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/4╥R2}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.
||
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. 
