Periodicity and Quasi-Periodicity for Super-Integrable Hamiltonian Systems

Integrable quantum many-body sensors for AC field sensing

Quantum sensing is inevitably an elegant example of the supremacy of quantum technologies over their classical counterparts. One of the desired endeavors of quantum metrology is AC field sensing. Here, by means of analytical and numerical analysis, we show that integrable many-body systems can be exploited efficiently for detecting the amplitude of an AC field. Unlike the conventional strategies in using the ground states in critical many-body probes for parameter estimation, we only consider partial access to a subsystem. Due to the periodicity of the dynamics, any local block of the system s…

Algebraic treatment of super-integrable potentials

The so$(2,1)$ Lie algebra is applied to three classes of two- and three-dimensional Smorodinsky-Winternitz super-integrable potentials for which the path integral discussion has been recently presented in the literature. We have constructed the Green's functions for two important super-integrable potentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we have considered two examples, one is maximally super-integrable and another one minimally super-integrable. The discussion is made in various coordinate systems. The energy spectrum and the suitably normalized wave functions o…

Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity

We study a reflectionless PT-symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the pair, we find an exotic supersymmetric structure based on three matrix differential operators that encode all the properties of the system, including its reflectionless (finite-gap) nature. The structure we revealed particularly sheds new light on the splitting of the discrete states into two families, related to the bound and resonance states in Hermitian …

From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics

It is shown that planar quantum dynamics can be related to 3-body quantum dynamics in the space of relative motion with a special class of potentials. As an important special case the $O(d)$ symmetry reduction from $d$ degrees of freedom to one degree is presented. A link between two-dimensional (super-integrable) systems and 3-body (super-integrable) systems is revealed. As illustration we present number of examples. We demonstrate that the celebrated Calogero-Wolfes 3-body potential has a unique property: two-dimensional quantum dynamics coincides with 3-body quantum dynamics on the line at …

Path integral treatment of a family of super-integrable systems in n-dimensional Euclidean space

The exact path integration for a family of maximally super-integrable systems generalizing the hydrogen atom in the $n$-dimensional Euclidean space is presented. The Green's function is calculated in parabolic rotational and spherical coordinate systems. The energy spectrum and the correctly normalized wave functions of the bound states are obtained from the poles of the Green's function and their residues, respectively.

调节多端扩散约瑟夫森结中电流-相位关系的基本周期性

Tuning the the fundamental periodicity of the current-phase relation in multiterminal diffusive Josephson junctions

本文提出一种具有4个超导触点的多端扩散SNS约瑟夫森结，其电流-相位关系表现为2$π$和4$π$周期分量的叠加，且相对强度可由另外两触点间的相位差调控，为定制超导量子电路的哈密顿量提供了潜在应用。