Subbarrier processes in LENR for particles in correlated states at action of damping and fluctuations
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It is well known that the presence of high and wide Coulomb barrier is the main obstacle to LENR. The method ofthe formation of coherent correlated state (CCS) with correlation coefficient1 r → of a particle, which can be used to giant increase of the transparency of this potential barrier from very small values 70 1000 D0 r10 ...10 -- --=[approximately] up to 2 11 0 1 r D D r r -- [right arrow] = [approximately] [right arrow] was considered in [1-3]. The uniqueness of this method is connected with the fact that the transparency of the barriers ("walls" of a potential well with a particle) and the probability of LENRcan be increased using a simple procedure of CCS formation: periodic modulation of the well width for the same barrier height 0 Lt L g t ( ) (1 cos ), =+ [omega]0 [omega] [omega] ( ) (1 cos ), t gt =+[omega]g<<1.The physical mechanism of the increase of barrier transparency for a CCS is associated with synchronization and periodic phasing of fluctuations of momentums ( ) [delta]p t n (t) of different eigenstatesin the given quantum-mechanical system. The presence of external stochastic perturbation can violate the phase relations between different eigenstates and may affect the formation of the CCS, determining both the rate of the increase in |r(t)| and the value of |rmax|. Another essential negative factors are the damping of these oscillations and anharmonicity at growth of amplitude of theseoscillations at periodic modulation. We consider peculiarities of the formation of CCS of a particle in a periodically modulated potential well with damping for various types of stochastic perturbation. It was shown that at the absence of stochastic perturbation, an optimal relation g = 2[gamma] exists between the damping coefficient [gamma] and the modulation depth, for which the "extrinsic" characteristics of the oscillator (amplitudes < > | | x of "classical" oscillation and the momentum < > | | p of a particle) remain unchanged and small, while the correlation coefficient rapidly increases from r = 0 to r[right arrow]1; this corresponds to completely CCS (Fig.2,a,b,c). It was shown that for optimal condition g < 2[gamma] the presence of a stochastic delta-correlated 1 2 1 2 < >= -- ft ft S t t ()() 2 ( ) [delta] force f t( ) substantially affects the rate ofincrease of normalized amplitude of oscillations, as well as the absolute value of correlation coefficient with time, but does not affect the final value1 r [right arrow] and giant increase of the transparency D1 r[right arrow] [right arrow]1! These effects can be used for LENR optimization in real physical systems at action of damping and fluctuations.