# Theory of Low-Temperature Quantum Tunneling

Андрей Викторович Лемешко

Low-temperature quantum tunneling describes a phenomenon in which atomic nuclei can overcome the Coulomb barrier and engage in fusion reactions, even if their energy is insufficient for classical barrier crossing. A technological and scientific breakthrough can be achieved by introducing temporal gradients that locally modify the properties of space-time and the energy parameters of particles.

Theory of Low-Temperature Quantum Tunneling


Key Idea

Low-temperature quantum tunneling describes a phenomenon in which atomic nuclei can overcome the Coulomb barrier and engage in fusion reactions, even if their energy is insufficient for classical barrier crossing. A technological and scientific breakthrough can be achieved by introducing temporal gradients that locally modify the properties of space-time and the energy parameters of particles.

Physical Model

1. Impact of Temporal Gradients

Temporal gradients alter the local flow of time and its effect on particles:

Kinetic Energy:

Upon entering the zone of time deceleration, a particle retains its energy relative to an external observer, but within the zone, its kinetic energy increases.

Energy Density:

Increased energy density within the time deceleration zone can modify the distribution of electrostatic energy around the nucleus.

2. Coulomb Barrier and Its Modification

The Coulomb barrier, as the primary energy barrier between positively charged nuclei, is defined by electrostatic repulsion forces. However, temporal gradients exert the following effects:

Energy Redistribution:

Temporal gradients redistribute the energy of Coulomb interactions, leading to barrier reduction.

Quantum Interference:

Time deceleration alters the phase characteristics of particle wave functions, increasing the likelihood of tunneling through the barrier.

Mathematical Model

1. Probability of Tunneling

The formula for the tunneling probability: [ P_t \propto e^{-\sqrt{\frac{2m}{\hbar^2} \left(V - (E + \eta \cdot \nabla T)\right)} \cdot \frac{1}{1 + \gamma \cdot \Delta T}} ] Where:

(P_t): Probability that a particle will overcome the Coulomb barrier under the given conditions.

(V): Classical Coulomb barrier defined by electrostatic repulsion between positively charged nuclei.

(E): Kinetic energy of the particle, depending on its mass and speed.

(\eta \cdot \nabla T): Additional energy resulting from the influence of temporal gradients (( \nabla T) is the spatial gradient of time, and (\eta) is the proportionality coefficient determining the intensity of time-induced energy changes).

(\Delta T): Local time difference between the external and internal observer within the temporal anomaly zone.

(\gamma): Coefficient describing the interaction of time with particle quantum parameters, characterizing the impact of temporal gradients on tunneling.

2. Effective Energy Barrier

Expression for the effective Coulomb barrier: [ V_{\text{eff}} = V - E_{\text{grad}} ] Where:

(V_{\text{eff}}): Effective barrier height perceived by the particle, considering temporal gradients.

(E_{\text{grad}} = \eta \cdot \nabla T): Energy "added" by the temporal gradient, facilitating barrier reduction.

3. Equation for Gravitational Objects

Expression for the gradient of time in massive stars and other gravitational systems: [ \nabla T \propto \frac{GM}{r2} ] Where:

(G): Gravitational constant ((6.674 \times 10^{-11} , \text{m}{-1}\text{s}^{-2})).

(M): Mass of the star or another massive object.

(r): Radius to the point where the temporal gradient is measured.

(c): Speed of light ((3 \times 10^8 , \text{m}/\text{s})).

(\nabla T): Describes how the flow of time changes depending on the distance from the object. The closer to the massive object, the more pronounced the gradient.

Experimental Approaches

1. Controlled Temporal Gradients

Creating temporal gradients in laboratory conditions using:

High-power lasers,

Magnetic fields,

Plasma reactors (e.g., tokamaks).

2. Studying Isotopes

Conducting reactions with light isotopes (deuterium, tritium, lithium-6) to test the influence of temporal gradients on tunneling.

3. Computer Modeling

Developing simulations that include:

Quantum wave functions considering time,

Gravitational effects and space-time deformation.

Applications

1. Stellar Fusion

The theory explains processes occurring in stars, where nuclei overcome the Coulomb barrier due to temporal anomalies.

2. Controlled Thermonuclear Fusion

Introducing temporal gradients into reactors can increase the efficiency of thermonuclear fusion on Earth.

3. Supernovae and Heavy Elements

Accelerated fusion reactions during stellar explosions can be explained by temporal gradients.

Cold Fusion Reactor

This theory unites quantum mechanics, general relativity, and temporal effects, offering new experimental approaches and promising applications in astrophysics and energy. Based on this theory, it is possible to mathematically describe the physical parameters required to initiate cold fusion reactions.

Physical Parameters

1. Tunneling Through the Coulomb Barrier

Formula for tunneling probability: [ P_t \propto e^{-\sqrt{\frac{2m}{\hbar^2} \left(V - (E + \eta \cdot \nabla T)\right)} \cdot \frac{1}{1 + \gamma \cdot \Delta T}} ] Where:

(V): Classical Coulomb barrier.

(E): Particle's kinetic energy.

(\eta \cdot \nabla T): Additional energy from the temporal gradient.

(\Delta T): Local time difference.

2. Particle Kinetic Energy

Entering the time deceleration zone leads to an increase in the local kinetic energy of particles: [ E_{\text{eff}} = E + E_{\text{grad}} ] Where (E_{\text{grad}} \propto \nabla T): Energy associated with the temporal gradient.

3. Reduction of Coulomb Barrier

The effective barrier in the temporal anomaly zone decreases: [ V_{\text{eff}} = V - E_{\text{grad}} ] Which increases the probability of successful fusion.

Usage Prospects

1. Energy

The reactor could become the basis for environmentally clean and safe energy production.

2. Space Applications

Possibility of using low-temperature fusion to power spacecraft.

3. Scientific Research

Expanding knowledge about temporal gradients and their impact on quantum processes.

References

-- Grifoni, M., & Hдnggi, P. (1998). Quantum tunneling at low temperatures: Results for weak damping. Physics Reports, 304(5-6), 229-354. https://www.physik.uni-augsburg.de/theo1/hanggi/Papers/70.pdf

-- Leggett, A. J. (2001). Quantum tunneling of helium isotopes in solids: A new analysis. Reviews of Modern Physics, 73(2), 307-356.

-- Sheka, E. F., & Ovcharenko, E. V. (2023). Tunneling as a marker of quantum mechanics: Review article. Low Temperature Physics, 50(11), 925-945. https://pubs.aip.org/aip/ltp/article/50/11/925/3318550/Tunneling-as-a-marker-of-quantum-mechanics-Review