Bridging closed and dissipative discrete time crystals in spin systems with infinite-range interactions

Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

Nonlinear, Dissipative, Infinite Dimensional Systems

Limits of discrete systems with long-range interactions

We prove that under some structure and decay hypotheses, limits of discrete systems with multi-neighbourhood interactions give rise to local energies with bulk and surface part.

Spin waves in antiferromagnetic spin chains with long-range interactions

We study antiferromagnetic spin chains with unfrustrated long-range interactions that decay as power laws with exponent b , using the spin-wave approximation. We find for sufficiently large spin S that the Neel order is stable at T50 for b,3, and survives up to a finite Neel temperature for b,2, validating the spin-wave approach in these regimes. We estimate the critical values of S and T for t...

Equivalence of a mixing condition and the LSI in spin systems with infinite range interaction

We investigate unbounded continuous spin-systems with infinite-range interactions. We develop a new technique for deducing decay of correlations from a uniform Poincaré inequality based on a directional Poincaré inequality, which we derive through an averaging procedure. We show that this decay of correlations is equivalent to the Dobrushin-Shlosman mixing condition. With this, we also state an...