Related papers: Exact evolution equation for the effective potenti…
A scale--dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
Fluctuation and dissipation dynamics is examined at all temperature ranges for the general case of a background time evolving scalar field coupled to heavy intermediate quantum fields which in turn are coupled to light quantum fields. The…
We present a new class of evolution equations which govern the high-energy behavior of power-suppressed scattering amplitudes. The equations can be viewed as a renormalization group flow with respect to the relevant effective field theory…
An exact renormalization group equation describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. It interpolates between the microphysical laws and the complex macroscopic phenomena. We…
We address optimal control of semilinear evolution equations on Banach spaces with finitely many control channels, a framework encompassing a broad class of infinite-dimensional dynamical systems, arising in many applications. For this…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
We critically examine the applicability of the effective potential within dynamical situations and find, in short, that the answer is negative. An important caveat of the use of an effective potential in dynamical equations of motion is an…
A linear growth-diffusion equation is studied in a time-dependent interval whose location and length both vary. We prove conditions on the boundary motion for which the solution can be found in exact form, and derive the explicit expression…
A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
The time evolution of correlation functions in statistical systems is described by an exact functional differential equation for the corresponding generating functionals. This allows for a systematic discussion of non-equilibrium physics…
It is well known that effective potentials can be gauge-dependent while their values at extrema should be gauge-invariant. Unfortunately, establishing this invariance in perturbation theory is not straightforward, since contributions from…
It was recently shown that the exact factorization of the electron-nuclear wavefunction allows the construction of a Schr\"odinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the…
Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity…
In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.
Non-perturbatively generated effective potentials play an extremely useful and often critical role in string and inflationary model building. These potentials are typically computed by methods that assume the system is in equilibrium. For…
Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states…
We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective…
For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting…