Related papers: Exact evolution equation for the effective potenti…
We consider a class of abstract second order evolution equations with a restoring force that is strictly superlinear at infinity with respect to the position, and a dissipation mechanism that is strictly superlinear at infinity with respect…
We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for…
We propose a proof of convergence of an adaptive method used in molecular dynamics to compute free energy profiles. Mathematically, it amounts to studying the long-time behavior of a stochastic process which satisfies a non-linear…
The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse grained free energy. A suitable truncation is solved numerically.
We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with…
Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term…
We develop a method for the construction of the effective potential at high temperatures based on the effective field theory approach and renormalization group. It allows one to sum up the leading logarithms in all orders of perturbation…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…
The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order…
The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
We demonstrate the feasibility of a nonperturbative analysis of quantum field theory in the worldline formalism with the help of an efficient numerical algorithm. In particular, we compute the effective action for a super-renormalizable…
The exact controllability to the origin for linear evolution control equation is considered.The problem is investigated by its transformation to infinite linear moment problem. Conditions for the existence of solution for infinite linear…
Assuming a schematic form of the nucleon effective mass as a function of nuclear excitation energy and mass, we provide a simple explanation for understanding the experimentally observed mass dependence of the nuclear caloric curve. It is…
Moments are expectation values of products of powers of position and momentum, taken over quantum states (or averages over a set of classical particles). For free particles, the evolution in the quantum case is closely related to that of a…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
The problem of a massive elastic string depinning from a linear defect under the action of a small driving force is considered. To exponential accuracy the decay rate is calculated with the help of the instanton method; then, fluctuations…