arXiv subjects

O. Yu. Shvedov

Publications and source records attributed to O. Yu. Shvedov.

24 records · Page 2Linked to original sources

arXiv1995

Geometrical Quantization in Fock Space

We investigate an infinite dimensional analog of the theory of Lagrangian manifolds with complex germs. To such a manifold we assign a canonical operator that depends on creation and annihilation operators. This operator is by definition the geometrical quantization for these isotropic manifolds with complex germs. We prove that for secondary quantized equations this quantization is the asymptotics for the Cauchy problem. Results of Berezin are used thouroughly in the construction of the canonical operator and in proofs of the theorems.

q-alg↗

arXiv1995

On the Problem of Chaos Conservation in Quantum Physics

We develop a new method of constructing a large N asymptotic series in powers of $N^{-1/2}$ for the function of N arguments which is a solution to the Cauchy problem for the equation of a special type. Many-particle Wigner, Schrödinger and Liouville equations for a system of a large number of particles are of this type, when the external potential is of order O(1), while the coefficient of the particle interaction potential is 1/N; the potentials can be arbitrary smooth bounded functions. We apply this method to equations for N-particle states corresponding to the N-th tensor power of an abstract Hamiltonian algebra of observables. In particular, we show for the case of multiparticle Schrödinger-like equations that the property of N-particle wave function to be approximately equal at large N to the product of one-particle wave functions does not conserve under time evolution, while the same property for the correlation functions of the finite order is known to conserve(such hypothesis being the quantum analog of the chaos conservation hypothesis put forward by M.Kac in 1956 was proved by the analysis of the BBGKY-like hierarchy of equations). In order to find a leading asymptotics for the N-particle wave function, one should use not only the solution to the well- known Hartree equation being derivable from the BBGKY approach but also the solution to another (Riccati-type) equation presented in this paper. We also consider another interesting case when one adds to the N-particle system under consideration one more particle interacting with the system with the coefficient of the interaction potential of order O(1).It happens that in this case one should investigate not a single Hartree-like equation but a set of such equations, and the chaos will not conserve even for the correlators.

quant-ph↗

arXiv1995

HIGH ORDER BEHAVIOUR OF PERTURBATION RECURSIVE RELATIONS

The problem of large order behaviour of perturbation theory for quantum mechanical systems is considered. A new approach to it is developed. An explicit mechanism showing the connection between large order recursive relations and classical euclidean equations of motion is found. Large order asymptotics of the solution to the recursive relations is constructed. The developed method is applicable to the excited states, as well as to the ground state. Singular points of the obtained asymptotics of the perturbation series for eigenfunctions and density matrices are investigated and formulas being valid near such points are obtained.

quant-ph↗

arXiv1995

LARGE ORDER ASYMPTOTICS OF SEMICLASSICAL EXPANSION: A NEW APPROACH

A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can apply not only functional integral technique, which has been used up to now, but also method of direct analysis of the semiclassical expansion recursive relations.

quant-ph↗

arXiv1995

ON THE LARGE ORDER ASYMPTOTICS OF THE WAVE FUNCTION PERTURBATION THEORY

The problem of finding the large order asymptotics for the eigenfunction perturbation theory in quantum mechanics is studied. The relation between the wave function argument x and the number of perturbation theory order k that allows us to construct the asymptotics by saddle-point technique is found: $x/k^{1/2}=const$, k is large. Classical euclidean solutions starting from the classical vacuum play an important role in constructing such asymptotics. The correspondence between the trajectory end and the parameter $x/k^{1/2}$ is found. The obtained results can be applied to the calculation of the main values of the observables depending on k in the k-th order of perturbation theory at larges k and, probably, to the multiparticle production problem.

quant-ph↗

arXiv1994

Sphalerons and Large Order Behavior of Perturbation Theory in Lower Dimension

Sphalerons -- unstable static solutions of classical field equations in (d+1)-dimensional space-time -- may be viewed as euclidean solutions in d dimensions. We discuss their role in the large order asymptotics of the perturbation theory. Specifically, we calculate their contribution to the large order behaviour of the ground state energy in a quantum mechanical model. When the number of negative modes is odd, single sphaleron contribution dominates, while this contribution vanishes when the number of negative modes is even. These results are confirmed by numerical calculations.

hep-ph↗