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| Tunneling – Information - Transferring |

Tunneling & Information

Description of Quantum Tunneling;

|| What is Quantum Tunneling?
 Quantum tunneling is a term within Quantum mechanics to describe the phenomena of when a particle passes though a potential finite barrier (Ea energy barrier)that the particle would not have the sufficient kinetic velocity that would come from barrowed momentum that is expressed with the constant (∆/E) (delta/changing in distance or velocity)that is necessary to cross over the axis of the height of the confining barrier normally, but instead exhibits behavior similar to a wavelength with the particle having the probability of being detected on the other side of the barrier that the particle tunnels through using each points of the entry and exit as respective reservoir points on both sides of the potential barrier using those reservoir points of the barrier as a form of linear polarization with the particle having the equivalent electric energy that is comparable to the  barrier's encompassing electric-volt energy inside of its energy wall and barrier Length which the particle reaches a transmission coefficient that is necessary to penetrate the finite barrier this process of "wave-function" or "eigen-functions" that the particle's behavior exhibits is described by physicist Erwin Schrodinger and his concept that was purposed  within the year of 1935 that was known as "Schrodinger's cat" to explain when a physical system (particle) can enter a into a Quantum superposition to be able predict the possible outcomes of when a subatomic atom is trapped inside of confining mass without experiencing decay.

Erwin Schrodinger's equations of delta function potential wells  and barriers (-h2/2m a2/ar2 u/ (r)=  E u/(r) ) (a2/ar2 u/ (r) = -2mE/h2 u/ (r) =-k2 u/ (r)

Erwin Schrodinger's equations of partial derivatives inside of wave-function
th2/2m a2 Ψ(x,t)/ax2 + U(x)Ψ(x,t) =ith 2Ψ (x,t)/A=aT


Quantum tunneling in organic chemistry
 Now that we know the basis of Quantum tunneling let's take a look within hydrogen tunneling and the intramolecular hydrogen atom transferring process within the cellular respiration of enzymes and gases in organic compounds.  a hydrogen atom transfer between one compound and another begins when the hydrogen atoms inside of the monosaccharide of a carbohydrate begins to oxidate and accelerate during the transfer process while the reducing agents such as Nicotinamie adeine dinuleotide (NAD+) Flavin adeine dinuleotide (FAD) polymerize during the Kreb's cycle or the tricarbioloxic cycle which is the process of accelerating the carbohydrates inside of gliosis forming the reducing agents of Nicotinamie adeine dinuleotide dehydrogense (NADH) and (FADH2) which becomes an electron accepter during the polymerization of the  reducing agents acts as a terminal enzyme inside of the complex of the cytochrome enzyme which is also used during an electron atom transferring process, which the agents (NADH) and (FADH2) become part of the cytochrome's respiratory chains. The hydrogen atoms inside of the reducing agents are deposited inside of the cytomchrome's transport chain and the agents (NADH) and (FADH2) become oxidated and the particle can polymerize with gases such as oxygen and becomes H2O


How is quantum tunneling evolved within this process?
 When the hydrogen particle is being accelerated though the kreb’s cycle after the reducing agents from the glyoisis has been polymerized the orbital momentum of the neutron begins to spin inside of the nucleus of the isotope (deterium)of the hydrogen atom which begins to create a molecular vibrational state utilizing the plank constant of speed and velocity inside of the enzymes "matter chain" or the "De Broglie wavelength" that was purposed by the physicist Louis de Broglie within 1924 about the kinetic energy of a particle and was soon adapted by Erwin Schrodinger's of the equation of matter and the hydrogen atom itself in the year of 1933 and the reaction path acting as an enzyme catalysis/enzyme catalytic power for the transition state within particle tunneling while the increasing thermal temperatures escalate between a kinetic velocity of 5 to 77 K per millisecond (Bose-Einstein condensate)during the oxidation process of the cytpochrome which normally this process would allow for the particle to jump over the activation barrier inside of the enzyme, but depending on the temperatures of the environment then enzyme is in for example if the enzyme was frozen at cryogenic temptures which cools the deterium isotope or causes it to crysalize and slows the veloctiy of the particle spin inside of the nucleus the particle would not have the sufficient velocity to cross over the activation barrier. in this instance the particle will go into a degenerate ground state or quantum annealing (manufactured particle spin) while the trapping potential of the particle wave-function expressed with the constant V(r) the particle begins to rotate into a vortex to tunnel though the barrier if the linear pathway is narrow and if the barrier is of a higher temperature of the particle, which will cause the enzyme to eject the particle during the kreb cycle reaction



Semiconductor Hetro-structures & Quantum effects in Hetro-structures in Quantum Tunneling
We will first focus on the quantum hetro-structures of quantum tunneling with the electron particle and what a quantum hetro-structure is for example. A quantum hetro-structure is a subtract of the original hetro-structure which are series of layered materials of different properties stacked upon one another such as aluminium gallium arenside/gallium arenside which is a ferroelectric semiconducting material which electrically absorbs the atoms inside of the polar planes in the process of quantum entanglement inside of the hetro-structures and charges the electrons though a electromagnetic current that travels though the aluminum nano-structure utilizing the nano-structure as axis points for the direction of the electron polarization though the tunneling junctions inside of the aluminum gallium arenside utilizing the principals for "Fowler–Nordheim tunneling and field emission"  that was purposed by the physicists Ralph Howard Fawler and Lothar Wolfgang Nordheim in the year 1928 about how a electron can tunnel though a tringular energy barrier using wave-function and the semiconducting material such as the aluminum arenside while inside of a strong electric flied which would be demonstrated with the Fawler-Nordheim formula for electron tunneling density see this link here (http://www.iue.tuwien.ac.at/phd/gehring/node112.html)


Quantum Tunneling in nuclear fusion and solar hetrostructures:
For an example of quantum tunneling within solar hetro-structures we will use the UNSM PERL c-si and Sayno HIT solar cells and the photovoltaic structuralization inside of the hetrojunction of these cells. Quantum tunneling begins when the particles inside of the hydrogenerated silicon solar cells begins to experience a recombinative velocity by doping diffusion (formula for doping profiles AC{x,t}/At=D A2c{x,t}/Ax2) this process of doping diffusion is to redistribute the atoms inside of the semiconducting materials of a hetrostrcure such as Silicon, Germanium, aluminium Antimondie, Gallium Aresnoide, Gallium phospheride, Indium Arenside, Indium phosperide and Indium Antimondie when the doping agents (Boron,Alliuminum,Gallium,Indium,Phophorus,Aresnic,Antimony,Bismuth,Copper,Lithum,Sodium,Potassium,Hydrogen and Helium) inside of the flims of the hetrostrure into a gas based structure with the temperatures ranging from 150% C from the I-layer of the heterostrucure and 200 % C for the n-layer created a chemical process known as chemical vapor deposition which is used for micro-waving plasma inside of materials. this process of chemical vapor deposition causes the hetro-structure layers to experience surface diffusion when the adatomic clusters become isolated from increasing temperatures and magnetization curves of the photovoltaic cells as the I-layers becomes oxidated the temperatures of the lattice inside of the adatomic clusters causes the equilibrium of the cluster to vibrate as described by the physicist Ludwig Boltzmann with the constant R divided by the Avogadro constant  NA by physicist Amedo Avogadro when the creating the constant of K=R/na to explain the microscopic relationship between the adatomic particle's vibration, pressure and the absolute temperature in mobile diffusion which the formula constant (R=ve-Ediff/kbt) explains when the particle jumps or hops when layers the I and N layers have low particle mass

Formula for tunneling jump
R tun=2w/3/2 2Ea/hw exp(2Ea/thw)


Nuclear fusion
The conceptualization of nuclear fusion was highlighted within the 1940's with both the successes of nuclear transmutation by physicist Ernest Rutherford and fusion of hydrogen isotopes by Mark Olipant which is applied into military research with the deployment of the hydrogen-bomb "ivy mike" on November 1 1952. the hydrogen bomb's schematics and materials are a phenomena within nuclear fusion such as the reactive properties of the polyethylene casing, the Uranium-238 fission booster and the TX-5 fission bomb around the plutonium -239 core sphere containing the metals of beryllium and polonium which under intense stress caused by raising temperatures and velocity of the thermal neurons inside of the tx5 fission bomb splits the nucleus of polonium and causes the promium to eject alpha particles into the atomic structure of the berylium while the neutron inside of the alpha particle contains about 3.27 MeV of energy while the proton inside of the alpha particle contains a energy of 4.03 MeV as it heats the fusing deuterons that is being compressed around the uranium-238 fission booster as it causes the compressed deuterium plasma to push pass the barriers created by electrostatic repulsion while the tritium nucleus polymerizes with the deuterium isotope to form a alpha particle containing a energy of 17.59 MeV while the deuterium isotopes inside of the nucleus of the plasma creates a heavy helium isotope. Another example of nuclear fusion occurs inside of the formation of the sun's core itself (the sun's core contains a compacted density of 151,300 kilograms) this formation occurs due to the ionization of methane gas of core reaches a temperature of 15.6 million Kelvin or (1.56X10 7 or utilizing the Stefan-Boltzmann constant of o=5.670 x 10 -8 j m-2 k-1 s-1 with the sun's radius constant R=6.955 x 10 8 meters creating the formula solution of Te={L/4R2}1/4=5780 kelvin while the boltzman law can also apply for other stars and while the protons inside of the core must be heated and have the appropriate velocity to counteract the gravitational composition from the mass of the sun which the gravitational thermal energy of the sun can be expressed with the formula of T= 3/2Tc=GMpM/R being the gravitational energy and the mass of the protons being mp=1.6726 x 10 - 27 with the solving formula being Tc=2Gmp M/3kR=1.56 x 107 kelvin ) which causes the hydrogen particles to burn to create the compounds of helium (named after the greek god Helios by Norman lockyer) which quantum tunneling occurs within this reaction process utilizes electric potential energy from the notion of coulomb's law within inverse physics of electrostatic repulsion by Charles-Augustin De Coulomb in 1785 with the formula of barrier penetration from the projectile neucli Vl (r)= Vn(r) + Vc(r) +th2 l ( l+1)/2ur2=Vo(r)+th2 l ( l+1)/  T l (E) = {1 +exp (2Se(E))}-1 and the formula for the penetration integral  Se(E)2u/th2 {r2l/r1l  dr {Vo(r)+th2  l (l+1)/ 2ur2-E ] -1/2 formula for wave potential barrier Vo(r) =V Bo -1/2u 2(omega)2 (r-r o)2/ To(E)={1+exp{2/th(omega)(E-V Bo} -1


Hawking Radiation/Quantum tunneling in black holes
We will first cover the realms of Quantum tunneling inside of black holes which stephen hawking showed the radius inside of thermal equilibrium of a black body will never decrease in size and that the black hole contains an entropy amongst the tidal gravity of the black holes horizon (formula for horizon's geometrical points or Schwarzschild radius ds2= - {1-rs/r}dt2+[1-rs/r}-1dr2+r2 do2} ) (formula for Kruskal-Szekeres metric rK +tK =2e{R+t}2/rK-tK=2e{R-t}2)which the black body's emissivity would  absorb  the encompassing electromagnetism that would come from phonons ( light particles) and antiparticles  that were to enter the radius of the black holes horizon being inversely proportional to the black holes mass as the thermal energy increases as the mass of the black hole decreases the trapped quark orbital oscillations inside of the magnetic flied of the gravitational red-shift  exhibits negative ionic charges while the phonons receive a positive ionic charge during the quantization intervals that effects the trajectory of the encompassing mass that is received with a positive ionic charge creating a stochastic fluctuation of phonons resulting in linear particle acceleration which during the transmission process of the particle accleration(x2-T2=1/a2)  utilizing the Minokowski coordinates the pinpoints the axis of the phonon's acceleration. the phonon travels at the speed of light being 299,792.458 kilometers per second that is necessary to escape the black hole which is supported with Newton's formula of escape velocity with the constant of  G=6.67  X 10 - 11 . Many other physicists have theorized that quantum tunneling is involved in Hawking's radiation theory of how a particle can escape a black hole and the hyperbolic properties of the Unruh effect. while it is imagined that when a pair of subatomic particles are formulated on the outside of the black holes horizon the pair of particles goes though a multiplicity state that is caused by the tidal gravity of the Unruh radiation as the particle that has exhibit the positive ionic charges tunnels though the gravitational barrier of the black holes event horizon causing the particle to tunnel backwards




Rectangular barriers
Unlike the traditional barrier within quantum tunneling the Rectangular barrier utilizes a reflection coefficient along with the standard transmission coefficient from one-dimensional particle tunneling  of when a particle enters into a superposition and becomes a wavelength the reflection coefficient transmits the wave-vector of the particle into either a free state, scattering state or a bound state when it approaches the quantum curb of the barrier, when the particle becomes magnetically trapped  inside of a Bose-condensate such as how cold thermal temperatures can be trapped inside of an alkali adatomic compounds the particle can obtain a superposition known as a "bare state" in which the atomic nuclei utilizes the "Coulomb energy shift" which the molecules inside of the nuclei begins to spin or orbit outside of the shell of the neuceli creating a quasiparticle (radical matrix element of quasiparticle {^n1/1ur/un2/2})  the quasimomentum of which utilizing the constants of the de broglie wavelength the quasiparticle can tunnel though the adjacent walls using the axis points of the rectangular geometry of the barrier as anchoring semiconductors to guide the quasiparticle though the barrier


Triangular barriers
With the geometry of the triangular barrier is compatible with that of an electron and opto-electronic particle while tunneling which can be indicated with the quantum dot that is also used within nano-electronics. The quantum dot acts as an energy profile  during the electron tunneling junection though barrier while quantum dot mass iis used as an  insulator  from  distances of  axis  points  entry an " exit  inside  confinement structure  process doping diffusion particles along  has  not exhibted negative kinetic voltage energy when the  semiconducting tunneling diodes on the oppositional ends of the quantum dot transmits the wave-function of the electron after the subatomic structure has been configured when tunneling though the triangular barrier. Triangular barriers also quasi-perdiodic  based structure that  can formulate with a rectangular barrier to create a multi-barrier, with multi-barrier tunneling or double barrier penetration the electron's transition states is dependent on the height and the width of the barriers that is theorized by the physicist Thomas Hartman that when a particle tunnels through a larger barrier that acts as a prism for the transmission coefficient of the particle transition, the particle will travel across the gap which while the virtual  particles can travel across the barrier gap at the speed of light. the particle will tunneling though the gap when the wave-function is being transmitted between one part of the barrier of the gap and the other which this would be known as the "Hartman effect" which was purposed in 1962

Trapezoidal barriers 
We will discuss on how particle tunneling occurs inside of trapezoidal barriers in graphene based insulators. particle tunneling inside of a trapezoidal barrier parameter (obtained by exploiting the parameters of a normal barrier potential Uo(x)+Ui(x) when measuring the geometry of the  parameter of the trapezoidal barrier being Uo(x)-Ui(x)) when the particle is penetrating the through the density of the barrier utilizing a scale factor to determine the particle's spin control through the quantum dot's bandgap which the energy-shifts and oscillations acts as a tunneling switching device or a quantum well when molecular beam epitaxy is introduced in the hetero-structure of the barrier when the particle's wave-function is being transported by a valance bond inside of the trapezoidal barrier when tunneling. When a particle is tunneling inside of the mono-layers of graphene the bandgap inside of the graphene exhibits magneto inductive based properties when it's electric field which begins to  quantize and absorb electrons inside of the trapezoidal barrier when the temperatures of the metal or a lower percentage then the width of the bandgap would affect the electron's velocity and momentum inside of the free charge carriers in the hetro-structure of the graphene, while the hetero-structure contains a hexagonal based crystalline compound known as Boron nitride, which the boron nitrides density is thin and acts as a stepping stone for the electron to tunnel through the trapezoidal barrier




What is Quantum Information?
Quantum information was founded by Claudie Shannon's theorem of a signal containing qubits can be compressed to the length of nHx(X)+ o (n) while the original signal still retains the probability of being transmitted from the sender and receiver arcs of signal transmission within the year of 1948. This is utilized within data compression in quantum computing, quantum mechanics and within quantum tunneling on how a particle can enter into a superposition through a "noiseless" protocol during the transfer of the qubits which is utilized the Dirac Notation that was introduced in 1939 by Paul Dirac. This notation aided in the possibility of how linear functional can act as a vector when transferring information that is used with quantum lambda calculus in quantum computation.


Photonic crystals
Photonic crystals acts as wavelength reflectors inside of the  Nitrogen-vacancy center of the diamond while utilizing the properties of quantum electrodynamics for entangling atoms and protons inside of the nano-cavities of the diamond within quantum information processing, while the atoms and protons are entangled the particle exhibits a magneto-electronic based property known as spintronics inside of the nano-cavity structure in the fluorescent center of the membrane of the diamond which goes into a form of dielectric material-manpluation during atoms/protons polarized spin while the diaelectric material can absorb the fluctuation of light-pulses that travels through the optical properties of the diamond within a femto-second while the atoms/protons exhibits rabi oscillations inside of the magneto-electronic field. These rabi oscillations occur when the atom becomes embedded inside of the photonic crystal structure's bandgap which acts as a semiconducting super-lattice which causes the rabi frequencies to oscillations at a high speed


Quantum computing
Quantum computation is based off the work of integer factorization, algorithm mathematics and cryptanalysis that was purposed by Charles Babbage and engernied into the first computer system by Konad Zuse in 1941. Within Quantum computation utilizes the quantic structures of the qubit within a programming language that begins with the logical state of 0 and 1 while the qubit can obtain a superposition though quantum parallelism  when the data fluctuation is being transferred between processor and another as the pair of qubits inside of the data information can be divided by the Boolean logic gates which acts as an electronic switch  which was recognized by Richard Feynman when he saw that when 500 qubits can enter into a quantum super-position being of 2/500 states which is used within radio waves.


Bloch sphere
The bloch sphere is a isometric geometrical representation of a pure state containing a set of convex states that acts as of a one-dimensional density matrix projector in the state space of the qubit which allows for a qubit to enter into a quantum superposition inside of the sphere's ket vectors which the coefficient is represented as (u/) =cos0 {0}+eio/ sin 0 {1} while each of the polar coordinates  and half angles inside of the bloch sphere can represent as R= sin 20/ X cos 0/ Y= sin 20/ X sin 0/ z=cos 20 which would make a pure state orthogonal in nature when utilizing Hilbert space and the hadamard matrix, as the surface of the bloch sphere effects the polarization process of particles during entanglement.
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As we discussing a lot about information that it is not depend on time, place, space and so these parameters are meaningless for information.
Now study all formulas of energy, from E = mc^2 of Relativity to quantum formulas.
(That read before in this essay.)
There is no also independent definition for energy. We study it as parameter after coordinates and mass and sometimes. Whether in classical scale or tiny scales or relativistic, energy is depend on these spatial parameters. So information can do tunneling through all potential barrier in all frames. To do this we should just change algorithm of storing and protocol of communication.
(That it s happening nowadays in lots of lab.)

More;


First it is superposition between bits that occurs as communication with minimum of data transferring then Entanglement that can transfer data about all features and properties of system A to system B. It is time to ensemble copy of A in coordinates of B or completely move A to B place.
Cause Potential Barrier is meaningless for Information.









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