共查询到20条相似文献,搜索用时 15 毫秒
1.
Jean Bricmont Jean-Raymond Fontaine Joel L. Lebowitz Thomas Spencer 《Communications in Mathematical Physics》1981,78(3):363-371
We consider perturbations of a massless Gaussian lattice field on ? d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities. 相似文献
2.
Jean Bricmont Jean-Raymond Fontaine Joel L. Lebowitz Elliott H. Lieb Thomas Spencer 《Communications in Mathematical Physics》1981,78(4):545-566
We prove that the expansion in powers of the temperatureT of the correlation functions and the free energy of the plane rotator model on ad-dimensional lattice is asymptotic to all orders inT. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures ford=3.Supported by NSF Grant No. MCS 78-01885Supported by NSF Grant No. PHY 78-15920Supported by NSF Grant No. DMR 73-04355Supported by NSF Grant No. PHY-7825390 A01On leave from: Institut de Physique Théorique, Université de Louvain, BelgiumAlso: Department of Physics 相似文献
3.
4.
5.
Tsutomu Momoi 《Journal of statistical physics》1996,85(1-2):193-210
We discuss conditions for the absence of spontaneous breakdown of continuous symmetries in quantum lattice systems atT=0. Our analysis is based on Pitaevskii and Stringari's idea that the uncertainty relation can be employed to show quantum fluctuations. For one-dimensional systems, it is shown that the ground state is invariant under a continuous transformation if a certain uniform susceptibility is finite. For the two- and three-dimensional systems, it is shown that truncated correlation functions cannot decay any more rapidly than|r|
–d+1 whenever the continuous symmetry is spontaneously broken. Both of these phenomena occur owing to quantum fluctuations. Our theorems cover a wide class of quantum lattice systems having not-too-long-range interactions. 相似文献
6.
7.
In this paper a partial unfolding for an analog to the fold-Hopf bifurcation in three-dimensional symmetric piecewise linear differential systems is obtained. A particular biparametric family of such systems is studied starting from a very degenerate configuration of nonhyperbolic periodic orbits and looking for the possible bifurcation of limit cycles. It is proved that four limit cycles can coexist after perturbation of the original configuration, and other two limit cycles are conjectured. It is shown that the described bifurcation scenario appears for appropriate values of parameters in the celebrated Chua's oscillator. 相似文献
8.
A. V. Burenin 《Optics and Spectroscopy》2010,109(6):861-867
Construction of the stationary state classification is considered for nonrigid molecular systems whose geometrical symmetry
of internal dynamics is determined by continuous axial groups. The construction is based on the methods of symmetry group
chains. 相似文献
9.
Operators of physical quantities of nonrigid molecular systems with continuous axial symmetry groups
A. V. Burenin 《Optics and Spectroscopy》2011,110(2):167-171
The construction of the effective operators of physical quantities is considered for nonrigid molecular systems whose geometrical
symmetry of internal dynamics is determined by continuous axial groups. The construction is based on the methods of a symmetry
group chain. 相似文献
10.
11.
Zwerger W 《Physical review letters》2004,92(2):027203
It is shown that the Goldstone modes associated with a broken continuous symmetry lead to anomalously large fluctuations of the zero field order parameter at any temperature below T(c). In dimensions 2相似文献
12.
13.
The Fermi liquid approach is applied to the problem of spontaneous violation of the C
4 symmetry in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to
the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the
quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states
becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point. 相似文献
14.
We consider a quantum field theory model in two dimensions analog to the three states Potts model. We prove the convergence of the mean field cluster expansion and the existence of at least three phases. 相似文献
15.
We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed. 相似文献
16.
Karl Kraus 《Communications in Mathematical Physics》1967,7(2):99-111
Concrete C*-algebras, interpreted physically as algebras of observables, are defined for quantum mechanics and local quantum field theory.Aquantum mechanical system is characterized formally by a continuous unitary representation up to a factorU
g
of a symmetry group
in Hilbert space and a von Neumann algebra on invariant with respect toU
g
. The set
of all operatorsX such thatU
g
X U
g
–1
, as a function ofg
, is continuous with respect to the uniform operator topology, is aC*-algebra called thealgebra of observables. The algebra is shown to be the weak (or strong) closure of
.Infield theory, a unitary representation up to a factorU(a, ) of the proper inhomogeneous Lorentz group
and local von Neumann algebras C for finite open space-time regionsC are assumed, with the usual transformation properties of
underU(a, ). The collection of allXC giving uniformly continuous functionsU (a, )X U
–1 (a, ) on
is then a localC*-algebra
, called thealgebra of local observables. The algebra
is again weakly (or strongly) dense in
c
. The norm-closed union
of the
for allC is calledalgebra of quasilocal observables (or quasilocal algebra).In either case, the group
is represented by automorphisms V
g
resp. V(a, ) — with V
g
X=U
g
X U
g
–1
— of theC*-algebra
, and this is astrongly continuous representation of
on the Banach space
. Conditions for V (a, ) can then be formulated which correspond to the usualspectrum condition forU (a, ) in field theory.Work supported in part by the Deutsche Forschungsgemeinschaft. 相似文献
17.
Wigner time reversal implemented by antiunitary transformations on the wavefunctions is to be refined if we are to deal with systems with internal symmetry. The necessary refinements are formulated. Application to a number of physical problems is made with some unexpected revelations about some popular models.This paper is presented in felicitation of Jean-Pierre Vigier with pleasant recollections of his infectious enthusiasm. This work is supported in part by DOE Grant No. DE-FG03-93ER40757. The authors thank Iwo Bialynicki-Birula and J. Bruce French for sharing their insights, and Luis J. Boya for discussions. 相似文献
18.
19.
We discuss the characterization of relative equilibria of Lagrangian systems with symmetry. 相似文献