Temporary time crystals and matrices

Compiled and written by Jedi Simon : Partly from the Introduction of a work called "Two dimensional photonic crystals" by Pi-Gang Luan and Zhen Ye

A **time crystal** or **
space-time crystal** is a structure that repeats in
time, as well as in
space. Normal
three-dimensional
crystals

have a repeating pattern in space, but remain unchanged as time passes. Time crystals repeat themselves in time as well,

leading the crystal to change from moment to moment. A time crystal never reaches thermal equilibrium, as it is a type of non-equilibrium

matter, a form of matter proposed in 2012, and first observed in 2017. Time crytals exist in dynamic equilibrium. Time crystals

symmetry-breaking, goes beyond conservation laws. Time crystals do not violate the laws of thermodynamics: energy in the overall

system is conserved. Such a crystal does not spontaneously convert thermal energy into mechanical work, and it cannot serve as a perpetual

store of work. But it may change perpetually in a fixed pattern in time for as long as the system can be maintained.

They possess "motion without energy" although their apparent motion does not represent conventional kinetic energy.

Researchers observed subharmonic oscillations during experiments. Rigidity of the time crystal, where the oscillation

frequency remained unchanged even when the time crystal was perturbed. Time crystal gained a frequency of its own and vibrated

according to it for some cycles, rather than only the added frequency of the drive. However, once the perturbation or frequency

of vibration grew too strong, the time crystal "melted" and lost this subharmonic oscillation, and it returned to the same state as before

where it moved only with the induced frequency. Using a diamond crystal doped with a high concentration of nitrogen vacancy centers,

which have strong dipole dipole coupling and relatively long-live spin coherence, We shall see the strong interacting dipolar spin system

driven with microwave fields change his mood. The ensemble spin state determined with an optical laser field, observed that the spin

polarization evolved at half the frequency of the microwave drive. The oscillations persisted for over 100 cycles.

This subharmonic response to the drive frequency is seen as a signature of time-crystalline order.

This melting, is what I called "loss of coherence".

This temporary phenomemon, so, told me that structured equilibrium, although we expect things to hold on to their normal matter state

in equilibrium, most of the time, when excited, presents such changes of mood that makes me believe that one day we shall really see things

disappear or melt in front of our eyes. Nothing new, if we consider Hutchisons effect, probably used together with thermite in the case

of the twin towers not too long ago, as evidence was immediately removed and molten metals poured in canals elsewhere

for as long as fifteen days. Now, we all remember the story of the walls of Jericho. Tesla's oscillator, is again, another way to play

with resonance and elasticity. It all depends on the susceptubility of the subject and a few other variables that might alter the equation's result.

Now, let's go air and consider "transient matter state matter". Some time ago in Taiwan two researchers claimed that....

"Over the past ten years, the propagation of classical waves in a periodic medium has attracted considerable

interest. This includes electromagnetic (EM) wave propagation in periodic dielectric structures, and acoustic and elastic wave

propagation in periodic elastic composites. A new research field emerges as the wave crystals including both photonic and sonic crystals.

The photonic or sonic crystals respectively refer to crystal-like structures that modulate EM or acoustic wave propagation and thus lead

to dispersion bands, in analogy with the electronic energy bands in solid state physics.

You could have asked. I have been composing every kind of music in the past years, and recording every possible work on tape and cds, hard disks,

and other media. 189 cds not considering the tape years. Most of which connected to space time travel, transient alterations of reality, opening portals,

tunneling, channeling, bending fields and transmutating man, emotions and matter. Quantu, Cymatics, considering the physical aspect of this work.

Metaphysical research, considering the meditative aspect of the spiritual works aimed to reach the soul. Now, sonic crystals are in fact what I built

most of the time programming synthesizers to the highest level possible. Then I used them to compose original music that has nothing to do with

commercial products, and enables direct and rapid shift from one level to another, as soos as resonance reaches its peak within our internal neural net.

The research on photonic crystals has been particularly intensified, after the suggestion that photonic band gaps (PBG) could hinder

spontaneous emission and block propagation of EM waves, thus providing the possibility to manipulate the propagation of EM waves.

Photonic crystals offer an unparallel opportunity to design new optical devices and hold a great potential for many significant appli

cations, such as semiconductor lasers and solar cells, high quality resonators and filters, controlling photon emission, optical fibers, guiding

and bending of EM waves with minimum losses, single mode waveguides for light, low dimensional efficient transport of electrons

and excitons by nanostructural networks, all polymer optoelectronic devices, semiconductor memory cells.

Many methods have been proposed for fabricating photonic crystals. These include square spiral microfabrication achitecture for large

three dimensional band gaps, filling the voids in titania with air by precipitation for the optical spectrum, using three dimensional carbon structures,

large scale synthesis of silicon photonic crystals, fabrication of photonic crystals for visible spectrum by holographic lithography, the

electrochemical techniques. Indeed, the past a few years have witnessed rapid advances in both better understanding of the exquisite

properties of photonic crystals and manipulation of EM waves by photonic crystals. A rich body of literature on photonic crystals exists

and can be found on the internet. Recently, scientists also investigated the spine from sea mouse. They discovered that the spine consists

of an array of regularly arranged hollow cylinders, and this simple structure gives rise to a spectacular iridescence.

This is a remarkable example of photonic crystals by a living organism.

Although three dimensional (3D) photonic crystals suggest the most intriguing ideas for novel applications, two dimensional (2D) structures

also find several unique uses, including the aforementioned waveguides and communication fibers and the 2D periodic structures

in living animals, feedback mirror in laser diodes and so on. In addition, fabricating 3D periodic structures in the near infrared regime

poses a significant challenge compared to the two dimensional situations. Due to these reasons, the study of 2D photonic crystals

has been overwhelmed in the last few years. The important issue in the fabrication of photonic crystals is to create large, robust complete

band gaps within which propagation of EM waves is prohibited in any direction. Several methods have been suggested

for obtaining large complete band gaps in 2D situations. For example, it has been shown that large band gaps can be obtained by such

as varying dielectric contrast ratio and filling factors, inserting a third component into the existing photonic crystals, reducing the structural

symmetry, using non-circular rods and subsequently by rotating the non-circular rods, rotating the lattice structures, using anisotropic

dielectric materials, using the effects of magnetic permeability, using metallic or metallodielectric rods, placing rods of various shapes

on different lattice configurations such as square, triangular, honeycomb and so on.

Each approach may have its advantages and shortcomings. For example, the dielectric contrast is limited by material availability.

The symmetry reduction and using non-circular rods may reduce the degeneracy of photonic bands at high symmetry points

in the Brillouin zone, thus increasing band gaps. Although the metallic photonic crystals can yield large band gaps, they suffer

from absorption. While the symmetry reduction method can enhance some high order band gaps, the low order gaps

are often reduced. Therefore each method has its own applicable situations. Inspecting these progresses made towards

better design of two dimensional photonic crystals, we realize that the topology, the symmetry involving the shape of dielectric cylinders,

and the lattice structure are among the most important ingredients in the architecture of photonic crystals. About the images that You have

seen in this web page, I shall tell You that these are reflection, or mirrored images of the crystalline 4 dimensional structure

that is oscillating around us. This is what planes of tality look like. Here you may find an expression of the first ten octaves propagation

of energy, included in what we might call "white noise". As you can see, all the planes show transient states but are truly indicating

that entire tality, from the sub atomic level to particles, electro-magnetic waves and so on, is structured as a pure quantum quasicrystal

entity, that is apparently cahotic, but only to those who do not know what the rules of the game are. Tality is scalar, harmonic, fractal,

and quantum cymatic, considering only the first four dimensions. Then curvature makes things a little more complex than We think

today.

Multistacked clusters of quasicrystalline planar fields intermingled in a temporal quasicrystalline oscillating structure. Where everything is

inteconnected, because gaps do not exist, and what we cannot see is infact space for the new borns of creation. The existent, so, ordered in

such a perfect way, that to misplace one thing, it would take more intelligence than that one God Himself put in the entire creation. A concept

that we will further inverstigate in the near future, and is based on Quantum Quantization, that is the basis of the temporal reality of the accepted

laws, although, in a different time frame, space time, and Quanta, the eventual change would alter introducing elasticity of the variables, could

make things a little more complex that what they look in solidity.

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The different combinations of these factors lead to applications for various purposes. We are therefore led to the task of deriving

systematically necessary formulas computing band structures for various configurations. This paper is one of our attempts.

In this paper, in an organized fashion we present the analytic results for computing the band structures of most commonly used lattice

structures and dielectric cylinders with many kinds of symmetries and rotations. With the aim in mind that the reader can readily

make use of these results, we summarize them in tables. This paper is organized as follows. The general theory for EM waves

in an arbitrary 2D periodic structures is presented in the next section. Using the plane wave expansion method, the secular equations

are derived for determining the band structures for both E-polarization mode and H-polarization mode with the electric field

and the magnetic field parallel to the longitudinal axis respectively.

The extension to sonic crystals is also discussed.

Partly from the Introduction of a work called "Two dimensional photonic crystals" by Pi-Gang Luan and Zhen Ye

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From another paper we can read:

The study of the dynamics of waves, even in simple linear media, initiated hundreds of year ago, ever and ever leads to surprisingly

new results and insights. One of such “surprises” was the discovery of band gaps in the propagation of light in materials with the refraction

index periodically modulated on the scale of the optical wavelength, the so called photonic crystals

. The theory of wave propagation in periodic materials was de veloped long time ago by Bloch and Floquet, and it found many

applications in solid state physics, in particular in the studies of electronic properties of semiconductors (calculation of valence and conduction

bands, etc). Nevertheless, the advent of the photonic crystals initiated a revival of the theory of wave propagation in periodic media.

The creation and control of photonic band gaps, the slowing down of light, and the photonic crystal waveguides are the main

applications to the date. Most of these studies concern the propagation of plane waves (not the beams), andresults in the modification of the

temporal dispersion relation (frequency versus propagationwavenumber). Later, the strong analogies between the propagation of light and

sound (which obey similar wave equations) motivated the study of sound propagation in periodic acoustic media, the so called sonic or

phononic crystals (SC). Many of the results obtained in the photonic case have been reported in the sonic case.

Most of the studies reported above concern the one-dimensional (1D) periodic structures, as the 1D case, being relatively simple,

allows an analytical treatment. The multidimensional cases (the 2D case as in our present study, or even the 3D case) are much more

difficult to be accessed analytically. The majority of these studies in multi-dimensional case are numeric, as using plane-wave expansion,

or finite difference time domain (FDTD) schemes. These studies also mostly concern the modification of the temporal dispersion

characteristics. It comes out recently, that the spatial periodicity can affec t not only temporal dispersion, but also the spatial one,

i.e. the dependence of the longitudinal component of the propagation constant versus the transverse component. These results

(again predominantly numeric) lead to so called management of spatial dispersion, i.e. to the management of diffraction

properties of narrow beams. This idea led to the prediction of the negative diffraction of light beams in photonic crystals,

of sound beams in sonic crystals, and of coherent atomic ensembles in Bose-Einstein condensates in periodic potentials. In particular

it has been found recently that between the normal diffraction and negative diffraction regimes a strong reduction of the diffraction

can be achieved, leading to the so called self-collimating, or nondiffractive light beams. The geometrical interpretation of wave

diffraction is as follows: wave beams of arbitrary shape can be Fourier decomposed into plane waves, which in propagation acquire phase

shifts depending on their propagation angles. This dephasing of the plane wave components results in a diffractive broadening of the beams.

We can see normal diffraction in propagation through an homogeneous material, where the longitudinal component of the

wavevector depends trivially on the propagation angle. In general, the normal or positive diffraction means that t

he surfaces of constant frequency are concave in the wavevector domain. The negative diffraction, geometrically means that the

surfaces of constant frequency are convex in wavevector domain. The intermediate case of the vanishing diffraction, where

the zero diffraction is supposed to occur at a particular point in the wavevector domain where the curvature of the surfaces of

constant frequency becomes exactly zero. Zero diffraction physically means that beams of arbitrary width can propagate without

diffractive broadening or, equivalently, that arbitrary wave structures can propagate without diffractive “smearing”.

The present study concerns the nondiffractive propagation of sound in periodic acoustic materials (sonic crystals).

We found, by applying the plane-wave expansion method, the existence of nondiffractive regimes similar to those in optics.

We check the nondiffractive propagation by integrating the wave equations bymeans of the FDTD technique. Moreover,

we also present the analytical treatment of the problem, leading to analytic relations, which among other are useful for the planning of the

corresponding experiment, and for designing the possible applications. In Section II of the article the propagation of sound is analized by

plane wave expansion, leading to the spatial dispersion curves, and in particular resulting into the straight (non diffractive) segments of the

spatial dispersion curves. In this way the nondiffractivepropagation regimes are predicted.