Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation

Stationary ensemble approximations of dynamic quantum states: Optimizing the Generalized Gibbs Ensemble

We reconsider the non-equilibrium dynamics of closed quantum systems. In particular we focus on the thermalization of integrable systems. Here we show how the generalized Gibbs Ensemble (GGE) can be constructed as the best approximation to the time dependent density matrix. Our procedure allows for a systematic construction of the GGE by a constrained minimization of the distance between the latter and the true state. Moreover, we show that the entropy of the GGE is a direct measure for the quality of the approximation. We apply our method to a quenched hard core bose gas. In contrast to the standard GGE, our correlated GGE properly describes the higher order correlation functions

Variational Truncated Wigner Approximation

In this paper we reconsider the notion of an optimal effective Hamiltonian for the semiclassical propagation of the Wigner distribution in phase space. An explicit expression for the optimal effective Hamiltonian is obtained in the short time limit by minimizing the Hilbert-Schmidt distance between the semiclassical approximation and the real state of the system. The method is illustrated for the quartic oscillator

Neo-liberalism at a time of crisis: the case of taxation

This essay explores how the global financial crisis of 2008–2009 has affected the stability of what Stephen Gill has termed the ‘new constitutionalism of disciplinary neo-liberalism’, more precisely, in the realm of international tax policy. Rather than providing an in-depth and complete empirical study of the matter, this essay will highlight certain interesting developments and touch upon a series of possibly relevant questions that could form the basis for a future research agenda. In the first section, we will examine the remarkable strength and resilience of the new constitutionalism as the institutional component of neo-liberal hegemony. Then we will proceed to an exploration of the impact of the crisis on this hegemony, also paying attention to deepening geopolitical multipolarity as an additional variable. The final, more empirical section will investigate the case of international taxation in this context, and demonstrate that new constitutionalism remains a crucial supporting pillar of neo-liberal globalisation

Chaos and thermalization in small quantum systems

Chaos and ergodicity are the cornerstones of statistical physics and thermodynamics. While classically even small systems like a particle in a two-dimensional cavity, can exhibit chaotic behavior and thereby relax to a microcanonical ensemble, quantum systems formally can not. Recent theoretical breakthroughs and, in particular, the eigenstate thermalization hypothesis (ETH) however indicate that quantum systems can also thermalize. In fact ETH provided us with a framework connecting microscopic models and macroscopic phenomena, based on the notion of highly entangled quantum states. Such thermalization was beautifully demonstrated experimentally by A. Kaufman et. al. who studied relaxation dynamics of a small lattice system of interacting bosonic particles. By directly measuring the entanglement entropy of subsystems, as well as other observables, they showed that after the initial transient time the system locally relaxes to a thermal ensemble while globally maintaining a zero-entropy pure state.Comment: Perspectiv