Statistical properties of random environment of 1D quantum N-particles system in external field

The investigation of 1D quantum N -particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonsta...

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Bibliographic Details
Published in:Physics of atomic nuclei 2010-02, Vol.73 (2), p.320-325
Main Authors: Gevorkyan, A. S., Gevorkyan, A. A., Oganesyan, K. B.
Format: Article
Language:English
Subjects:
AMPLITUDES
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
Elementary Particles and Fields Theory
EQUATIONS
FIELD THEORIES
INTERACTIONS
MANY-BODY PROBLEM
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
Particle and Nuclear Physics
PHASE TRANSFORMATIONS
Physics
Physics and Astronomy
QUANTUM FIELD THEORY
RANDOMNESS
RENORMALIZATION
STOCHASTIC PROCESSES
ULTRAVIOLET DIVERGENCES
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Summary:The investigation of 1D quantum N -particle system (PS) with relaxation in the random environment under the influence of external field is conducted within the framework of the stochastic differential equation of the Langevin—Schrödinger (L—Sch) type. Using L—Sch equation, the 2D second-order nonstationary partial differential equation is found, which describes the quantum distribution in the environment, depending on the energy of nonperturbed 1D quantum N -PS and on the external field parameters. It is shown that the average value of the interaction potential between 1D disordered quantum N -PS and the external field, has the ultraviolet divergence. This problem is solved by the renormalization of the equation for the function of quantum distribution. It is shown that it has a sense of dimensional renormalization which is characteristic for the quantum field theory. Critical properties of the environment are investigated in detail. The possibility of the first-order phase transition in the environment distribution depending on amplitude of an external field is been shown.
ISSN:1063-7788
1562-692X
DOI:10.1134/S1063778810020183