipative effects matter close to equilibrium.
Among the Markov chains breaking detailed-balance that have been proposed in the field of Monte-Carlo sampling in order to accelerate the convergence towards the steady state with respect to the detailed-balance dynamics, the idea of Lifting consists in duplicating the configuration space into two copies $sigma=pm$ and in imposing directed flows in each copy in order to explore the configuration space more efficiently. The skew-detailed-balance Lifted-Markov-chain introduced by K. S. Turitsyn, M. Chertkov and M. Vucelja [Physica D Nonlinear Phenomena 240 , 410 (2011)] is revisited for the Curie-Weiss mean-field ferromagnetic model, where the dynamics for the magnetization is closed. The large deviations at various levels for empirical time-averaged observables are analyzed and compared with their detailed-balance counterparts, both for the discrete extensive magnetization $M$ and for the continuous intensive magnetization $m=frac{M}{N}$ for large system-size $N$.
A systematic theory of product and diagonal states is developed for tensor products of $mathbb Z_2$-graded $*$-algebras, as well as $mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {it fermionic $C^*$-tensor product} of $mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.
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