Discrete Systems

Michele Cini

Umpon Pon Jairuk, Sikarin Yoo-Kong

We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero-Moser (CM) system. In the discrete level, the Lax pairs with a parameter are introduced and, of course, the discrete-time equations of motion are obtained as well as their corresponding discrete-time Lagrangian. The integrability feature of this new system can be captured through the discrete Lagrangian closure relation by employing a connection with the temporal Lax matrices of the discrete-time Ruijsenaars-Schneider (RS) system, exact solution, and the existence of the classical r-matrix. Under the appropriate limit on the parameter, which in this case is approaching zero, the standard CM system is retrieved both discrete-time and continuous-time.

Michele Cini

Jared Rovny, Robert L. Blum, Sean Barrett

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear magnetic resonance observations of DTC signatures in a third, strikingly different system: an ordered spatial crystal. We use a novel DTC echo experiment to probe the coherence of the driven system. Finally, we show that interactions during the pulse of the DTC sequence contribute to the decay of the signal, complicating attempts to measure the intrinsic lifetime of the DTC.

Natig M. Atakishiyev, Sh. M. Nagiyev, Luis Edgar Vicent +1 more

We propose a discretization strategy for systems with axial symmetry. This strategy replaces the continuous position coordinates by a discrete set of sensor points, on which the discrete wave fields transform covariantly with the group of 2 x 2 symplectic matrices. We examine polar arrays of sensors (i.e., numbered by radius and angle) and find the complete, orthonormal sets of discrete-waveguide Meixner functions; when the sensors come closer together, these tend to the Laguerre eigenmodes of the continuous waveguide. In particular, the fractional Hankel transforms are discretized in order to define the fractional Hankel-Meixner transforms and similarly for all axis-symmetric linear optical maps. Coherent states appear in the discrete cylindrical waveguide. Covariant discretization leads to the same Wigner phase-space function for both the discrete and the continuum cases. This reinforces a Lie-theoretical model for the phase space of discrete systems.

Gourab Das, Saptarshi Saha, Rangeet Bhattacharyya

Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust subharmonic response. However, the DTC phase is fragile in the presence of environmental dissipation. Here, we propose and exemplify a DTC phase in a noninteracting system that owes its stability to environmental dissipation. The lifetime of this DTC is independent of initial conditions and the size of the system, though it depends on the frequency of the external driver. We experimentally demonstrate this realization of DTC using Nuclear Magnetic Resonance spectroscopy.