共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate some properties of the Bogoliubov measure that appear in statistical equilibrium theory for quantum systems and establish the nondifferentiability of the Bogoliubov trajectories in the corresponding function space. We prove a theorem on the quadratic variation of trajectories and study the properties implied by this theorem for the scale transformations. We construct some examples of semigroups related to the Bogoliubov measure. Independent increments are found for this measure. We consider the relation between the Bogoliubov measure and parabolic partial differential equations. 相似文献
2.
V. R. Fatalov 《Theoretical and Mathematical Physics》2008,157(2):1606-1625
We consider problems of integrating over the Bogoliubov measure in the space of continuous functions and obtain asymptotic formulas for one class of Laplace-type functional integrals with respect to the Bogoliubov measure. We also prove related asymptotic results concerning large deviations for the Bogoliubov measure. For the basic functional, we take the Lp norm and establish that the Bogoliubov trajectories are Höldercontinuous of order γ < 1/2. 相似文献
3.
4.
We generalize the Bogoliubov functional hypothesis to the case of multiparticle interaction depending on both the coordinates and momenta of particles. We illustrate this with the examples of two weakly relativistic models: the Darwin model in the theory of charged particles and the Fock model in the general theory of relativity. For these models, based on the chain of the BBGKY equations, we calculate weakly relativistic corrections to the classical transport coefficients and find the conditions under which there is no bijective relation between the parameters of the local equilibrium distribution and the hydrodynamic variables. 相似文献
5.
M. Yu. Malyshev E. V. Prokhvatilov R. A. Zubov V. A. Franke 《Theoretical and Mathematical Physics》2017,190(3):411-423
We discuss a perturbation theory on the light front regularized by a method analogous to Pauli–Villars regularization for the (2+1)-dimensional SU(N)-symmetric gauge theory. This allows constructing a correct renormalized light-front Hamiltonian. 相似文献
6.
The relation between the Wightman axioms in quantum field theory and the “S-matrix” Bogoliubov axioms is discussed. The choice
of the Fock representation of the canonical commutation relations for asymptotic field variables is interpreted as a condition
for the correct formulation of the relativistic scattering problem.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 120, No. 3, pp. 380–393, September, 1999. 相似文献
7.
J. Honkonen 《Theoretical and Mathematical Physics》2013,175(3):827-834
We briefly review the functional formulation of the perturbation theory for various Green’s functions in quantum field theory. In particular, we discuss the contour-ordered representation of Green’s functions at a finite temperature. We show that the perturbation expansion of time-dependent Green’s functions at a finite temperature can be constructed using the standard Wick rules in the functional form without introducing complex time and evolution backward in time. We discuss the factorization problem for the corresponding functional integral. We construct the Green’s functions of the solution of stochastic differential equations in the Schwinger-Keldysh form with a functional-integral representation with explicitly intertwined physical and auxiliary fields. 相似文献
8.
Using a unitary mapping to the “action-angle” variables, we formulate the perturbation theory with respect to the inverse
coupling constant in the neighborhood of a nontrivial critical point of the action. We also describe the standard perturbation
theory in this neighborhood.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 3, pp. 433–451, June, 2000. 相似文献
9.
Carl M. Bender 《Advances in Mathematics》1978,30(3):250-267
For many quantum mechanical models, the behavior of perturbation theory in large order is strikingly simple. For example, in the quantum anharmonic oscillator, which is defined by−″ + (x2/4+εx4/4−E)y=0, y(±∞)=0,the perturbation coefficients An in the expansion for the ground-state energysimplify dramatically as n → ∞:.We use the methods of applied mathematics to investigate the nature of perturbation theory in quantum mechanics and we show that its large-order behavior is determined by the semiclassical content of the theory. In quantum field theory the perturbation coefficients are computed by summing Feynman graphs. We present a statistical procedure in a simple λ4 model for summing the set of all graphs as the number of vertices → ∞. Finally, we discuss the connection between the large-order behavior of perturbation theory in quantum electrodynamics and the value of α, the charge on the electron. 相似文献
10.
We study the mixed 0-1 knapsack polytope, which is defined by a single knapsack constraint that contains 0-1 and bounded continuous variables. We develop a lifting theory for the continuous variables. In particular, we present a pseudo-polynomial algorithm for the sequential lifting of the continuous variables and we discuss its practical use.This research was supported by NSF grants DMI-0100020 and DMI-0121495Mathematics Subject Classification (2000): 90C11, 90C27 相似文献
11.
Christian Hainzl Enno Lenzmann Mathieu Lewin Benjamin Schlein 《Annales Henri Poincare》2010,11(6):1023-1052
We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree–Fock and Hartree–Fock–Bogoliubov-type
equations, which describe the evolution of attractive fermionic systems (e.g. white dwarfs). Our main results are twofold:
first, we extend the recent blowup result of Hainzl and Schlein (Comm. Math. Phys. 287:705–714, 2009) to Hartree–Fock equations
with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time
blowup for spherically symmetric solutions of a Hartree–Fock–Bogoliubov model, where an angular momentum cutoff is introduced.
We also explain the key difficulties encountered in the full Hartree–Fock–Bogoliubov theory. 相似文献
12.
E. Yu. Spirina O. A. Khrustalev M. V. Chichikina 《Theoretical and Mathematical Physics》2000,122(3):347-354
We define the Bogoliubov group variables for the space-time translations in the secondarily quantized system. We propose a
scheme for quantizing a scalar field that has a nonzero classical component and interacts with a charged scalar field. The
polaron is treated as a result of the interaction of the charged particle with the classical component of the neutral field.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 122, No. 3, pp. 417–425, March, 2000. 相似文献
13.
Jürgen Voigt 《Acta Appl Math》1984,2(3-4):311-331
We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting.In Section 1 we present spectral properties of the semigroup operatorsW
a(t) of the absorption semigroup and its generatorT
a. In Section 2 we treat the full semigroup (W(t);t0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility ofW(·).In four appendices we present abstract methods used in Sections 1, 2 and 3. 相似文献
14.
R. S. Pusev 《Theoretical and Mathematical Physics》2010,165(1):1348-1357
We obtain results on small deviations of Bogoliubov’s Gaussian measure occurring in the theory of the statistical equilibrium
of quantum systems. For some random processes related to Bogoliubov processes, we find the exact asymptotic probability of
their small deviations with respect to a Hilbert norm. 相似文献
15.
16.
A. V. Marshakov 《Theoretical and Mathematical Physics》2008,154(3):362-384
We discuss the microscopic origin of integrability in the Seiberg-Witten theory. In particular, we discuss the theory in more
detail with the simplest higher perturbation in the ultraviolet, where additional explicit results are obtained using bosonization
and elliptic uniformization of the spectral curve.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 424–450, March, 2008. 相似文献
17.
We consider the superfluidity properties of a two-dimensional system of polaritons in an optical cavity. Deriving an expression
for the effective low-energy action for thermodynamic phase fluctuations, we simultaneously obtain the expression for an analogue
of superfluid density in the system in terms of the current-current correlation function and also find the expression for
the current operator. We describe the Bogoliubov approximation for a polariton system and calculate the superfluid density.
We discuss the Berezinskii-Kosterlitz-Thouless transition in the system under study.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 2, pp. 372–384, February, 2008. 相似文献
18.
G.W. Patrick 《Mathematische Zeitschrift》1999,232(4):747-788
An interesting situation occurs when the linearized dynamics of the shape of a formally stable Hamiltonian relative equilibrium
at nongeneric momentum 1:1 resonates with a frequency of the relative equilibrium's generator. In this case some of the shape
variables couple to the group variables to first order in the momentum perturbation, and the first order perturbation theory
implies that the relative equilibrium slowly changes orientation in the same way that a charged particle with magnetic moment moves on a sphere under the influence of a radial magnetic monopole. In the course of showing this a normal form is constructed
for linearizations of relative equilibria and for Hamiltonians near group orbits of relative equilibria.
Received August 27, 1998; in final form February 20, 1999 相似文献
19.
M. D. Missarov 《P-Adic Numbers, Ultrametric Analysis, and Applications》2012,4(2):109-114
We discuss algebraic similarity of the Wilson’s renormalization groups in the Euclidean and p-adic spaces. Automodel Hamiltonians have identical form in both cases in the framework of perturbation theory. Fermionic
p-adic model has exact renormalization group solution which generates a list of non-trivial conjectures for the Euclidean case. 相似文献
20.
Asymptotic behavior of small deviations for Bogoliubov’s Gaussian measure in the L
p
norm, 2 ≤ p ≤ ∞
V. R. Fatalov 《Theoretical and Mathematical Physics》2012,173(3):1720-1733
We prove several results on exact asymptotic formulas for small deviations in the Lp-norm with 2 ~ p ~ ∞ for Bogoliubov’s stationary Gaussian process ξ(t). We prove the property of mutual absolute continuity for the conditional Bogoliubov measure and the conditional Wiener measure and calculate the Radon-Nikodym derivative. 相似文献