O. V. Zhirov

Frenkel-Kontorova model with cold trapped ions

Abstract.We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. We show that at zero temperature the quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. After melting the ion chain can slide in an optical lattice. The obtained results are also relevant for a Wigner crystal placed in a periodic potential.

Complexity of quantum states and reversibility of quantum motion

We present a quantitative analysis of the reversibility properties of classically chaotic quantum motion. We analyze the connection between reversibility and the rate at which a quantum state acquires a more and more complicated structure in its time evolution. This complexity is characterized by the number M(t) of harmonics of the [initially isotropic, i.e., M(0)=0 ] Wigner function, which are generated during quantum evolution for the time t . We show that, in contrast to the classical exponential increase, this number can grow not faster than linearly and then relate this fact with the degree of reversibility of the quantum motion. To explore the reversibility we reverse the quantum evolution at some moment T immediately after applying at this moment an instant perturbation governed by a strength parameter xi . It follows that there exists a critical perturbation strength xic approximately sqrt 2/M(T) below which the initial state is well recovered, whereas reversibility disappears when xi > or approximately xic(T) . In the classical limit the number of harmonics proliferates exponentially with time and the motion becomes practically irreversible. The above results are illustrated in the example of the kicked quartic oscillator model.

Quantum phase transition in the Frenkel-Kontorova chain: From pinned instanton glass to sliding phonon gas

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devils staircase. By extensive quantum Monte Carlo simulations we show that for the effective Planck constant

Fractal spin glass properties of low energy configurations in the Frenkel-Kontorova chain

\hbar

Dissipative decoherence in the Grover algorithm

smaller than the critical value

How well a chaotic quantum system can retain memory of its initial state

\hbar_c

Phase diagram for the Grover algorithm with static imperfections

the quantum chain is in the pinned instanton glass phase. In this phase the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons which have an exponentially small excitation energy. At

Quantum vacuum of strongly nonlinear lattices

\hbar=\hbar_c

Elastic enhancement factor: From mesoscopic systems to macroscopic analogous devices

the quantum phase transition takes place and for

Wigner crystal in snaked nanochannels

\hbar>\hbar_c