Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSmooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory
182
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.
rate research
Read More
We examine in detail the theoretical underpinnings of previous successful applications of local molecular field (LMF) theory to charged systems. LMF theory generally accounts for the averaged effects of long-ranged components of the intermolecular interactions by using an effective or restructured external field. The derivation starts from the exact Yvon-Born-Green hierarchy and shows that the approximation can be very accurate when the interactions averaged over are slowly varying at characteristic nearest-neighbor distances. Application of LMF theory to Coulomb interactions alone allows for great simplifications of the governing equations. LMF theory then reduces to a single equation for a restructured electrostatic potential that satisfies Poissons equation defined with a smoothed charge density. Because of this charge smoothing by a Gaussian of width sigma, this equation may be solved more simply than the detailed simulation geometry might suggest. Proper choice of the smoothing length sigma plays a major role in ensuring the accuracy of this approximation. We examine the results of a basic confinement of water between corrugated wall and justify the simple LMF equation used in a previous publication. We further generalize these results to confinements that include fixed charges in order to demonstrate the broader impact of charge smoothing by sigma. The slowly-varying part of the restructured electrostatic potential will be more symmetric than the local details of confinements.
The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 80s by Gotze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field theoretic formulation that arrives at very similar mode-coupling equation but which is based on a variational principle and on a controlled expansion in a small dimensioneless parameter. Our approach applies to such physical systems as colloids interacting via a mildly repulsive potential. It can in principle, with moderate efforts, be extended to higher orders and to multipoint correlation functions.
Understanding quantum dissipation is important from both theoretical perspective and applications. Here, we show how to describe dissipation in a scalar field theory. We treat dissipation non-perturbatively, represent it by a bilinear term in the Lagrangian and quantize the theory. We find that dissipation promotes a gap in momentum space and reduces the particle energy. As a result, particle mass becomes dressed by dissipation due to self-interaction. The underlying mechanism is similar to that governing the propagation of transverse collective modes in liquids. We discuss the interplay between the dissipative and mass terms, the associated different regimes of field dynamics and the emergence of ultraviolet and infrared cutoffs due to dissipation.
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of the so-called numerical topological invariants. For each invariant it is possible to derive a field theory that describes the statistical behavior of knotted and linked polymer rings following a straightforward algorithm. The treatment is not limited to the partition function of the system, but it allows also to express the expectation values of general observables as field theory amplitudes. Our strategy is illustrated taking as examples the Gauss linking number and a topological invariant belonging to a class of invariants due to Massey. The consistency of the new method developed here is checked by reproducing a previous field theoretical model of two linked polymer rings. After the passage to field theory, the original topological constraints imposed on the fluctuating paths of the polymers become constraints over the configurations of the topological fields that mediate the interactions of topological origin between the monomers. These constraints involve quantities like the cross-helicity which are of interest in other disciplines, like for instance in modeling the solar magnetic field. While the calculation of the vacuum expectation values of generic observables remains still challenging due to the complexity of the problem of topological entanglement in polymer systems, we succeed here to reduce the evaluation of the moments of the Gauss linking number for two linked polymer rings to the computation of the amplitudes of a free field theory.
We discuss the time-dependent formulation of perturbation theory in the context of the interacting zeroth-order Hamiltonians that appear in multi-reference situations. As an example, we present a time-dependent formulation and implementation of second-order n-electron valence perturbation theory. The resulting t-NEVPT2 method yields the fully uncontracted n-electron valence perturbation wavefunction and energy, but has a lower computational scaling than the usual contracted variants, and also avoids the construction of high-order density matrices and the diagonalization of metrics. We present results of t-NEVPT2 for the water, nitrogen, carbon, and chromium molecules, and outline directions for the future.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
