Abstract The classical pendulum has a long and rich history in physics. On the other hand, the history of the quantum pendulum can only stretch back as far as the appearance of quantum mechanics itself in 1925–1926. Yet within three years of that exciting time, a paper on the quantum pendulum appeared in Physical Review authored by one of the pioneers of atomic physics, Edward Condon (Condon 1928). Condon’s paper laid out the basic problem and the means to its solution. Contributions to the study of the quantum pendulum continue to be made even in recent times. See, for example, (Pradhan and Khare 1973; Aldrovandi and Ferreira 1980; Cook and Zaidins 1986; Baker et al. 2002). In this tale we describe some of the novel and surprising features of the pendulum when it is analyzed according to the rules of quantum physics.Abstract The classical pendulum has a long and rich history in physics. On the other hand, the history of the quantum pendulum can only stretch back as far as the appearance of quantum mechanics itself in 1925–1926. Yet within three years of that exciting time, a paper on the quantum pendulum appeared in Physical Review authored by one of the pioneers of atomic physics, Edward Condon (Condon 1928). Condon’s paper laid out the basic problem and the means to its solution. Contributions to the study of the quantum pendulum continue to be made even in recent times. See, for example, (Pradhan and Khare 1973; Aldrovandi and Ferreira 1980; Cook and Zaidins 1986; Baker et al. 2002). In this tale we describe some of the novel and surprising features of the pendulum when it is analyzed according to the rules of quantum physics.

Jun 2, 20050 citations

Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions"

Vedika Khemani, Roderich Moessner, Shivaji L. Sondhi

In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal.In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal.

arXiv:2001.11037Jan 29, 20205 citations

The quantum pendulum as spin

Piotr Garbaczewski

Physics Letters AApr 1, 19795 citations

From a quantum theory to a classical one

Alessandro Coppo, A. Cuccoli, C. Foti +1 more

arXiv:2004.00301Soft ComputingMay 8, 20206 citations

Quantum coupling between gravity and mass in bouncing ball dynamics

A. Feoli, Elmo Benedetto, Fabiano Feleppa

Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.Abstract We review the dynamics of a bouncing ball, both from the classical and the quantum points of view, studying the role of its inertial and gravitational masses. We analyze the behavior of quantum particles of different masses, embedded in a uniform gravitational field. We show that the bouncing ball is a useful didactic example to show that the coupling between rest mass and gravity cannot be avoided at the quantum level and that the equivalence principle must be reformulated in quantum mechanics. Galileo’s experiment of falling bodies can be still satisfied if one considers only the average quantum values of observables.

European Journal of PhysicsNov 15, 20185 citations

{\it and}

they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system--allowing for this elevates the pendulum of Galileo and Huygens to a genuine time crystal.