Related papers: Exact evolution equation for the effective potenti…
Significance of the chiral symmetry restoration is studied by considering the role of the modification of the nucleon mass in nuclear medium at finite density and temperature. Using the Korea-IBS-Daegu-SKKU density functional theory, we can…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
We study a class of infinite-dimensional singular stochastic control problems with applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially-ordered…
We compute the effective potential for $\phi^4$ theory with a squeezed coherent state type of construct for the ground state. The method essentially consists in optimising the basis at zero and finite temperatures. The gap equation becomes…
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…
In this short paper, we investigate the consequences of observer dependence of the quantum effective potential for an interacting field theory. Specializing to $d+2$ dimensional Euclidean Rindler space, we develop the formalism to calculate…
The method of the effective action for the composite operators $\Phi^2(x)$ and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field with $\lambda\Phi^4$ interaction. An expansion of the finite temperature effective…
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in…
The gauge parameter dependence of the effective potential is determined by partial differential equations involving also the Higgs boson field expectation value. Solving these equations by the method of characteristics leads to complete…
The temporal evolution of step-edge fluctuations under electromigration conditions is analysed using a continuum Langevin model. If the electromigration driving force acts in the step up/down direction, and step-edge diffusion is the…
Solvable structures are exploited in order to find families of explicit solutions to evolution PDEs admitting suitable differential constraints. The effectiveness of the method is verified on several explicit examples.
A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
We show that a general, exact cosmological solution, where dynamics of scalar field is assigned by an exponential potential, fulfils all the issues of dark energy approach, both from a theoretical point of view and in comparison with…
The 1/N expansion of the two-particle irreducible (2PI) effective action is employed to compute universal properties at the second-order phase transition of an O(N)-symmetric N-vector model directly in three dimensions. At next-to-leading…
It is widely believed that the top loop corrections to the Higgs effective potential destabilise the electroweak (EW) vacuum and that, imposing stability, lower bounds on the Higgs mass can be derived. With the help of a scalar-Yukawa…
The original Miura transformation, considered as a nonlinear potential transformation, is applicable to a continual class of evolution equations, not only to discrete integrable equations and their hierarchies. The same continual class of…
We study the low-temperature effective potential of the Ising model. We evaluate the three-point and four-point zero-momentum renormalized coupling constants that parametrize the expansion of the effective potential near the coexistence…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…