{"id":47,"date":"2024-01-30T19:25:08","date_gmt":"2024-01-30T19:25:08","guid":{"rendered":"https:\/\/stringtimecrystal.com\/stringtimecrystal\/?page_id=47"},"modified":"2024-05-20T18:24:16","modified_gmt":"2024-05-20T18:24:16","slug":"time-crystals","status":"publish","type":"page","link":"https:\/\/stringtimecrystal.com\/stringtimecrystal\/time-crystals\/","title":{"rendered":"Time Crystals"},"content":{"rendered":"\n

Timetronics and Quantum Holistic Theory<\/h1>\n\n\n\n

Time Crystals Multiply: New Discoveries and Innovations in Spin Systems and Magnons<\/h2>\n\n\n\n
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Time Crystal Tunnels Time Techs<\/figcaption><\/figure>\n\n\n\n

Recent advancements in the study of time crystals have unveiled remarkable new findings, significantly broadening our understanding of these unique states of matter. Researchers have discovered evidence of two new time crystals in systems of spins periodically driven by nuclear magnetic resonance (NMR) pulses, and a separate team has created a space-time crystal consisting of magnons at room temperature. These discoveries challenge existing theories and open new avenues for practical applications.<\/p>\n\n\n\n

A time crystal is a state of matter where a collection of objects spontaneously forms a repeating pattern in time, analogous to how atoms form a regular pattern in space within a traditional crystal. First predicted theoretically in 2012 by Nobel laureate Frank Wilczek, time crystals were experimentally demonstrated in 2017. Unlike conventional time-periodic systems like pendulums or beating hearts, time crystals oscillate with a period that is an integer multiple of their driving mechanism’s period.<\/p>\n\n\n\n

Spin Systems and NMR Pulses<\/h4>\n\n\n\n
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Time Crystals where spins star-shaped moleculs are shifted by NMR Pulses<\/figcaption><\/figure>\n\n\n\n

The first new discoveries involve spin systems controlled by NMR techniques. Sean Barrett’s team at Yale University observed time-crystal signatures in an ordered spatial crystal of ammonium dihydrogen phosphate. Using radio frequency pulses to periodically rotate the spins of phosphorus-31 nuclei, they found that the spins oscillated with a period twice that of the pulse sequence, exhibiting time-crystal behavior despite the absence of disorder in the lattice structure. Barrett’s team developed innovative NMR techniques to probe this phenomenon.<\/p>\n\n\n\n

In a separate NMR experiment, Ganesh Sreejith and colleagues from the Indian Institute of Science Education and Research in Pune identified time-crystal behavior in a liquid state. They used star-shaped molecules with a central spin surrounded by several satellite spins, subjected to spin-rotating radio pulses. The molecules’ magnetization oscillated at twice the pulse period, stable even against perturbations such as changes in the spin-rotation angle. These findings were published in Physical Review Letters<\/em> and Physical Review B<\/em>.<\/p>\n\n\n\n

Space-Time Crystals and Magnons<\/h4>\n\n\n\n

Adding to the groundbreaking discoveries, a German-Polish research team has successfully created a micrometer-sized space-time crystal consisting of magnons at room temperature. This achievement, published in Physical Review Letters<\/em>, was a collaboration between scientists from the Max Planck Institute for Intelligent Systems in Stuttgart, Germany, and the Adam Mickiewicz University and the Polish Academy of Sciences in Pozna\u0144, Poland.<\/p>\n\n\n\n

Using the scanning transmission X-ray microscope Maxymus at Bessy II at Helmholtz Zentrum Berlin, the team captured the recurring periodic magnetization structure in a crystal on film. This live video of a space-time crystal shows a periodic pattern formed by magnons, highlighting a structure that exists not only in space but also in time. This pattern repeatedly disappears and reappears, demonstrating a quantum effect.<\/p>\n\n\n\n

In their experiment, the researchers used a strip of magnetic material on a microscopic antenna through which they sent a radio-frequency current. This current triggered an oscillating magnetic field, stimulating the magnons \u2013 quasiparticles of a spin wave. These magnetic waves migrated into the strip from both directions, spontaneously condensing into a recurring pattern in space and time. Remarkably, the pattern formed before the converging waves could meet and interfere.<\/p>\n\n\n\n

First author Nick Tr\u00e4ger from the Max Planck Institute for Intelligent Systems, who worked on the project with Pawel Gruszecki, explained, \u201cWe took the regularly recurring pattern of magnons in space and time, sent more magnons in, and they eventually scattered. Thus, we were able to show that the time crystal can interact with other quasiparticles. No one has yet been able to show this directly in an experiment, let alone in a video.\u201d<\/p>\n\n\n\n

The scanning transmission X-ray microscope used in the experiment is incredibly advanced. Dr. Gisela Sch\u00fctz from the Max Planck Institute noted, \u201cNot only can it make the wavefronts visible with very high resolution, which is 20 times better than the best light microscope, but it can also do so at up to 40 billion frames per second and with extremely high sensitivity to magnetic phenomena.\u201d<\/p>\n\n\n\n

Implications and Future Applications<\/h4>\n\n\n\n

These discoveries highlight the robustness and versatility of space-time crystals. The ability to form such crystals at room temperature and observe interactions with other quasiparticles suggests vast potential applications. As Pawel Gruszecki from Adam Mickiewicz University emphasized, \u201cOur crystal condenses at room temperature and particles can interact with it \u2013 unlike in an isolated system. This opens up numerous potential applications.\u201d Joachim Gr\u00e4fe from the Max Planck Institute added, \u201cClassical crystals have a very broad field of applications. Now, if crystals can interact not only in space but also in time, we add another dimension of possible applications. The potential for communication, radar, or imaging technology is huge.\u201d<\/p>\n\n\n\n

These advancements mark a pivotal moment in the study of time crystals, suggesting that the phenomena are more robust and prevalent than previously thought. The future holds promising possibilities for practical applications, potentially transforming various technological fields.<\/p>\n\n\n\n

References<\/h3>\n\n\n\n

Schirber, M. (2018, May 1). Time crystals multiply<\/a>. Physics<\/em>, 11, s51. <\/p>\n\n\n\n

Max Planck Institute for Intelligent Systems. (2021, February 10). World’s first video of a space-time crystal<\/a>. Max Planck Institute for Intelligent Systems<\/em>.<\/p>\n\n\n\n

Tr\u00e4ger, N., Gruszecki, P., Sch\u00fctz, G., & Gr\u00e4fe, J., et al. (2021). Real-space observation of magnon interaction with driven space-time crystals<\/a>. Physical Review Letters<\/em>, 126(5), 057201. <\/p>\n\n\n\n

Frequency Oscillator for Quantum Bioresonance\u200b<\/h2>\n\n\n\n

The study of time crystals, particularly in the context of timetronics, requires thorough examination of both theoretical foundations and experimental findings. Time crystals, representing a new phase of matter, have attracted significant attention for their potential use in quantum computing and simulations. Initially proposed by Wilczek in 2006 [1], these crystals are characterized by the breaking of continuous time symmetry, similar to the breaking of spatial symmetry in ordinary crystals. Theoretical research has been extensive, with key studies on periodically driven systems (Yao & Nayak, 2012) [2], the absence of quantum time crystals (Watanabe & Oshikawa, 2009) [3], Floquet time crystals (Else, Bauer, & Nayak, 2010) [4], boundary time crystals (Iemini et al., 2012) [5], and quasi time crystals (Wu, 2016) [6]. These studies have deepened our understanding of the fundamental properties and limitations of time crystals.<\/p>\n\n\n\n

Experimental efforts have also been significant, with notable discoveries including the observation of a continuous time crystal (Kongkhambut et al., 2016) [7], photonic time crystals (Zeng et al., 2011) [8], and the dynamics in periodically driven quantum systems (Kenmoe & Fai, 2010) [9]. These experiments provide empirical support for the existence of time crystals and their applicability in various physical settings.<\/p>\n\n\n\n

The potential impact of time crystals in quantum computing and simulations is a topic of great interest. In the field of timetronics, the use of periodically driven systems to engineer bound states in the quasienergy spectrum has been a focus (\u017dlabys et al., 2015) [10] (Bai, 2015) [11]. The relevance of time crystals in simulating time-independent Hamiltonian systems is also noteworthy (Verdeny et al., 2010) [12].<\/p>\n\n\n\n

In summary, both theoretical and experimental research on time crystals has significantly advanced our understanding of this unique phase of matter. The exploration of their existence in various systems, the absence of quantum time crystals, and empirical observations have collectively contributed to a comprehensive understanding. The implications of time crystals for timetronics and their applications in quantum computing and simulations highlight the importance of continued research in this field.<\/p>\n\n\n\n

The wave function is a bi-component entity (\u04711, \u04712) expressible as a complex number \u0471 = \u04711 + j\u04712. Its absolute square, |\u0471|^2 = \u04711^2 + \u04712^2, represents the probability density.<\/p>\n\n\n\n

\n
\\hat {H}[B]|\\Psi (t)\\rangle => \\Psi_1 + j\\Psi_2 = RLognormal[(\\Delta f) h]+ j \\frac{\\varphi(t)}{RLognormal(O)}<\/span><\/span>(1)<\/span><\/div>\n
\\Psi(x, t) = A e^{j(kx - 2\u03c0ft)}<\/span><\/span>(2)<\/span><\/div>\n
|\u03a8|^2 = \u03a8_1^2 + \u03a8_2^2<\/span><\/span>(3)<\/span><\/div>\n
T(t) = 1 - \\frac{j\\hat{H}t}{\\hbar} + \\frac{(\\hat{H}t)^2}{2!\\hbar^2} - \\frac{(j\\hat{H}t)^3}{3!\\hbar^3} + \\frac{(\\hat{H}t)^4}{4!\\hbar^4} - \\cdots;\u2003 i\\hbar \\frac{dT(t)}{dt} = HT(t)<\/span><\/span>(4)<\/span><\/div>\n
4\\pi \\Delta f \\Delta t = N<\/span><\/span>(5)<\/span><\/div>\n
4\u03c0 \u0394f \u0394t > 1<\/span><\/span>(6)<\/span><\/div>\n
E = h\u2217f<\/span><\/span>(7)<\/span><\/div>\n
P(i) = \\frac {N(i)}{ N}, N = \\sum_{i=0}^{k} N(i)<\/span>\n<\/span>(8)<\/span><\/div>\n
R_1R_2C_1C_2 \\frac{d^2I (t)}{dt^2} +(R_1C_1+R_2C_2) \\frac{dI(t)}{dt} + I(t) = C_1C_2(R_1+R_2) \\frac{d^2U(t)}{dt^2}+(C_1+C_2) \\frac{dU(t)}{dt}<\/span>, [17]<\/span>(9)<\/span><\/div>\n
\u22ef<\/div>\n
\\prod_{N=2}^{26}(R_NR_{N-1})\\prod_{N=2}^{26}(C_NC_{N-1}) \\frac{d^NI (t)}{dt^N} +\\sum_{N=2}^{26} (R_NC_N+R_{N-1}C_{N-1}) \\frac{d^{N-1}I(t)}{dt^{N-1}} + I(t) = \\prod_{N=2}^{26} (C_NC_{N-1})\\sum_{N=2}^{26} (R_N+R_{N-1}) \\frac{d^NU(t)}{dt^N}+\\sum_{N=2}^{26} (C_N+C_{N-1}) \\frac{d^{N-1}U(t)}{dt^{N-1}}, N\u22082Z<\/span><\/span>(10)<\/span><\/div>\n\n
\\prod_{N=1}^{26} R_N\\prod_{N=1}^{26} C_N \\frac{d^NI (t)}{dt^N} +\\sum_{N=1}^{26} (R_NC_N) \\frac{d^{N-1}I(t)}{dt^{N-1}} + I(t) = \\prod_{N=1}^{26} C_N\\sum_{N=1}^{26} R_N \\frac{d^NU(t)}{dt^N}+\\sum_{N=1}^{26} C_N \\frac{d^{N-1}U(t)}{dt^{N-1}} , N\u2208Z<\/span><\/span>(11)<\/span><\/div>\n\n<\/div>\n\n\n\n

Time crystal oscillator model<\/p>\n\n\n\n

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Model Time Crystal describing a bifurcation quantum oscillator [13]<\/em>
Figure 2D from Dikopoltsev et al.’s study shows a lognormal distribution of the power carried by electromagnetic radiation versus radiation angle highlighting a strong agreement between analytic calculations and FDTD simulations. This demonstrates the accurate prediction of the lognormal emission pattern of light in photonic time crystals, validating both the theoretical approach and simulation methods in capturing the dynamics of light emission influenced by medium modulation [19].
x_{n+1} = r x_n (1 - x_n)<\/span><\/figcaption><\/figure>\n\n\n\n