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Letters in Mathematical Physics - 相似文献
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Models of quantum and classical particles on a lattice d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;2 tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with pair interactions possessing the translation invariance, has also been shown. 相似文献
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Sergio Albeverio Agnieszka Kozak Yuri Kozitsky 《Communications in Mathematical Physics》2004,251(1):1-25
We study the two-dimensional gauge theory of the symmetric group Sn describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of Sn, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling. 相似文献
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A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products
, where \mathfraka
t
, t
are time automorphisms and F
j
are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F
j
taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator. 相似文献
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Yuri Kozitsky Piotr Oleszczuk 《Journal of Mathematical Analysis and Applications》2003,277(2):423-437
Differential operators ?(Δθ,ω), where ? is an exponential type entire function of a single complex variable and Δθ,ω=(θ+ωz)D+zD2, D=∂/∂z, , θ?0, , acting in the spaces of exponential type entire function are studied. It is shown that, for ω?0, such operators preserve the set of Laguerre entire functions provided the function ? also belongs to this set. The latter consists of the polynomials possessing real nonpositive zeros only and of their uniform limits on compact subsets of the complex plane . The operator exp(aΔθ,ω), a?0 is studied in more details. In particular, it is shown that it preserves the set of Laguerre entire functions for all . An integral representation of exp(aΔθ,ω), a>0 is obtained. These results are used to obtain the solutions to certain Cauchy problems employing Δθ,ω. 相似文献
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Yuri Kozitsky 《Letters in Mathematical Physics》2000,53(4):289-303
A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N
, correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough. 相似文献
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Yuri V. Kozitsky 《Journal of statistical physics》1997,87(3-4):799-820
The hierarchical ferromagneticN-dimensional vector spin model as a sequence of probability measures onR
N
is considered. The starting element of this sequence is chosen to belong to the Lee-Yang class of measures that is defined in the paper and includes most known examples (4 measures, Gaussian measures, and so on). For this model, we probe two thermodynamic limit theorems. One of them is just the classical central limit theorem for weakly dependent random vectors. It describes the convergence of classically normed sums of spins when temperature is sufficiently high. The other theorem describes the convergence of more than normally normed sums that holds for some fixed temperature. It corresponds to the strong dependence of spins, which appears at the critical point of the model. 相似文献
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The evolution of an infinite population of interacting point entities placed in is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition. 相似文献
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S. Albeverio Y. G. Kondratiev Y. V. Kozitsky 《Communications in Mathematical Physics》1997,187(1):1-18
Hierarchical models of quantum anharmonic oscillators with a
polynomial anharmonicity and interaction decaying as
(distance)-1-λ are considered. For a class of such models (including ϕ4-type anharmonicity ones), it is shown that the critical fluctuations of the position operator are absent, for all λ > 0
and all temperatures, provided the oscillators mass in less than some threshold value depending on the anharmonicity parameters.
This result may be interpreted as a rigorous mathematical justification of physical arguments showing that quantum fluctuations
can damp phase transitions.
Received: 12 April 1996 / Accepted: 25 October 1996 相似文献