Gennady P. Berman

The Fermi-Pasta-Ulam problem: Fifty years of progress

A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.A brief review of the Fermi-Pasta-Ulam (FPU) paradox is given, together with its suggested resolutions and its relation to other physical problems. We focus on the ideas and concepts that have become the core of modern nonlinear mechanics, in their historical perspective. Starting from the first numerical results of FPU, both theoretical and numerical findings are discussed in close connection with the problems of ergodicity, integrability, chaos and stability of motion. New directions related to the Bose-Einstein condensation and quantum systems of interacting Bose-particles are also considered.

Beam wandering in the atmosphere : The effect of partial coherence

The effect of a random phase screen on laser beam wander in a turbulent atmosphere is studied theoretically. The photon distribution function method is used to describe the photon kinetics of both weak and strong turbulence. By bringing together analytical and numerical calculations, we have obtained the variance of beam centroid deflections caused by scattering on turbulent eddies. It is shown that an artificial distortion of the initial coherence of the radiation can be used to decrease the wandering effect. The physical mechanism responsible for this reduction and the applicability of our approach are discussed.

Quantum computer on a class of one-dimensional Ising systems

Abstract We discuss the problem of designing a quantum computer based on one-dimensional “alternating” Ising systems (linear chains with periodically recurring spin groups) in an external magnetic field which exceeds the interaction between spins. Loading and processing of information in the alternating Ising system may be accomplished by using a scheme suggested recently by Lloyd for heteropolymer systems. The detailed operation of a simple quantum logical device is described in the framework of a binary Ising system. Estimates of physical parameters are presented that show that the experimental realization of such quantum computer elements would be feasible as a research task. However, many difficulties remain to be addressed, before the approach discussed here would be applicable in real devices.

Suppression of intensity fluctuations in free space high-speed optical communication based on spectral encoding of a partially coherent beam

A new concept of a free space, high-speed (Gbps) optical communication system based on spectral encoding of radiation from a broadband pulsed laser is developed. It is shown that, in combination with the use of partially coherent laser beams and a relatively slow photosensor, scintillations can be suppressed by orders of magnitude for distances of more than 10 km.

Resonance theory of decoherence and thermalization

Abstract We present a rigorous analysis of the phenomenon of decoherence for general N -level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use a semiclassical, balance-equation approach, which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free-electron lasers, chaos may be observable in SSL{close_quote}s. We clarify the nature of this interesting nonlinear dynamics in the superlattice{endash}external-field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field, and to Josephson junctions. {copyright} {ital 1996 The American Physical Society.}

Relaxation and the Zeno effect in qubit measurements.

We consider a qubit interacting with its environment and continuously monitored by a detector represented by a point contact. Bloch-type equations describing the entire system of the qubit, the environment, and the detector are derived. Using these equations we evaluate the detector current and its noise spectrum in terms of the decoherence and relaxation rates of the qubit. Simple expressions are obtained that show how these quantities can be accurately measured. We demonstrate that due to interaction with the environment, the measurement can never localize a qubit even for infinite decoherence rate.

Solid-state nuclear-spin quantum computer based on magnetic resonance force microscopy

We propose a nuclear-spin quantum computer based on magnetic resonance force microscopy ~MRFM! .I t is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: ~a! preparation of the ground state, ~b! one- and two-qubit quantum logic gates, and ~c! a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1 K.

Interference effects in resonant magnetotransport

We study nonequilibrium magnetotransport through a single-electron transistor or an impurity. We find that due to spin-flip transitions, generated by the spin-orbit interaction, the spectral density of the tunneling current fluctuations develops a distinct peak at the frequency of Zeeman splitting. This mechanism explains modulation in the tunneling current at the Larmor frequency observed in scanning tunneling microscope experiments and can be utilized as a detector for single spin measurement.

Decoherence and thermalization.

We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs of free massless bosonic fields. We apply our general results to the specific case of the qubit. Our approach does not involve master equation approximations and applies to a wide variety of systems which are not explicitly solvable.