“Time Crystals” could revolutionize theoretical physics. Comment by jiajia

MOSCOW, October 7 - RIA Novosti. For the first time, American scientists were able to create an exotic structure - the so-called “time crystal”, inside which time flows not continuously, but in peculiar “steps,” according to an article posted in the electronic library arXiv.org

Time crystals are unusual structures whose existence was predicted in February 2012 by Nobel laureate Frank Wilczek. Their main property is that in them the laws of physics will behave in a special way, giving rise to unusual periodic structures not in space, as in ordinary crystals, but in time.

Almost all physical laws under normal conditions work the same at any point in time. Formulas describing physical processes do not change when time is shifted back or forward by an arbitrary value. Four years ago, Wilczek suggested that this rule - the so-called homogeneity of time - could be violated inside exotically arranged matter, the maintenance of which requires the least amount of energy.

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When observing such a crystal, it will seem to us that it is moving, although in fact it will be in a state of absolute rest. Its "motion" would be composed of discrete elements repeating in time, similar to the particles of matter in ordinary crystals, which led Wilczek to call this form of matter a "time crystal".

Many scientists doubted that such a form of matter could exist in principle, since the laws of quantum mechanics would interfere with it, but Jiehang Zhang from the University of Maryland in College Park (USA) and his colleagues found a way to circumvent these restrictions and for the first time see a similar crystal. To do this, they created a quantum system that is in a constant state of instability and changes over time.

The quantum time crystal created by Zhang and his colleagues is a collection of ytterbium ions cooled to near absolute zero and arranged relative to each other so that their spins constantly interact, switching each other "in turns."

These interactions lead to the fact that rare earth metal atoms actually cease to behave like quantum objects and are localized - become clearly visible - at some specific point in space, and do not remain in a “smeared” form, like “normal” inhabitants of the quantum world.
Changing the spins of these atoms using a laser, American scientists noticed something unusual - some time after the manipulations, the frequency of spin “switching” suddenly doubled.

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Since the atoms did not otherwise interact with the outside world and scientists did not interfere with their work, such behavior, according to Zhang and his colleagues, can only be explained by the fact that this structure is a time crystal in which the uniformity of time is violated. This is confirmed by the fact that any manipulations with the laser did not change the “switching” frequency in the crystal itself - it was always the same, despite the increase or decrease in the laser spin switching frequency.

Scientists believe such structures could be used to create quantum memories and a number of other esoteric devices, but they acknowledge that many scientists will want to double-check their findings first before thinking about possible practical applications.

Recently, a group of American physicists was able to construct a so-called “time crystal” - a structure whose existence had been predicted for a long time.

A feature of the crystal is the ability to periodically become asymmetric not only in space, but also in time. Therefore, it can be used to make an ultra-precise chronometer.

Crystals are generally very paradoxical formations. Take their relationship with symmetry: as we know, the crystal itself, judging by its appearance, can be considered simply an example of spatial symmetry. However, the process of crystallization is nothing more than its malicious violation.

This is very well illustrated by the example of the formation of crystals in a solution, for example, of some salts. If we analyze this process from the very beginning, it will be clear that in the solution itself the particles are located chaotically, and the entire system is at a minimum energy level. However, interactions between particles are symmetrical with respect to rotations and translations. However, after the liquid has crystallized, a state arises in which both of these symmetries are broken.

Thus, we can conclude that the interaction between particles in the resulting crystal is not at all symmetrical. A number of important properties of crystals follow from this - for example, these structures, unlike liquid or gas, conduct electric current or heat differently in different directions (they can conduct to the north, but not to the south). In physics, this property is called anisotropy. This crystalline anisotropy has long been used by humans in various industries, such as electronics.

Another interesting property of crystals is that they, as a system, are always at a minimum energy level. What is most curious is that it is much lower than, for example, in the solution that “gave birth” to the crystal. We can say that in order to obtain these structures, it is necessary to “take away” energy from the original substrate.

So, during the formation of a crystal, the energy level of the system decreases and the original spatial symmetry is broken. And not so long ago, two physicists from the USA, Al Shapir and Frank Wilczek (by the way, a Nobel laureate), wondered whether it was possible for the existence of a so-called “four-dimensional” crystal, where symmetry breaking would occur not only in space, but also in time.

Using complex mathematical calculations, scientists were able to prove that this is quite possible. The result is a system that exists, like a real crystal, at a minimum energy level. But the most interesting thing is that, due to the formation of certain periodic structures not in space, but in time, it would come to an asymmetrical final state. The authors of the work called such a system very solemnly - “time crystal”.

After some time, a group of experimental physicists led by Professor Zhang Xiang from the University of California (USA) decided to create such a system not on paper, but in reality. Scientists created a cloud of beryllium ions and then “locked” it in a circular electromagnetic field. Because the electrostatic repulsion of similarly charged ions from each other causes them to be distributed evenly around the circle, the researchers essentially created a gaseous crystal. And while the field characteristics were unchanged, the state of the system, in theory, should not have changed either.

At the same time, calculations and then observations showed that this very ionic ring will not be stationary. The gaseous crystal was constantly rotating, and the interactions of the ions were sometimes symmetrical, sometimes not. All this was observed even when the crystal was cooled to almost absolute zero. Thus, this structure is truly a “time crystal”: it exhibits the properties of periodicity and asymmetry in both space and time.

It is curious that the slowly rotating ring of ions constructed by Professor Zhang's group has caused many non-specialists to associate it with a perpetual motion machine. Of course, a gas crystal looks like a perpetum mobile, but in reality it is not. After all, this system cannot do any work, since all its components are at the same energy level (moreover, minimal). And according to the second law of thermodynamics, work is possible only in a system whose components are at least two energy levels.

At the same time, this does not mean at all that the “time crystal” cannot be used for practical needs. Professor Zhang is convinced that on its basis it is possible to construct, for example, an ultra-precise chronometer. After all, the transition from symmetry to asymmetry has a pronounced periodicity. In the meantime, the professor and his colleagues want to engage in a more detailed study of the properties of the wonderful structure they created...

Physicists from Harvard University have created a new form of matter - the so-called "time crystal" - that could explain the mysterious behavior of quantum systems.
Crystals, including salts, sugars or diamonds, are at their core simply a periodic arrangement of atoms in a three-dimensional lattice. On the other hand, time crystals are believed to add a fourth dimension to this definition. It is assumed that under certain conditions, some materials can manifest themselves in their structure and time.

Led by physics professors Mikhail Lukin and Eugene Demler, the team built a quantum system using a small diamond with millions of atomic-scale impurities known as a nitrogen-substituted vacancy (NV center). They used microwave pulses to throw the system out of balance, causing rotation at the center and flipping them over at regular intervals.

“Currently, ongoing work is underway to understand the physics of nonequilibrium quantum systems. This is an area that is of interest to many quantum technologies because it is basically a quantum system that is far from equilibrium. In fact, there is a lot to explore here, and we are still only at the very beginning,” said Mikhail Lukin.

It initially seemed unlikely that such systems could be created. In fact, some researchers have gone very far on this issue. They proved that it is impossible to create a time crystal in a quantum system that is in equilibrium. Physicists explain that most objects around us are in equilibrium. If you have something hot and cold and you combine them, the temperature will equalize. But not all systems work on this principle. One of the most common examples of a material out of balance is diamond. It is a crystallized form of carbon that forms under high temperature and pressure. Diamond is unusual in that it is meta-stable, meaning that once it has its shape, it remains unchanged even after the factors of heat and pressure are removed from it.

Only recently have scientists begun to understand that nonequilibrium systems can exhibit the characteristics of a time crystal. One of these characteristics is that the crystal's response remains stable over time to various stimuli. The time crystal effect has a lot to do with the idea that a system is excited but does not absorb energy.

To create such a system, Lukin and his colleagues started with a small diamond that had many NV centers embedded in it. Using microwave pulses, the scientists periodically changed the orientation of their rotation to see if the material would continue to react like a time crystal.

Such systems could be critical in the development of useful quantum computers and quantum sensors. They demonstrate the fact that the two critical components of long quantum memory and high quantum bit density are not mutually exclusive. Physicists say the research will enable the creation of a new generation of quantum sensors, possibly with applications for things like atomic clocks.

These are acquired from disenchanting epic gear with an iLvl of 650 and above.
Currently it is unknown whether these can also be gained from combining 5 Azurite Shards , it is however quite likely.

Comment from Eido

One of three main types of Enchanting reagents introduced in Warlords of Draenor:
Acquired primarily through the Enchanting spell: Disenchant .

1. Time Crystal - YOU ARE ON THIS PAGE

• Time Crystal appears to be the WoD version of other "crystals" in past expansions and is the hardest of the three materials to obtain.
  It is most-commonly received when disenchanting Epic quality, ilvl 640 and up gear and weapons from WoD (perhaps except for items from a random upgrade1 ).
  NOTE: Even with the , non-enchanters cannot disenchant Epic-quality items. You will receive the red, error text "Cannot Disenchant".
  It appears you CAN disenchant epic quality items, even if you are not an enchanter.
• Non-Enchanters and Enchanters alike can "craft" this item through Work Orders, with the Enchanting Pavilion Level 1. .
  1. Work Orders yield a number of Shattered Time Crystal , which can later be combined to form a full Time Crystal .
     Having a follower(Requires Enchanting Pavilion Level 2) at this building can result in higher Work Order yields.
     Percent chance of receiving more increases with follower level. ()
• Additionally, Enchanters can create these crystals in two ways:
  1. Enchanting lvl 600: using Glowing Shard with the Fractured Temporal Crystal recipe (the Wowhead tooltip for this is a bit strange) to create Fractured Time Crystal (amount awarded increases by Enchanting lvl), which can later be combined to form a full Time Crystal . There is no cooldown for this option.
  2. Enchanting lvl 700: (replaces the previous option) using Glowing Shard with the Time Crystal recipe to create a full Time Crystal ONCE A DAY.

• The previous, data-mined item, , is no longer available to players.
• According to the loot table, it appears Rare and Uncommon quality items from WoD can now also yield a Time Crystal
• 1 Credit to Exeila for this information.
• Edit 1/21/15: Adjusted information to reflect the loot table, it seems Rare-quality items no longer yield a Time Crystal and the ilvl required has been increased.
• Edit 7/5/15: It appears you CAN disenchant epic quality items, even if you are not an enchanter.

Comment from jiajia

Wondering disenchanting what ilvl gear I get this instead of Sha crystal, it seems like disenchanting 608 item gives you these and those under 590s gives you Sha. 598 give sha crystals too.

Comment from Hypersonguy

These are generated by disenchanting epic items of 600 ilvl or higher. The easiest way to tell if you will get a temporal crystal or a sha crystal is whether the items says Disenchantable (575) or just plain disenchantable. Anything featuring the (575) will yield a sha crystal.

Comment from Kelthuza

quick question..

how do you get the recipe with 3 charges? and is it the same way for other professions?

Comment from MisterCrow

Anyone have any suggestions on the best way to turn these into a vendorable item?

I"m not really interested in undercutting goblins on the AH, but I also want to find a way to put these to use that translates directly into gold.

"Crystal in time" is an unusual physical concept, theoretically proposed several years ago as an illustration of the spontaneous violation of the time invariance of the laws of physics. In familiar words, this is a system in which, in a state with the lowest energy and without any external influence, internal movement would spontaneously arise. It quickly became clear, however, that such a system was impossible - at least in its original formulation. However, quite recently, physicists predicted that if instead of the continuous flow of time we take its discrete analogue, such “crystallization” will no longer contradict anything. The other day in a magazine Nature Two articles by different teams of experimenters were published reporting on the successful implementation of such “crystals in discrete time.”

Terminological preface

It seems necessary to begin this story with a terminological explanation. This topic has already passed through the news feeds recently, when the articles described here just appeared in the archive of electronic preprints. They talked about a system called by the authors discrete time crystal. All notes translated the term time crystal as a “time crystal” or, even more mysteriously, a “time crystal”. Word discrete almost everywhere it was omitted, and if it appeared, it was in the combination “discrete time crystal”, which also did not clarify the situation too much - the crystal is already discrete! Finally, when the experimental articles were published in the journal Nature, its cover featured an equally mysterious artistic illustration (Fig. 1). All this evoked beautiful and mysterious images, which, unfortunately, were far from what the authors actually put into the title.

In this note we tried to choose a translation that is closer to the original meaning. Of course, it is not time that crystallizes, but a certain system of particles, and this crystallization can be noticed by studying the movement of the system in time. Hence the term “crystal in time”, as opposed to the usual “crystal in space”. Here's the word discrete should be attributed In time, and not to the crystal. Such “crystallization” can be noticed by the periodic movement not in the present time, but in its discrete analogue, in the “counts” of external periodic influence. Therefore, we call such a system a “discrete-time crystal.”

However, we understand that so far this all seems completely incomprehensible, so let’s get to the point.

"Crystallization in Time"

Theoretical physicist and Nobel laureate Frank Wilczek is famous for his contributions and innovative ideas in various areas of theoretical physics. Therefore, when in 2012, in a couple of short articles (first, second), he proposed the controversial but very interesting idea of ​​“crystals in time,” the scientific community paid close attention to it.

The starting point of this proposal is the phenomenon of spontaneous symmetry breaking, which occurs in a wide variety of areas of physics, ranging from ordinary thermodynamics to the world of elementary particles. The word “spontaneous” means that, although the physical laws themselves have a certain symmetry, the matter that obeys them still prefers to assemble into a configuration that violates this symmetry. Nobody “forces” the system to break symmetry; it does it itself, spontaneously.

Perhaps the most striking example of this effect is the very existence of crystalline bodies. If we imagine for a moment a hypothetical situation where atoms do not interact with each other at all, then any substance would be an ideal gas, completely homogeneous in space. This spatial homogeneity is a manifestation of the fact that the laws governing the movement of atoms have symmetry: they do not change with an arbitrary displacement in space in any direction. However, the interaction between atoms does exist, and if it is strong enough, it causes matter to organize itself into a periodic spatial structure - a crystal. The crystal is symmetrical with respect to shifts not at any distance, but only at very specific steps in specific directions. We can say that the original shear symmetry has spontaneously broken, and the interaction between atoms is responsible for this breaking.

Wilczek wondered: is it possible to find a system that would demonstrate spontaneous breaking of symmetry with respect to time shifts, and not in space? Such a system would behave extremely unusually. If we are talking, for example, about a many-particle system, a real piece of matter, then in a state of thermal equilibrium, without any external influences, periodic motion would spontaneously arise in it. It would be a kind of “spontaneously ticking clock”, the course of which is not set by any external metronome. Visual similarity with spatial periodicity in an ordinary crystal, spontaneous periodicity, a kind of “crystallization” in time, gave the idea such a catchy name.

Let us immediately emphasize two important points. This must be movement in a state of thermodynamic equilibrium, and not in a disturbed state, and therefore it is no longer possible to extract energy from it by stopping the movement. In addition, the movement must be detectable. Let's say a multi-electron atom is not suitable here: although the electrons in the ground state of the atom can rotate around the nucleus, this does not lead to any observable flow of electron density.

Wilczek himself admitted that such a hypothetical system looked unnatural, but hoped that by specially selecting the law of interaction, it would be possible to create it. However, it quickly became clear that this radical proposal was not feasible. Objections began to appear immediately, and in 2015 it was finally proven that no spontaneous periodic motion could arise in a state of thermodynamic equilibrium.

"Crystal in discrete time"

It would seem that we could put an end to this. But here the inquisitive mind of the theorists manifested itself: the idea of ​​spontaneous violation of invariance in time was so attractive that theorists began to try to find at least something similar to it, slightly weakening the original requirements.

One such option, proposed last year, was called discrete time crystal, “discrete time crystal” (see the article by N. Y. Yao et al., 2017. Discrete Time Crystals: Rigidity, Criticality, and Realizations and the earlier article by D. V. Else et al., 2016. Floquet Time Crystals). It refers to a situation where a system of many interacting particles is not in complete isolation, but experiences strictly periodic shocks, an external influence with a period t. If there is a source of disorder in the system, then external shocks will not endlessly rock the oscillations or heat the system, but will simply transfer it to a new, special state - it is, as it were, equilibrium, but only under conditions of periodic external influence. (This statement in itself is also a very recent result, which laid the foundation for “crystals in discrete time.”)

In such a new equilibrium state, of course, there may already be some movement with a period t- after all, the system is periodically pushed! Initial symmetry w.r.t. arbitrary there are no longer any time shifts, but the laws of motion remain unchanged with respect to “discrete time”, that is, time shifts for a period t. And now, instead of the smooth evolution of a system with present time, you can study how it behaves in discrete time, through several “jumps” in time by the amount t.

Is it possible to organize crystallization in time in such a “discrete time”? This would mean that a long-period motion with a period spontaneously starts in the system T, which is not equal, but several times greater t. Since there is no longer a strictly equilibrium situation, the prohibition discovered for real crystals in time no longer applies here. The authors of last year's theoretical article came to the conclusion that such “crystals in discrete time” really do not contradict the laws of physics, and even proposed and numerically analyzed a specific approach to their implementation.

Let's make a small digression here and figure out what is important in this idea and what is not. In fact, there are well-known examples when, in response to a periodic influence, the system moves not with exactly the same period, but with a multiple of it. Remember, for example, how you swing while standing on a swing: you squat and stand up at twice the frequency of the swing. Or in other words, you act on the swing, periodically changing the moment of inertia (and thereby creating a parametric resonance), and the oscillation in the system increases with twice as much period.

The peculiarity of this and other similar examples is the lack of “rigidity” of the result. Yes, there is a response with a period T > t, but the attitude T/t- not fixed, it is malleable. We can change the frequency of exposure and see that T/t will change. For example, on the same swing, if you slightly change the tempo of a squat relative to the ideal value, then instead of swinging oscillations, beats will be observed - the amplitude of the oscillations either gradually increases or gradually decreases - and this is a sign of the superposition of two oscillations with close but different frequencies.

In a real crystal there should be no beats in discrete time. Attitude T/t must remain unchanged even with slight distortions of the system, with a conscious shift in the frequency of the influencing force relative to the ideal value. Figuratively speaking, a crystal must have a kind of “rigidity” in time - but this is not spatial rigidity, but temporary.

In addition, this rigidity must be ensured by the interaction of individual particles. It should appear when the interaction becomes stronger than a certain threshold, and disappear when the disordered noise overpowers its ordering tendency. In other words, the system should demonstrate phase transitions: “solidify in discrete time” as interaction increases and “melt” as noise increases.

Two experimental works

Two experimental works published in the latest issue Nature, offer two different implementations of “discrete-time crystal” (Fig. 2). They differ in the original material carrier and the subtleties of the experiment, but in essence they are very similar. In one case, it was 10 individual ytterbium ions trapped and suspended in space three microns apart. Because the ions are separated from each other, physicists could blast laser pulses either at all of them at once, or at each ion independently. In the second article, these were nitrogen atoms introduced as an impurity into a diamond crystal. There, there were about a million such impurity atoms per micron-sized crystal, and all of them were simultaneously exposed to pulses of microwave radiation.

Please note an important point. In both cases, "crystallization" refers not to the material movement of the atoms themselves, but to their orientation spins. The atoms did not move anywhere: they were either held in traps or firmly lodged inside the crystal. But their backs were quite mobile; It was they who were influenced by physicists and it was they who formed the crystalline order in time. Therefore, one should not visualize these achievements as some kind of new substance that periodically turns into a physically tangible crystal, as in Fig. 1; everything here was much more prosaic.

The spins were controlled using cyclic effects of short pulses of laser light or microwave radiation. In each cycle there was an impact impulse that synchronously rotated all spins to a strictly defined angle. This is that precisely measured blow to the system. This was followed by a special pulse that temporarily “switched on” the pairwise interaction of atoms, which depended on the mutual orientation of the spins and their distance from each other. The intensity of this interaction could be controlled within wide limits. Finally, in the case of a chain of ions, a third pulse was also used to forcefully create disorder - and here it was very helpful that each ion could be influenced independently. In the case of impurities in the crystal, this was not required; disorder is already present there in the form of a chaotic arrangement in the crystal. This combination of impulses - impact, interaction, disorder - is one cycle lasting t. The entire procedure is repeated over and over again, up to hundreds of times. At the end of the effects, physicists measure the resulting state of spins - either individually, as in the case of a chain of ions, or as a whole in the entire crystal.

The phenomenon that occurs under such conditions is shown schematically in Fig. 3. The first cycle of exposure almost exactly turns the spins from the up position to the down position, and the second cycle of exposure returns the backs almost to their original state. Together we get a periodic motion with double the period. The chaotic influence tends to break this order, but due to the interaction, the backs cling to each other and try to stay co-directed. And the most important point: even if the impact impulse turned out to be insufficiently calibrated, for example, it did not completely turn its backs, then the atoms, with their collective effort, compensate for this inaccuracy and still maintain a strict two-period cycle. The response period is fixed at 2 t, even if the impact impulse tries to “impose” a different period on the atoms. This is the notorious rigidity of the crystal, the ability to resist deflection to the side.