Path integrals and time-dependent mean-field theories

Work Distribution and Path Integrals in General Mean-field Systems

– We consider a mean-field system described by a general collective variable M , driven out of equilibrium by the manipulation of a parameter µ. Given a general dynamics compatible with its equilibrium distribution, we derive the evolution equation for the joint probability distribution function of M and the work W done on the system. We solve this equation by path integrals. We show that the J...

Hierarchical Mean-field Theories

Fast Converging Path Integrals for Time-Dependent Potentials

We calculate the short-time expansion of the propagator for a general many-body quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used...

Time Dependent Relativistic Mean-field Theory

The relativistic mean-field theory provides a framework in which the nuclear manybody problem is described as a self-consistent system of nucleons and mesons. In the mean-field approximation, the self-consistent time evolution of the nuclear system describes the dynamics of collective motion: double giant resonances, nuclear compressibility from monopole resonances, regular and chaotic dynamics...

The pseudoparticle approach for solving path integrals in gauge theories

We present a numerical technique for calculating path integrals in non-compact U(1) and SU(2) gauge theories. The gauge fields are represented by a superposition of pseudoparticles of various types with their amplitudes and color orientations as degrees of freedom. Applied to Maxwell theory this technique results in a potential which is in excellent agreement with the Coulomb potential. For SU(...