ON THE DIMERIZATION OF LINEAR POLYMERS

1989 ◽  
Vol 03 (02) ◽  
pp. 125-133 ◽  
Author(s):  
C. ARAGÃO DE CARVALHO
Keyword(s):  
Free Energy ◽  
Effective Potential ◽  
Ground State ◽  
Finite Temperature ◽  
Continuum Limit ◽  
Linear Polymers ◽  
Renormalization Condition ◽  
Loop Approximation ◽  
The One ◽  
The Continuum

We use the continuum limit of the Su-Schrieffer-Heeger model for linear polymers to construct its effective potential (Gibbs free energy) both at zero and finite temperature. We study both trans and cis-polymers. Our results show that, depending on a renormalization condition to be extracted from experiment, there are several possibilities for the minima of the dimerized ground state of cis-polymers. All calculations are done in the one-loop approximation.

Ring-diagram summations in the finite-temperature effective potential

1993 ◽  
Vol 71 (5-6) ◽  
pp. 227-236 ◽  
Author(s):  
M. E. Carrington
Keyword(s):  
Phase Transition ◽  
Standard Model ◽  
Effective Potential ◽  
Finite Temperature ◽  
Electroweak Phase Transition ◽  
First Order ◽  
Ring Diagram ◽  
First Order Phase Transition ◽  
The Standard Model ◽  
The One

There has been much recent interest in the finite-temperature effective potential of the standard model in the context of the electroweak phase transition. We review the calculation of the effective potential with particular emphasis on the validity of the expansions that are used. The presence of a term that is cubic in the Higgs condensate in the one-loop effective potential appears to indicate a first-order electroweak phase transition. However, in the high-temperature regime, the infrared singularities inherent in massless models produce cubic terms that are of the same order in the coupling. In this paper, we discuss the inclusion of an infinite set of these terms via the ring-diagram summation, and show that the standard model has a first-order phase transition in the weak coupling expansion.

scholarly journals Ground-state energy of a Richardson-Gaudin integrable BCS model

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Yibing Shen ◽  
Phillip Isaac ◽  
Jon Links
Keyword(s):  
Integral Equation ◽  
Ground State Energy ◽  
Ground State ◽  
Continuum Limit ◽  
State Energy ◽  
Mean Field ◽  
Bcs Model ◽  
Energy Expression ◽  
The Continuum

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

FINITE TEMPERATURE EFFECTIVE POTENTIAL IN A KALUZA-KLEIN UNIVERSE

1990 ◽  
Vol 05 (02) ◽  
pp. 353-361 ◽  
Author(s):  
PINAKI ROY
Keyword(s):  
Low Temperature ◽  
Effective Potential ◽  
Finite Temperature ◽  
Scalar Fields ◽  
Walker Metric ◽  
The One ◽  
Kaluza Klein

We evaluate the finite temperature one-loop effective potential for scalar fields in Kaluza-Klein universe consisting of the product of a space with open Robertson-Walker metric and the N sphere SN. The one-loop effective potential has been computed in both high and low temperature limits.

THE (ORBIFOLD) EULER CHARACTERISTIC OF THE MODULI SPACE OF CURVES AND THE CONTINUUM LIMIT OF PENNER'S CONNECTED GENERATING FUNCTION

1991 ◽  
Vol 03 (03) ◽  
pp. 285-300 ◽  
Author(s):  
NOUREDDINE CHAIR
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Euler Characteristic ◽  
Generating Function ◽  
Moduli Space ◽  
Continuum Limit ◽  
Recursion Relation ◽  
Moduli Space Of Curves ◽  
Genus Zero ◽  
The Continuum

The generating function that gives rise to the orbifold Euler characteristic of the moduli space of punctured compact Rieman surfaces [Formula: see text], g ≥ 0 is derived explicitly. In the derivation, we show that we do not need to use the three-term recursion relation for the orthogonal polynomials. Also the continuum limit of Penner's connected generating function is considered and is shown to be formally equivalent to the free energy obtained recently by Distler and Vafa which exhibits the logarithmic divergences found for genus zero and one in D = 1 matrix models. Finally, it is shown that the free energy and its s-derivatives are nothing but the continuum limit of a certain generating function introduced by Harer and Zagier in obtaining the true Euler characteristic with any number of punctures,[Formula: see text], s ≥ 0.

Finite-Temperature Quasi-Continuum

2013 ◽  
Vol 65 (1) ◽  
Author(s):  
E. B. Tadmor ◽  
F. Legoll ◽  
W. K. Kim ◽  
L. M. Dupuy ◽  
R. E. Miller
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Finite Temperature ◽  
Theoretical Background ◽  
Review Article ◽  
Test Cases ◽  
Loading Conditions ◽  
Atomistic Region ◽  
Quasistatic Loading ◽  
The Continuum

A generalization of the quasi-continuum (QC) method to finite temperature is presented. The resulting “hot-QC” formulation is a partitioned domain multiscale method in which atomistic regions modeled via molecular dynamics coexist with surrounding continuum regions. Hot-QC can be used to study equilibrium properties of systems under constant or quasistatic loading conditions. Two variants of the method are presented which differ in how continuum regions are evolved. In “hot-QC-static” the free energy of the continuum is minimized at each step as the atomistic region evolves dynamically. In “hot-QC-dynamic” both the atomistic and continuum regions evolve dynamically in tandem. The latter approach is computationally more efficient, but introduces an anomalous “mesh entropy” which must be corrected. Following a brief review of related finite-temperature methods, this review article provides the theoretical background for hot-QC (including new results), discusses the implementational details, and demonstrates the utility of the method via example test cases including nanoindentation at finite temperature.

INTERACTING BOSE GAS CONFINED BY AN EXTERNAL POTENTIAL

2007 ◽  
Vol 22 (27) ◽  
pp. 4923-4936 ◽  
Author(s):  
G. GNANAPRAGASAM ◽  
M. P. DAS
Keyword(s):  
Specific Heat ◽  
Ground State ◽  
Finite Temperature ◽  
Continuum Limit ◽  
Spectral Representation ◽  
Equation Of Motion ◽  
Bose Gas ◽  
External Potential ◽  
Green Functions ◽  
Motion Method

Interacting Bose gas confined by an external potential is studied using Green functions in spectral representation. The calculation is presented transparently using the equation of motion method. With this, the interplay between the condensed and the non-condensed atoms is inevitably seen. An expression for the condensate number at finite temperature is obtained in the lowest and first orders, from which depletion of bosons from the ground state is qualitatively analyzed. Finally, we discuss the behaviour of the specific heat of a trapped interacting Bose gas in the quasi-continuum limit.

THE GAUSSIAN APPROXIMATION FOR THE λφ4THEORY AT FINITE TEMPERATURE REVISITED

1991 ◽  
Vol 06 (26) ◽  
pp. 4579-4638 ◽  
Author(s):  
FRÉDÉRIQUE GRASSI ◽  
RÉMI HAKIM ◽  
HORACIO D. SIVAK
Keyword(s):  
Free Energy ◽  
Effective Mass ◽  
Effective Potential ◽  
Finite Temperature ◽  
Energy Momentum Tensor ◽  
Gaussian Approximation ◽  
Dimensional Regularization ◽  
Momentum Tensor ◽  
Effects Of Temperature ◽  
Physical Quantities

This paper is devoted to a systematic study of the λφ4 theory in the Gaussian approximation and at finite temperature. Although our results can be extended in a straightforward manner to other dimensions, only the case of four (1+3) dimensions is dealt with here. The Gaussian approximation is implemented via the moments of the field φ, a method somewhat simpler than the Gaussian functional approach. Furthermore, the effective potential (equivalently, the free energy) is calculated through the evaluation of the energy-momentum tensor of quasiparticles endowed with an effective mass. This effective mass generally obeys a gap equation, which is analyzed and solved. Besides the “precarious” solution of Stevenson or the “autonomous” one of Stevenson and Tarrach, which are recovered and rediscussed, several nonperturbative solutions, either exhibiting “spontaneous symmetry breaking” or not, are obtained with the help of systematic expansions of various physical quantities in powers of ε, the parameter occurring in the dimensional regularization scheme used throughout this paper. The effects of temperature are discussed in detail: phase transitions in the precarious or autonomous solutions occur. Other simple Gaussian (but not minimal) solutions for the effective potential (free energy) are also obtained.

NON-PERTURBATIVE CALCULATION OF EFFECTIVE POTENTIAL IN SUPERSYMMETRIC LIOUVILLE MODEL

1990 ◽  
Vol 05 (26) ◽  
pp. 2115-2125
Author(s):  
ROSE P. IGNATIUS ◽  
K. P. SATHEESH ◽  
V. C. KURIAKOSE ◽  
K. BABU JOSEPH
Keyword(s):  
Effective Potential ◽  
Ground State ◽  
Finite Temperature ◽  
Temperature Effects ◽  
Liouville Theory ◽  
Translational Symmetry ◽  
Zero Temperature ◽  
Perturbative Calculation ◽  
Gaussian Effective Potential

The Gaussian effective potential for the supersymmetric Liouville model is computed both at zero temperature and at a finite temperature. It is noted that the supersymmetric Liouville theory, just like the ordinary Liouville model, does not possess a translationally invariant ground state. The broken translational symmetry is not restored by temperature effects. The supersymmetric Liouville theory is also non-trivial.

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