Condensed Matter

2011 Submissions

[2] viXra:2011.0034 [pdf] submitted on 2020-11-04 20:26:12

Many-Body Fermions and Riemann Hypothesis

Authors: Xindong Wang, Alex Shulman
Comments: 11 Pages.

We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and the complete single fermion excitation energy spectrum is constructed using the non-interacting fermions that are eigenstates of the quadratic matrix related to the system Hamiltonian. Connection to the Riemann Hypothesis is discussed.
Category: Condensed Matter

[1] viXra:2011.0017 [pdf] replaced on 2020-11-03 03:59:25

Fractional Dynamics and Hamiltonian Time Crystals

Authors: Ervin Goldfain
Comments: 4 Pages.

Hamiltonian time crystals (HTC) are time-dependent solutions of the equation of motion that develop in a minimum energy configuration. A subset of HTC’s includes periodic solutions with minimal energy that spontaneously break time-translation invariance. Recent studies suggest that HTC’s may be realized as novel topological structures formed by knotted molecules. In this brief note we show that fractional dynamics of harmonic oscillators may replicate the properties of HTC’s outside the realm of traditional condensed matter applications.
Category: Condensed Matter