tag:blogger.com,1999:blog-13869903.post3315920675928840386..comments2017-03-23T21:22:10.350-05:00Comments on nanoscale views: What is a time crystal?Douglas Natelsonhttps://plus.google.com/101165937354831985246noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-13869903.post-70239525005735688962017-02-14T03:13:42.881-06:002017-02-14T03:13:42.881-06:00I have the same question. Perhaps an even simpler ...I have the same question. Perhaps an even simpler example would be a dynamical system whose Hamiltonian alternates between that of a harmonic oscillator and zero, i.e. the Hamiltonian H = (q^2+p^2)/2 for time t=0 to pi and H = 0 from time t = pi to 2pi. From time 0 to pi, the phase space point (q,p) traces a semicircle. From time pi to 2pi, it stays at the same point. Therefore, the phase space trajectory has a period 4pi, whereas the Hamiltonian has period 2pi. <br /><br />I think the situation perhaps is the opposite to that of a conventional symmetry breaking. A finite system would never spontaneously break a conventional symmetry. However, it seems that one can easily come up a finite system that "spontaneously breaks" the discrete time-translation symmetry. This makes me worry to what extent spontaneous time-translation symmetry breaking is a well defined concept.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-13869903.post-18349315657159314342017-02-13T08:54:35.155-06:002017-02-13T08:54:35.155-06:00Anon, that's a good question, and I think it g...Anon, that's a good question, and I think it gets right to these thorny definitional issues, particularly in driven systems. I am no authority on this, but my sense is that a time crystal requires some many-body interaction piece that leads to the spontaneous onset of discrete time translation invariance. Douglas Natelsonhttp://www.blogger.com/profile/13340091255404229559noreply@blogger.comtag:blogger.com,1999:blog-13869903.post-48281096531565639062017-02-12T18:08:37.448-06:002017-02-12T18:08:37.448-06:00Just wondering - why can't we call a Hopf bifu...Just wondering - why can't we call a Hopf bifurcation of a dynamic nonlinear oscillator a 'time crystal'? I mean this in the sense that the equations of motion, for example, those of the Van der Pol oscillator, do have time-periodic symmetry, but the system spontaneously develops periodic solutions: https://en.wikipedia.org/wiki/Hopf_bifurcation.Anonymousnoreply@blogger.com