The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

В. И. Высоцкий, STANISLAV V. ADAMENKO, Mykhaylo V. Vysotskyy

Journal of Experimental and Theoretical PhysicsOct 1, 201235 citations

Theoretical and Mathematical Physics

Correlated coherent states of the two-dimensional quantum oscillator with a nonstationary mode coupling

M. E. Veĭsman, S. Kalmykov

Published May 1, 1997• 0 citations

Publisher

DOI: 10.1007/bf02634274

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The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

В. И. Высоцкий, STANISLAV V. ADAMENKO, Mykhaylo V. Vysotskyy

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the “extrinsic” characteristics of the oscillator (amplitudes of “classical” oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|max ≈ 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|max → 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|max → 0. The influence of the CCS formation on the averaged probability 〈D〉 of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value 〈D r=0〉 = 10−80 to 〈D〉 ≈ 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the “extrinsic” characteristics of the oscillator (amplitudes of “classical” oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|max ≈ 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|max → 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|max → 0. The influence of the CCS formation on the averaged probability 〈D〉 of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value 〈D r=0〉 = 10−80 to 〈D〉 ≈ 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.

Journal of Experimental and Theoretical PhysicsOct 1, 201235 citations

Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components

{q}_{1}

and

{q}_{2}

is examined. The \ensuremath{\delta}- and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two-mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature. The photon distribution function (PDF) in the thermal state reveals oscillatory behavior for both high and low temperature, the oscillations decrease while the temperature increases. The PDF in the CCS can be either oscillatory or smooth, whereas the photon statistics is essentially non-Poissonian. The nonclassical intermode photon-number correlations in the CCS are briefly studied.