Localized systems coupled to small baths: from Anderson_{nderson} to Zeno_{eno}

We investigate what happens if an Anderson localized system is coupled to a small bath, with a discrete spectrum, when the coupling between system and bath is specially chosen so as to never localize the bath. We find that the effect of the bath on localization in the system is a non-monotonic function of the coupling between system and bath. At weak couplings, the bath facilitates transport by allowing the system to 'borrow' energy from the bath. But above a certain coupling the bath produces localization, because of an orthogonality catastrophe, whereby the bath 'dresses' the system and hence suppresses the hopping matrix element. We call this last regime the regime of "Zeno-localization", since the physics of this regime is akin to the quantum Zeno effect, where frequent measurements of the position of a particle impede its motion. We confirm our results by numerical exact diagonalization

Entanglement spectrum degeneracy and the Cardy formula in 1+1 dimensional conformal field theories

We investigate the effect of a global degeneracy in the distribution of the entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement Hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the noninteger degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spinchains provides strong analytical evidences corroborating our results

A practical constructive scheme for deterministic shared-memory access

Abstract. We present three explicit schemes for distributing M variables among N memory modules, where M = �(N 1.5), M = �(N 2), and M = �(N 3), respectively. Each variable is replicated into a constant number of copies stored in distinct modules. We show that N processors, directly accessing the memories through a complete interconnection, can read/write any set of N variables in worstcase time O(N 1/3), O(N 1/2), and O(N 2/3), respectively for the three schemes. The access times for the last two schemes are optimal with respect to the particular redundancy values used by such schemes. The address computation can be carried out efficiently by each processor without recourse to a complete memory map and requiring only O(1) internal storage. 1

An O(√n)-worst-case-time solution to the granularity problem

none2In this paper we deal with the granularity problem, that is, the problem of implementing a shared memory in a distributed system where n processors are connected to n memory modules through a complete network (Module Parallel Computer). We present a memory organization scheme where m=O(n^2) variables, each replicated into a 2c — 1 copies (for constant c), are evenly distributed among the n modules, so that a suitable access protocol allows any set of at most n distinct read/write operations to be performed by the processors in O(sqrt(n)) parallel steps in the worst case. The well known strategy based on multiple copies is needed to avoid the worst-case O(n)-time, since only a majority of the copies of each variable need be accessed for any operation. The memory organization scheme can be extended to deal with m=O(n^3) variables attaining an O(n^(2/3))-time complexity in the worst case.noneA. Pietracaprina;F. P. PreparataPietracaprina, ANDREA ALBERTO; F. P., Preparat

A new scheme for the deterministic simulation of PRAMs in VLSI

A deterministic scheme for the simulation of (n, m)-PRAM computation is devised. Each PRAM step is simulated on a bounded degree network consisting of a mesh-of-trees (MT) of siden. The memory is subdivided inn modules, each local to a PRAM processor. The roots of the MT contain these processors and the memory modules, while the otherO(n 2) nodes have the mere capabilities of packet switchers and one-bit comparators. The simulation algorithm makes a crucial use of pipelining on the MT, and attains a time complexity ofO(log2 n/log logn). The best previous time bound wasO(log2 n) on a different interconnection network withn processors. While the previous simulation schemes use an intermediate MPC model, which is in turn simulated on a bounded degree network, our method performs the simulation directly with a simple algorithm

Constructive Deterministic PRAM Simulation on a Mesh-Connected Computer

The PRAM model of computation consists of a collection of sequential RAM machines accessing a shared memory in lock-step fashion. The PRAM is a very high-level abstraction of a parallel computer, and its direct realization in hardware is beyond reach of the current (or even foreseeable) technology. In this paper we present a deterministic simulation scheme to emulate PRAM computation on a mesh-connected computer, a feasible machine where each processor has its own memory module and is connected to at most four other processors via point-to-point links. In order to achieve a good worst-case performance, any deterministic simulation scheme has to replicate each variable in a number of copies. Such copies are stored in the local memory modules according to a Memory Organization Scheme (MOS), which is known to all the processors. A variable is then accessed by routing packets to its copies. All deterministic schemes in the literature make use of a MOS whose existence is proved via the prob..