单模光腔中N个二能级原子系统的有限温度特性和相变

本文研究单模光场中N个二能级原子Dicke模型的有限温度特性和相变. 把原子赝自旋转换为双模费米算符, 用虚时路径积分方法推导出系统的配分函数, 对作用量变分求极值得到系统的热力学平衡方程, 及原子布居数期待值和平均光子数随原子-光场耦合强度变化的解析表达式. 重点研究了在量子涨落起主导作用的低温区, 由耦合强度变化产生的从正常相到超辐射相的相变, 指出该相变遵从Landau连续相变理论, 平均光子数可作为序参数, 零值表示正常相, 大于零则为超辐射相. 在零温极限下本文的结果和量子相变理论完全符合. 另外, 本文也讨论了系统的热力学性质, 比较有限温度相变和量子相变的异同. 发现, 在强耦合区低温稳定态的光子数和平均能量都和绝对零度的值趋于一致, 而超辐射相的熵则随耦合强度的增强迅速衰减为零.     

The parameter in an Sp(2N)×U(1) model

We present a model based upon the gauge group Sp(2N)×U(1) which contains the SU(2)×U(1) electroweak model as an exact subsector. The parameter in this symplectic model is calculated to leading order in 1/N. We illustrate the general dependence of upon the Higgs coupling constant λ with particular interest in th e large λ limit. Finally, the 1/N result is compared with conventional one-and two-loop expressions for in the standard model.     

The large N limit of the O(N) Heisenberg spin system in two dimensions

The large N limit of the O(N) Heisenberg spin system in two dimensions (a lattice version of the non-linear σ-model) is analysed by the collective field technique. A compact expression for the mass gap and the β-function is obtained for arbitrary but fixed gN. The strong and weak coupling limits of this expression correctly reproduce the known results.     

The self-dual Chern-Simons CP(N) models

We study the Chern-Simons CP(N) models with a global U(1) symmetry and found the self-dual models among them. The Bogomolnyi-type bound in these self-dual models is a nontrivial generalization of that in the pure CP(N) models. Our models have quite a rich vacuum and soliton structure and approach the many known gauged self-dual models in an appropriate limit.     

The large-N phase transition in the U(N) chiral models

We prove the existence of a large-N phase transition in the d = 2 chiral model and calculate via strong-coupling methods the phase-transition point. The critical coupling constant is 0.324. We also treat the chiral model chains (equivalent to the gauge model on polyhedrons) and our approximate calculations come very close to the exact results for the solvable cases.     

The thermodynamic Bethe ansatz and the 1/N correction to the density phase transition in the Gross-Neveu model

We compute the 1/N correction to the location of the previously found first-order phase transition in the Gross-Neveu model at a chemical potential where m is the fermion mass. We employ an expression for the free energy f(μ) given by the thermodynamic Bethe ansatz under the approximation that the fundamental fermions dominate the ground state, and combine it with the effective potential evaluated at zero chemical potential.

Our result is .     

The large-N phase transition in the U(N) lattice gauge theory

We present an outline for a proof (the precise details of which will be presented in a follow-up paper) of a large-N phase transition in dimensions greater than two. The critical couplings are calculated in d=3 and d=4 and are found to be β=0.44 and β=0.40, respectively.     

Anomalies in gravity-coupled SU(N) Yang-Mills theory

In a general even space-time dimension I consider spin-1/2 fermions coupled to SU(N) Yang-Mills fields and to gravity. It is shown (unexpectedly) that, once the chiral gauge anomaly is cancelled, gravitational anomalies do not further constrain the fermion representation.     

Deformations of multiparameter quantum gl(N)

Multiparameter quantum gl(N) is not a rigid structure. This Letter defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first-order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constantr-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.     

Effects of additional Higgs doublets on the Coleman-Weinberg SU(2) × U(1) → U(1)em phase transition

In the standard electroweak theory with a Coleman-Weinberg Higgs doublet, it has been shown that the SU(2) × U(1) → U(1)_em phase transition is driven by chiral symmetry breaking and that a phenomenologically dangerous amount of entropy is produced. We show that the addition of a second, sufficiently heavy Coleman-Weinberg doublet will make the transition go via tunneling and will suppress excessive entropy generation.     

Deconfining phase transition in the U(1) model with Wilson's action

In dimensiond4, the lattice U(1) gauge theory defined with the Wilson action is shown to have a deconfining phase transition at weak coupling. The proof uses a higher dimensional analogue of the Higgs mechanism and a correlation inequality to remove the massless modes of the theory. The remaining modes are controlled by a simple cluster expansion.Research supported in part by U.S. National Science Foundation grant PHY 8117463     

The action of SU(N) lattice gauge theory in terms of the heat kernel on the group manifold

We consider the heat kernel on the group manifold as an alternative to the Wilson action in lattice gauge theory, and we exhibit its strict analogy with the well-known Berezinski-Villain action. With the heat kernel action, the Gross-Witten singularity is rigorously absent in two dimensions. The similarity of the heat kernel action to the hamiltonian approach should provide a better convergence of the lagrangian strong coupling expansion, while its behaviour at weak coupling should simplify the analysis of the weak coupling perturbative expansion.     

Large N expansion for strongly-coupled boson–fermion mixtures

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson–fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.     

Exact monodromy group of N = 2 heterotic superstring

We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b_1,1 = 2 and b_1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU(2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.     

Non-perturbative effects in two-dimensional lattice O(N) models

Non-abelian analogues of Kosterlitz-Thouless vortices may have important effects in two-dimensional lattice spin systems with O(N) symmetries. Renormalization group equations which include these effects are developed in two ways. The first set of equations extends the renormalization group equations of Kosterlitz to O(N) spin systems, in a form suggested by Cardy and Hamber. The second is derived from a Villain-type O(N) model using Migdal's recursion relations. Using these equations, the part played by topological excitations in the crossover from weak to strong coupling behavior is studied. Another effect which influences crossover behavior is also discussed: irrelevant operators which occur naturally in lattice theories can make important contributions to the renormalization group flow in the crossover region. When combined with conventional perturbative results, these two effects may explain the observed crossover behavior of these models.     

Matching exact results and one-instanton predictions in supersymmetric SU(N) theories

A one-instanton level test is performed for the proposed reparameterisation scheme matching the conjectured exact low energy results and instanton predictions for supersymmetric SU(N) gauge theories with 2N massless fundamental matter hypermultiplets across the entire quantum moduli space. The constants within the scheme which ensure agreement between the exact results and the instanton predictions for general N are derived. This constitutes a non-trivial test of the scheme, which eliminates the discrepancies arising when the two sets of results are compared.     

Dynamics of O(N) chiral supersymmetry at finite energy density

We consider an O(N) version of a massive, interacting, chiral supersymmetry model solved exactly in the large N limit. We demonstrate that the system approaches a stable attractor at high energy densities, corresponding to a non-perturbative state for which the relevant field quanta are massless. The state is one of spontaneously broken O(N), which, due to the influence of supersymmetry, does not become restored at high energies. Introducing soft supersymmetry breaking to the Lagrangian results in scalar masses at the soft breaking scale m_s independent of the mass scale of supersymmetry μ, with even smaller masses for the fermions.     

GLq(N)-covariant braided differential bialgebras

We study the possibility of defining the (braided) comultiplication for the GL _q (N)-covariant differential complexes on some quantum spaces. We discover suchdifferential bialgebras (and Hopf algebras) on the bosonic and fermionic quantum hyperplanes (with additive coproduct) and on the braided matrix algebra BM _q (N) with both multiplicative and additive coproducts. The latter case is related (forN = 2) to theq-Minkowski space andq-Poincaré algebra.     

The n = 0 replica limit of U(n) and U(n)/SO(n) models

Recently the replica limit n = 0 of the U(n) and U(n)/SO(n) models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and U(n)/SO(n). This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and U(n)/SO(n) and draw consequences for these functions in this limit.