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Journal of Experimental and Theoretical Physics

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

Published Oct 1, 2012• 35 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776112080183

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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 prerequisites and investigate some optimal methods for the formation of a correlated coherent state of interacting particles in nonstationary systems. We study the influence of the degree of particle correlation on the probability of their passage through the Coulomb barrier for the realization of nuclear reactions at low energies. For such processes, the tunneling probability and, accordingly, the probability of nuclear reactions can grow by many orders of magnitude (in particular, the barrier transparency increases from D r = 0 ≈ 10−42 for an uncorrelated state to D |r| = 0.98 ≈ 0.1 at a correlation coefficient |r| ≈ 0.98). The formation of a correlated particle state is considered in detail for different types of monotonic decrease in the frequency of a harmonic oscillator with the particle located in its parabolic field. For the first time, we have considered the peculiarities and investigated the efficiency of the creation of a correlated state under a periodic action on a harmonic oscillator. This method is shown to lead to rapid formation of a strongly correlated particle state that provides an almost complete clearing of the potential barrier even for a narrow range of oscillator frequency variations.
A method for the formation of correlated coherent states of low-energy particles in a parabolic potential well owing to the full-scale low-frequency modulation ω( t ) = ω 0 sinΩ t of the parameters of this well has been considered. It has been shown that such a modulation in the absence of a stochastic force acting on a particle results in the fast formation of correlated coherent states and in an increase in the correlation coefficient and transparency of the potential barrier to the limiting values | r ( t )| max → 1 and D → 1. The presence of the stochastic force significantly affects the evolution of correlated coherent states, decreasing the rate of an increase in the correlation coefficient | r ( t )| max (at Ω ≤ 10 −4 ω 0 ) and limiting it at the level | r (∞)| max < 1 (at Ω = (0.001–0.1)ω 0 ); | r (∞)| max increases with a decrease in the frequency of modulation and decreases with an increase in the intensity of the stochastic force. It has been shown that, at a realistic relation between the parameters, low-frequency modulation can ensure such | r | max value that the transparency of the potential barrier for low-energy particles increases by a factor of 10 50 –10 100 or larger. The mechanism of the formation of correlated coherent states for charged particles in a gas or a low-pressure plasma placed in a low-frequency magnetic field has been considered. We have determined the relation between the magnetic field strength and modulation frequency, as well as the relation between the temperature and density of the gas (plasma), at which the method under consideration can be used to optimize nuclear reactions at low energies.
Premises for the formation of a correlated coherent state of particles in nonstationary quantum systems are considered. The relation between the correlation factor of particles and the probability of their passage through the potential barrier (including that in nuclear reactions) is analyzed. The optimal regime for parametric excitation of a harmonic oscillator is found, in which the asymptotic formation of the correlated state of particles takes place, the dispersion of their coordinates increases manifold, and the barrier transparency becomes many orders of magnitude higher at a low energy of interacting particles.
The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient | r | → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 10 50 –10 100 or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the “walls” of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as | r |, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum | r | value and result in the fast relaxation of correlated coherent states with | r | → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.
We consider peculiarities of the formation of a coherent correlated state (CCS) of a low-energy particle under frequency modulation of parameters of a harmonic oscillator that contains this particle by a broadband nonmonochromatic or asymmetric pulsed action. It is shown that in the case of modulation with frequency-normalized intensity, the maximum efficiency of CCS formation corresponds to a narrow-band action, while broadband modulation is optimal for the action with a constant spectral density. As in the case of monochromatic modulation, the maximum correlation coefficient, |r|max, under the nonmonochromatic action corresponds to parametric resonance at frequency Ω ≈ 2ω0. Under a pulsed action, the maximum efficiency of CCS formation and, hence, the maximum probability of the tunnel effect, correspond to pulsed modulation with a short leading edge and a long trailing edge. In particular, under the action of a pulsed magnetic field with an amplitude of 10 kOe and the leading edge duration of 2 × 10–7 s on a gas with deuterium ions, a CCS can be formed with the correlation coefficient |r|max ≈ 0.9998, for which the tunneling effect probability under the dd interaction at temperature T ≈ 300–500 K increases from D r = 0 ≈ 10−80 to D∣r∣max⁡=0.9998≈0.1{D_{|r{|_{\max }} = 0.9998}} \approx 0.1D∣r∣max​=0.9998​≈0.1 . This process can occur in a gas with particle number density n < n cr ≈ 1017 cm−3. The method of CCS formation makes it possible to explain the results of an experiment in which substantial isotope changes were detected when a pulsed electric current and magnetic-field generation occurred.
We consider a method for optimizing the tunnel effect for low-energy particles by using coherent correlated states formed under controllable pulsed action on these particles. Typical examples of such actions are the effect of a pulsed magnetic field on charged particles in a gas or plasma. Coherent correlated states are characterized most comprehensively by the correlation coefficient r ( t ); an increase of this factor elevates the probability of particle tunneling through a high potential barrier by several orders of magnitude without an appreciable increase in their energy. It is shown for the first time that the formation of coherent correlated states, as well as maximal | r ( t )| max and time-averaged 〈| r ( t )|〉 amplitudes of the correlation coefficient and the corresponding tunneling probability are characterized by a nonmonotonic (oscillating) dependence on the forming pulse duration and amplitude. This result makes it possible to optimize experiments on the realization of low-energy nuclear fusion and demonstrates the incorrectness of the intuitive idea that the tunneling probability always increases with the amplitude of an external action on a particle. Our conclusions can be used, in particular, for explaining random (unpredictable and low-repeatability) experimental results on optimization of energy release from nuclear reactions occurring under a pulsed action with fluctuations of the amplitude and duration. We also consider physical premises for the observed dependences and obtain optimal relations between the aforementioned parameters, which ensure the formation of an optimal coherent correlated state and optimal low-energy tunneling in various physical systems with allowance for the dephasing action of a random force. The results of theoretical analysis are compared with the data of successful experiments on the generation of neutrons and alpha particles in an electric discharge in air and gaseous deuterium.