Effect of noise for two interacting particles in a random potential

We investigated the effect of noise on propagation of two interacting particles pairs in a quasi one--dimensional random potential. It is shown that pair diffusion is strongly enhanced by short range interaction comparing with the non--interacting case.Comment: 8 Latex pages + 3 postscript figures uu- compressed submitted to Europhysics Letter

Shielding and localization in presence of long range hopping

We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited states subspace is shielded from long range hopping, namely it occurs as if long range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale which diverges with the system size. We named this effect {\it Cooperative Shielding}. We also discuss the consequences of our findings on Anderson localization. Long range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long range coupling. A brief discussion on the extension of our results to generic power-law decaying long range hopping is also given. Our preliminary results confirms that the effects found for the infinite range case are generic.Comment: 7 pages, 9 figur

Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles

This review is devoted to the problem of thermalization in a small isolated conglomerate of interacting constituents. A variety of physically important systems of intensive current interest belong to this category: complex atoms, molecules (including biological molecules), nuclei, small devices of condensed matter and quantum optics on nano- and micro-scale, cold atoms in optical lattices, ion traps. Physical implementations of quantum computers, where there are many interacting qubits, also fall into this group. Statistical regularities come into play through inter-particle interactions, which have two fundamental components: mean field, that along with external conditions, forms the regular component of the dynamics, and residual interactions responsible for the complex structure of the actual stationary states. At sufficiently high level density, the stationary states become exceedingly complicated superpositions of simple quasiparticle excitations. At this stage, regularities typical of quantum chaos emerge and bring in signatures of thermalization. We describe all the stages and the results of the processes leading to thermalization, using analytical and massive numerical examples for realistic atomic, nuclear, and spin systems, as well as for models with random parameters. The structure of stationary states, strength functions of simple configurations, and concepts of entropy and temperature in application to isolated mesoscopic systems are discussed in detail. We conclude with a schematic discussion of the time evolution of such systems to equilibrium.Comment: 69 pages, 31 figure

A semiquantal approach to finite systems of interacting particles

A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well defined classical analog which can be easily obtained from the classical equations of motion. Therefore, the occupation numbers for single-particle states can be represented as a convolution of the classical SE with the quantum occupation number operator for non-interacting particles. The latter takes into account the wavefunctions symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers $n_s$ can be numerically found for a very large number of interacting particles. Using the model of interacting spins we demonstrate that this approach gives a correct description of $n_s$ even in a deep quantum region with few single-particle orbitals.Comment: 4 pages, 2 figure

Cooperative shielding in many-body systems with long-range interaction

In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of long-range interacting systems, which we name "Cooperative Shielding". It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative Shielding can be tested in current experiments with trapped ions.Comment: 9 pages, 5 figures (accepted at Phys. Rev. Lett.

Cooperative Robustness to Static Disorder: Superradiance and localization in a nanoscale ring to model natural light-harvesting systems

We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: $i)$ weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; $ii)$ strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.Comment: 12 pages, 7 figs., Superradiance, Anderson Localization, Cooperative effects. Accepted for publication in Phys. Rev.

The Topological Non-connectivity Threshold in quantum long-range interacting spin systems

Quantum characteristics of the Topological Non-connectivity Threshold (TNT), introduced in F.Borgonovi, G.L.Celardo, M.Maianti, E.Pedersoli, J. Stat. Phys., 116, 516 (2004), have been analyzed in the hard quantum regime. New interesting perspectives in term of the possibility to study the intriguing quantum-classical transition through Macroscopic Quantum Tunneling have been addressed.Comment: contribution to NEXTSIGMAPHI 3r