Related papers: Localization without recurrence and pseudo-Bloch o…
By the Magnus-Floquet approach we calculate the effective Hamiltonian for a charged particle on the lattice subject to a homogeneous high frequency oscillating electric field. The obtained result indicate the absence of dynamic localization…
The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of…
The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic…
We present numerical evidence to show that the wavefunctions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of…
In this paper we study in detail the localized wave functions defined in Phys. Rev. Lett. {\bf 76}, 1613 (1994), in connection with the scarring effect of unstable periodic orbits in highly chaotic Hamiltonian system. These functions appear…
Non-Hermitian systems with complex-valued energy spectra provide an extraordinary platform for manipulating unconventional dynamics of light. Here, we demonstrate the localization of light in an instantaneously reconfigurable non-Hermitian…
We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the…
We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems…
We recapitulate the principle enabling the phenomenon of dynamic localization, and provide model calculations for ultracold atoms in driven optical lattices which indicate that the localization effect remains almost unaffected by interband…
We investigate quantum tunneling phenomena for an optical lattice subjected to a bichromatic ac force. We show that incommensurability of the frequencies leads to super Bloch oscillation. We propose directed super Bloch oscillation for the…
We consider N interacting quantum particles on a one-dimensional lattice, and subjected to an external linear potential. For N = 1, the corresponding Hamiltonian is explicitly diagonalizable, with superexponentially localized eigenstates.…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
The fundamental concept underlying topological phenomena posits the geometric phase associated with eigenstates. In contrast to this prevailing notion, theoretical studies on time-varying Hamiltonians allow for a new type of topological…
We explore an unusual type of quantum matter that can be realized by qubits having different physical origin. Interactions in this matter are described by essentially different coupling operators for all qubits. We show that at least the…
We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a…
Photonic lattices have emerged as a promising approach to localize light in space, for example, through topologically protected edge states and Aharonov-Bohm caging. They are of particular importance in the study of flat band systems via…
Collective temporal organization in complex systems is commonly attributed to synchronization, resonance, or proximity to dynamical instabilities. Here we identify a distinct mechanism by which coherent, synchronization-like behavior can…
We reveal that nonlocality can provide a simple physical mechanism for stabilization of multi-hump optical solitons, and present the first example of stable rotating dipole solitons and soliton spiraling, known to be unstable in all types…
We consider multi-dimensional Schr\"odinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on…
Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization"…