اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn a field theoretical model of polymeric $2s-$plats and some of its consequences
59
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The field theory approach to the statistical mechanics of a system of N polymer rings linked together is generalized to the case of links that have a fixed number $2s$ of maxima and minima. Such kind of links are called plats and appear for instance in the DNA of living organisms. The topological states of the link are distinguished using the Gauss linking number. This is a relatively weak link invariant in the case of a general link, but its efficiency improves when $2s-$plats are considered. It is proved that, if we restrict ourselves to $2s-$plat conformations, the field theoretical model established here is able to take into account also the interactions of topological origin involving three chains simultaneously. It is shown that these three-body interactions have nonvanishing contributions when three or more rings are entangled together, enhancing for instance the attractive forces between monomers. The model can be used to study the statistical mechanics of polymers in confined geometries, for instance when $2s$ extrema of a few polymer rings are attached to membranes. Its partition function is mapped here into that of a multi-layer electron gas. Such quasi-particle systems are studied in connection with several interesting applications, including high-$T_c$ superconductivity and topological quantum computing. At the end an useful connection with the cosh-Gordon equation is shown.
قيم البحث
اقرأ أيضاً
Quantum Brownian motion in ratchet potentials is investigated by means of an approach based on a duality relation. This relation links the long-time dynamics in a tilted ratchet potential in the presence of dissipation with the one in a driven dissip
ative tight-binding model. The application to quantum ratchet yields a simple expression for the ratchet current in terms of the transition rates in the tight-binding system.
Continuum models with critical end points are considered whose Hamiltonian ${mathcal{H}}[phi,psi]$ depends on two densities $phi$ and $psi$. Field-theoretic methods are used to show the equivalence of the critical behavior on the critical line and at
the critical end point and to give a systematic derivation of critical-end-point singularities like the thermal singularity $sim|{t}|^{2-alpha}$ of the spectator-phase boundary and the coexistence singularities $sim |{t}|^{1-alpha}$ or $sim|{t}|^{beta}$ of the secondary density $<psi>$. The appearance of a discontinuity eigenexponent associated with the critical end point is confirmed, and the mechanism by which it arises in field theory is clarified.
In this work we will review the main properties of brane-world models with low tension. Starting from very general principles, it is possible to obtain an effective action for the relevant degrees of freedom at low energies (branons). Using the cross
sections for high-energy processes involving branons, we set bounds on the different parameters appearing in these models. We also show that branons provide a WIMP candidate for dark matter in a natural way. We consider cosmological constraints on its thermal and non-thermal relic abundances. We derive direct detection limits and compare those limits with the preferred parameter region in the case in which the EGRET excess in the diffuse galactic gamma rays is due to dark matter annihilation. Finally we will discuss the constraints coming from the precision tests of the Standard Model and the muon anomalous magnetic moment.
A nonperturbative renormalization of the phi^4 model is considered. First we integrate out only a single pair of conjugated modes with wave vectors +/- q. Then we are looking for the RG equation which would describe the transformation of the Hamilton
ian under the integration over a shell Lambda - d Lambda < k < Lambda, where d Lambda -> 0. We show that the known Wegner--Houghton equation is consistent with the assumption of a simple superposition of the integration results for +/- q. The renormalized action can be expanded in powers of the phi^4 coupling constant u in the high temperature phase at u -> 0. We compare the expansion coefficients with those exactly calculated by the diagrammatic perturbative method, and find some inconsistency. It causes a question in which sense the Wegner-Houghton equation is really exact.
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the $u$ plane
for the model in one dimension and on infinite-length quasi-one-dimensional strips. In the case of real $h=H/(k_BT)$, these results provide new insights into features of our earlier study of this case. We also consider complex $h=H/(k_BT)$ and $mu=e^{-2h}$. Calculations of complex-$u$ zeros of the partition function on sections of the square lattice are presented. For the case of imaginary $h$, i.e., $mu=e^{itheta}$, we use exact results for the quasi-1D strips together with these partition function zeros for the model in 2D to infer some properties of the resultant phase diagram in the $u$ plane. We find that in this case, the phase boundary ${cal B}_u$ contains a real line segment extending through part of the physical ferromagnetic interval $0 le u le 1$, with a right-hand endpoint $u_{rhe}$ at the temperature for which the Yang-Lee edge singularity occurs at $mu=e^{pm itheta}$. Conformal field theory arguments are used to relate the singularities at $u_{rhe}$ and the Yang-Lee edge.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
