Avoided crossings are common in the quasienergy spectra of strongly driven nonlinear quantum wells. In this paper we examine the sinusoidally driven particle in a square potential well to show that avoided crossings can alter the structure of Floquet states in this system. Two types of avoided crossings are identified: one type leads only to temporary changes (as a function of driving field strength) in Floquet state structure while the second type can lead to permanent delocalization of the Floquet states. Radiation spectra from these latter states show a significant increase in high harmonic generation as the system passes through the avoided crossing. 42.50.Hz,05.45.+b,42.65.Ky
The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the eigenvalues of random Hermitian matrices. The statistical properties of random numbers and eigenvalues of random Hermitian matrices are examined and the connection between these properties and the statistics of eigenvalues of quantum systems is illustrated, using the quantum standard map as an example. The relevance of these ideas to some problems in the theory of prime numbers is explored.
Complex coordinate scaling (CCS) is used to calculate resonance eigenvalues and eigenstates for a system consisting of an inverted Gaussian potential and a monochromatic driving field. Floquet eigenvalues and Husimi distributions of resonance eigenfunctions are calculated using two different versions of CCS. The number of resonance states in this system increases as the strength of the driving field is increased, indicating that this system might have increased stability against ionization when the field strength is very high. We find that the newly created resonance states are scarred on unstable periodic orbits of the classical motion. The behavior of these periodic orbits as the field strength is increased may explain why there are more resonance states at high field strengths than at low field strengths. Close examination of an avoided crossing between resonance states shows that this type of avoided crossing does not delocalize the resonance states, although it may lead to interesting effects at certain field strengths.Comment: 11 pages, 11 figures, submitted to PR
The second law of thermodynamics, which states that the entropy of an isolated macroscopic system can increase but will not decrease, is a cornerstone of modern physics. Ludwig Boltzmann argued that the second law arises from the motion of the atoms that compose the system. Boltzmann's statistical mechanics provides deep insight into the functioning of the second law and also provided evidence for the existence of atoms at a time when many scientists (like Ernst Mach and Wilhelm Ostwald) were skeptical.1
There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.
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