China
Africa
Explore chapters and articles related to this topic
Transient Quantum Transport in Nanostructures
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2019
Pei-Yun Yang, Yu-Wei Huang, Wei-Min Zhang
In the steady-state limit, all the Green functions usually depend only on the differences of time arguments, i.e. G(t,t′) = G(t − t′) because of time-translation symmetry. Thus, we can express Green function Gi,αk<(t,t) in the frequency domain,
Symmetry Principles and Group-Theoretical Methods in Electromagnetics of Complex Media
Published in Filippo Capolino, Theory and Phenomena of Metamaterials, 2017
In addition to the continuous Space- and Time-translation symmetry, Maxwell’s equations possess some discrete symmetries. They are Space inversion, Time reversal, and charge conjugation (P, T, and C, respectively), and combinations of these symmetries.
Hinductor Not Memristor—Synthesis
Published in Anirban Bandyopadhyay, Nanobrain, 2020
The physical realization of a quantum clock to build a quantum time crystal: The difference between quantum and fractal time crystal? This book explores the possibility of a fractal time crystal spread over 12 imaginary worlds, it could have a classical or a quantum version. We have summarized several basic physical situations encountered in the time crystal exploration in Figure 8.13b. The idea is to make the reader visualize how very well known school level quantum studies contribute to the new understanding of time crystal with a twist. A quantum clock satisfies two types of constraints—first is bound on the time resolution of the clock which provides by the difference between the minimum and maximum energy eigenvalue; another one is Holevo’s bound which tells about how much classical information can be encoded in a quantum system. In this work explains results such as optimal quantum clock using trapped ions (Buzek et al., 1999). As the Figure 8.14b explains the phase diagram of a large number of clocks working as a single system (Khemani et al., 2016). There are three domains; when an interaction between the participating clocks (e.g., spins of an array of electrons) is very low, symmetry does not break and if the energy is more then thermalization breaks the coupling between the clocks. In between the two limits there could be a new phase of matter in the pre-thermal regime which is protected by discrete time translation symmetry (Else et al., 2016, 2017). The clock assembly breaks time symmetry and automatically regenerates it. If the quantum ground state is essential, then quantum mechanically no one could realize a quantum time crystal (Bruno, 2013). The demand for quantum time crystal is beautiful (Figure 8.14b, top left), there is a thermodynamic restriction, once measurement is done the system would not remain in the universal ground state, for complete and autonomous measurement, the clock or periodically oscillating system must find a meta-ground state so that later, post-measurement the system returns to the universal ground state (Erker et al., 2017). The space-time could be symplectic, i.e., differentiable, geometric (measure length and angle; McDuff and Wehrheim, 2012), some of the quantum clocks are same as which characteristic of broken symmetry and topological order and other are new which characteristic by order and non-trivial periodic dynamics. In simple words, slow down the energy exchange process finding cool imaginary ideas (Peres, 1980). Quantum has only one imaginary world, so it is difficult to keep imaginary relation intact and still switch between global minima and excited state. Quantum time crystal (Wilczek, 2012) is impossible, such an argument has valid points (Watanabe and Oshikawa, 2015) in spite of prescriptions on how to build a practical time crystal (Yao et al., 2017) and subsequent claims to realize the same. In this book, 12 imaginary worlds layered one inside another achieves one incredible feature a higher topology of clocking between the imaginary world (2 × 2 × 3. 2 × 3 × 2, 3 × 2 × 2) that feature has the ability to hold on to a time crystal. Just dumping noise to higher-dimensional worlds is not enough; only then one could achieve a truly autonomous machine (Woods et al., 2016).
Lie symmetry analysis and soliton solutions for complex short pulse equation
Published in Waves in Random and Complex Media, 2022
Vikas Kumar, Abdul-Majid Wazwaz
The three-dimensional Lie algebra of system (5) is admitted with the following generatorsFurther, with the application of one-parameter symmetry groups (6), one can obtain the following one-parameter groups generated by where is Scaling transformation, is a time translation and is a space translation. is an arbitrary constant. Then we have the following Theorem.
Noether-type theorem for fractional variational problems depending on fractional derivatives of functions
Published in Applicable Analysis, 2021
M. J. Lazo, G. S. F. Frederico, P. M. Carvalho-Neto
Let S be an autonomous functional given by the problem (35), and let us consider the time translation transformation given by and . If S is invariant in the meaning of Definition 3.7, then the equality holds along any solutions of the Euler–Lagrange Equation (14), and for any .
Light, the universe and everything – 12 Herculean tasks for quantum cowboys and black diamond skiers
Published in Journal of Modern Optics, 2018
Girish Agarwal, Roland E. Allen, Iva Bezděková, Robert W. Boyd, Goong Chen, Ronald Hanson, Dean L. Hawthorne, Philip Hemmer, Moochan B. Kim, Olga Kocharovskaya, David M. Lee, Sebastian K. Lidström, Suzy Lidström, Harald Losert, Helmut Maier, John W. Neuberger, Miles J. Padgett, Mark Raizen, Surjeet Rajendran, Ernst Rasel, Wolfgang P. Schleich, Marlan O. Scully, Gavriil Shchedrin, Gennady Shvets, Alexei V. Sokolov, Anatoly Svidzinsky, Ronald L. Walsworth, Rainer Weiss, Frank Wilczek, Alan E. Willner, Eli Yablonovitch, Nikolay Zheludev
Perhaps the most fundamental symmetry of all is time translation symmetry. It is the statement that the laws of physics are unchanging and eternal. Strangely enough, there does not seem to be a convenient shorthand for the seven-syllable phrase “time translation symmetry”; here I will call it τ (tau). τ is related, through Emmy Noether’s fundamental theorem, to the conservation of energy.